The torque-angular velocity relationship in human muscular...
156
THE TORQUE- BNGTJIAB VELCCITY RELATXONSHIP IW HUMAN PUSCULBR GOl?TRBCTZON by David Jchn Sanderson B.Sc, [Kirtesiofoqy) Simon Prasef University, 1972 @ DAVID JOHB SANDERSON 1975 SLHQW PRASER UWPVEBSITY AUGDST 1935 All riqfits sesesv'ed, This thesis my not be reproduced in whole or in part, by vhotoccpy or other means without per~ission of the authcr,
Transcript of The torque-angular velocity relationship in human muscular...
THE TORQUE- B N G T J I A B
VELCCITY RELATXONSHIP IW
HUMAN PUSCULBR GOl?TRBCTZON
by
David Jchn S a n d e r s o n
B.Sc, [Kirtesiofoqy) Simon Prasef University, 1972
@ DAVID JOHB S A N D E R S O N 1975
SLHQW PRASER UWPVEBSITY
AUGDST 1935
A l l riqfits sesesv'ed, T h i s t h e s i s m y n o t be reproduced in whole or i n part, by v h o t o c c p y or other means w i t h o u t p e r ~ i s s i o n o f t h e authcr,
APPROV WI,
N A M E :
D E G R E E :
David John S a n d e r s o n
q a s t er of S c i e n c e (Kinesioloqy)
T I T L E OP THESIS: The t o r q u e - a n q u l a s velocf k y r e l a t k o n s h i ~ in human muscalar contraction
Dr, N,M,G, Bhakthan
Dlcl A, E. Chapraant Senior S u p e r v i s o r
Dr- J,B, Wsrrison Externaf Examiner Associate P rofessos
Kiaesiol oqy Depar t a e n t S i a e n Fsaser University
PARTIAL COPYRIGHT LICENSE
I hereby g r a n t t o Simon F r a s e r U n i v e r s i t y t h e r i g h t t o lend
my t h e s i s o r d i s s e r t a t i o n ( t h e t i t l e of which i s shown below) t o u s e r s
of t h e Simon F r a s e r U n i v e r s i t y L i b r a r y , and t o make p a r t i a l o r s i n g l e
c o p i e s o n l y f o r - s u c h u s e r s o r i n r e s p o n s e t o a r e q u e s t from t h e l i b r a r y
of a n y o t h e r u n i v e r s i t y , o r o t h e r e d u c a t i o n a l i n s t i t u t i o n , on i t s 'own
beha l f o r f o r one of i t s u s e r s . I f u r t h e r a g r e e t h a t pe rmiss ion f o r
m u l t i p l e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d
b y me o r t h e Dean of Graduate S t u d i e s . It is unders tood t h a t copying
o r p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l lowed
wi thou t my w r i t t e n pe rmiss ion ,
T i t l e of Thesis / ~ i s s e r t a t i o n : I
Author : - ( s i g n a t u r e )
( d a t e )
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T h i s s t u d y p r o p o s e d e x a ~ i n a t i o n o f the c h a r a c t e r i s t i c s of
an assumed m o d e l o f m u s c u l a r c o n t r a c t i o n fo r i n t a c t human
t ~ u s c l c s , T h i s model c o ~ p r i s e s three c o m p o n e n t s ; a c o n t r a c t i l e
c o m p o n e n t (CC) , a n e l a s t i c c o m p o n e n t i n series with t h e
c o n t r a c t i l e component . f S E C ) a n d a n e l a s t i c c o m p o n e n t i n
p a r a l l e l with t h e o t h e r tua c o m p o n e n t s [PEC), It h a s b e e n shown
o n i s o l a t e d m u s c l e p r e p a r a t i o n s t h a t t h e r e is a d i f f e r e n c e i a
t h e f o r c e - v e l o c i t y c u r v e a s c r i b a b l e t o t h e m e t h o d u s e d i n t h e
d e t e r w i n a t i o n of t h a t c u r v e , This o b s e r v a t i o n s t i ~ u l a t e d t h e
present i n v e s i g a t i o n .
T h e saae a p p a r a t u s %as used f o r two separate e x p e r i n t e n t s
t o d e t e r m i n e t h e t o r q u e - a n g u l a r v e l o c i t y r e l a t i a n s h i p of t b e
e lboa f l e x o r s over a r a n g e o f e x c u r s i o n o f t h e e l b o w - j o i n t -
E x p e r i m e n t 1 u s e d t h e m e t h o d d e s c r i b e d by f l lacPhsrson 11953) for
i s o l a t e d m u s c l e s a n d a d a p t e d it to i n t a c t human ~ u s c u l a r
c o n t r a c t i o n , T h i s me thod , b a s e d o n n o n - l i n e a r d i f f e r e n t i a f
equa t i ons , was s u c c e s s f u l l y a d a p t e d t o t h e present e x p e r i m e n t a l
s i t u a t i o n , However , t h e e x p e r i m e n t a l r e s u l t s exposed s u m
c u r i o u s events, A n e c e s s a r y c o n d i t i o n f o r t h e c o m p l e t i o n of t h e
a n a l y s i s was t h a t t h e rise i n t c r q u e i n a n i s o m e t r i c
c o n t r a c t i o n b e q u i c k e r t h a n when t h e r e was a n a d d e d series
c o ~ p l i a n c e . W h i l e o t h e r research h a s shown t h a t t h i s c o n d i t i o n
can be s a t i s f i e d o n i s c l a t e d p s e p a r a t i o n s the e x a c t o p p o s i t e
e v e n t was r e c o r d e d r e p e a t e d l y h e r e , P o s s i b l e a n a t o a i c a f and
p h y s i o P o y i c a l e x p l a n a t i o n s were discussed b u t i t w a s c o n c l u d e d
that further research was r e q u i r e d ,
Kxyeciment, 2 d e a l * w i t h t h e d e v e l o p ~ e n t of t h e
t o r q u e - a n g u l a r vcf ocitp c u r v e from d y n a m i c con t r a c t i o n s , To
obtain p o i n t s o n t h e t o r q u e - a n g u l a r velocity c u r v e when the
v e l o c i t y was zero some isometric c o n t r a c t i o n s were c o ~ p l e t e d a t
f i v e elbow p o s i t i o n s f r o m 0-5 r a d i a n s t o 2-0 r ad i a ra s where 0-0
r a d i a n s was full e x t e n s i o ~ , T h e r e a p p e a r e d t o b e a v a r i a t i o n i n
t h e t o r q u e - a n g u l a r v e l c c i t y c u r v e a s a c o n s e q u e n c e o f the
p o s i t i o n o f t h e e l b o w - j o i n t , T h i s v a r i a t i o n arose o u t of the
interaction of two c o ~ ~ c n e n t s ; t h e effect of t h e change i n
length of t h e m u s c l e i n r e d u c i n g t h e p r o d u c t i o n of t o r q u e a t
l o n g lengths, and the m d i f i c a t i o n s t o the a n g l e of p u l l of the
t e n d o n on the r a d i u s as a c o n s e q u e n c e of t h e joint a n a t m y .
T h e c o m p l i a n c e of t h e SEC was d e t e r m i n e d froin t h e
t o r q u e - a n g u l a r velocity c u r v e d e r i v e d from d y n a a i c c o n t r a c t i o n s
a n d t h e rise of torque d u r i n g an isometric c o n t r a c t i o n , The
c o m p l i a n c e - t o r q u e c u r v e appeared s i ~ l l a r 4x1 c u r v e s shown i n
o t h e r s t u d i e s , T h e s h a p e cf t h e c o m p P i a ~ c e - t o r q u e c u r v e was
similar regardless of the angle of t h e e lbow- - jo in t , T h i s
implied t h a t t h e c h a x a c t e r i s t i c s of t h e SEC did n o t c h a n g e w i t h
e l b o w p o s i t i o n ,
TABLE CF CONTENTS
ABSTRACT
E f S T OF TABLES
L I S T OF FEGUPES
f IN TWO DUCT ION
11 RELATED LITEXATUHE Bis tor ica l d e v e l o p m e n t C h a r a c t e r i s t i c s o f i s o l a t e d muscle C h a r a c t e r i s t i c s of i n t a c t m u s c l e S t a t e m e n t o f P r o b l e m
PAGE
iii
v i i
v i i
111 &ATERIALS, SETHODS and PRQCEDUBES Raterials ? j e t h a i s
a) The a p p a r a t u s u s e d for t h e measu fen ten t of t o r q u e , d i s p l a c e m e n t , a n a a c c e l e r a t i o n
b) The d y n a m o m e t e r u s e d f o r the t r a n s d u c t i o n of t o r q u e , d i s p f a c e m e n t , a a d a c c e l e r a t i o n i) T r a n s d u c t i o n o f t o r g u e
iif T r a n s d u c t i o n o f d i s p l a c e n e a t iii) Transduc t ion of a c c e f e r a t i o n
c) C a l i b r a t i a n of t r a n s d u c e r s i) S t a t i c p r o p e r t i e s
ii) Dynarilic propert ies d) F i l t e r i n g t h e o u t p u t f r o m t h e t r a n s d u c e r s e ) P e r m a n e n t r e c o r d i n g of the o u t p u t f r o m
t h e t r a n s d u c e r s i) T h e f r e q u e n c y m o d u l a t e d (FB)
tape- r e c o r d e r ii) A n a l o g u e t o d i g i t a l c o n v e r s i o n
iii) B e c o r d i n g o s c i l l o y r a p h P r o c e d u r e s
a) P r o c e u u r e s - E x p e r i m e n t 1 i) h ' o r k - s e s s i o n 1
ii) W o r k - s e s s i o n 2 iii) Ktsr k - s e s s i o n 3
tt) P c a c e d u r e s - E x p e r i ~ l e n t 2
IV EETtiOU C f AMALYSIS a) C a l i b r a t i o n d u r i n g t h e e x p e r i m e n t
i) C a l i b r a t i o n c o n s t a n t s ii) D e t e r m i n a l i o n cf t h e inornent of i n e r t i a
o f t h e f o r e a t a iii) Est i a t a t i o n of t h e g r a v i t a t i o n a l effect
o n t h e l e v e r w i t h t h e cast and forearm a t t a c h e d
b) E x p e r i m e n t 1 - D e t e r a i n a t i o n of the torque- a u a u l a r v e l o c i t y r e l a t i o n s h i p from two isometric c o n trac t i o r i s i) RacPhersons s method ii) ~ o d i f i c a t i o n t o fit r o t a t i o n a l s y s t e a
iii) Data manipu la t ion c) E x p e r i m e n t 2 - D e t e r m i n a t i o n of t h e t o r q u e -
angular velocity r e l a t i c n s h i p fro^ dyna~ic con t r a c t i o n s
i) Data m a n i p u l a t i o n ii) ~ e t e r l f t i n a t i o n of t h e t ime-cons tan t ol
t h e rise i n torque iii) Determination of t h e compliance of
t h e SEC
V ACCUXACY OF RESGLTS 76
Vlt RESULTS 78
YXI D I S C U S S I O N a) Experiment 1 b ) Experiment 2
V I I I CONCLUSIONS 729
IX S U B M A R Y 13 1
APPEW DIXES 138
v i i
LIST O F TABLES
TABLE 1: Time c o n s t a n t s for t h e rise in torque d u r i n g i s o m e t r i c c o n t r a c t i o n s for s u b j e c t s AC and BW,
F I G U R E 1 : T h e l e n g t h - t e n s i o n c u r v e f o r i s c fa ted f rog muscle,
FfGUWE 2 : T h e f o r c e - v e l o c i t y - l e n g t h c u r v e for i s o l a t e d r a t y r a c i i u s a n t i c u s ~ u s c f e ,
FIGURE 3 : 'The f i n e a r h o r i z o n t a l e g u i v a f e l n t @ode1 u s e d t o d e s c r i b e e l b o w f l e x i o n $ o r i n t a c t human m u s c l e ,
F I G U R E 4 2 T h e a - p p a r a t u s u s e d i n t h e p r e s e n t s t u d y ,
F I G U R E 5 : T h i s s p r i n q ~ r o v i d e d a c o a p l i a n t c o n n e c t i o n b e t w e e n t h e two h a l f s h a f t s ,
F IGURE 6 : T h i s shows t h e t u o h a l v e s of t h e c a s t u s e d t o p r e v e n t grist Elexicn d u r i n y coa t ract ion,
F I G U R E 7 : T h i s is a s c h e m a t i c of t h e d y n a m o m e t e r u s e d i n the experiment,
f I G U B E 8 : T h i s 3s the c i r c u i t d i a g r a m for each of the t r a n s d u c e r s ,
FIGURE 9 : T h i s is the main a m p l i f y i n g u n i t ,
F I G U R E 10 : T h i s is a d r a w i n g of t h e s y s t e u d e s c r i b e d by B a c P h e r s o n (1 953) -
PXGUBE 1 1 : T h i s is a d r a w i n g of t h e system d e s c r i b e d i n figure 10 as modified to s u i t the p r e s e n t s t u d y ,
BIGfJSE 1 2 : The rise i n t o r q u e i n two c o n t r a c t i o n s , one with t h e added c o m p l i a n c e a n d t h e o t h e r w i t h o u t t h e a d d e d c o m p l i a n c e ,
FIGURE 13 : T h e t o r q u e - a n g l e c u r v e f o r s u b j e c t AC,
PIGUXE 1 4 : T h e S o r q u e - a n g l e c u r v e for s u b j e c t , fly.
P I G U R E 95 : The t o r q u e - a n g u l a r v e l o c i t y c u r v e s f o r d i f f e r e n t sessions and a t d i f f e r e n t j o i n t angles fo r s u b j e c t AC,
iZ F I G U R E 16 : The t o r q u e - a n g u l a r v e l o c i t y c u r v e s d e t e r ~ i n e d by d r a w i n g a s m o o t h l i n e t h r o u g h t h e points d i s p l a y e d i n f i g u r e 15.
F I G U R E 17 : T h e t o r q u e - a n g u l a r velocity c u r v e s f o r d i f f e r e a t s e s s i o n s a n d a t d i f f e r e n t joint a n g f c s for s u b j e c t H&,
FIGURE 18 : The t o r q u e - a n g u l a r velocity curves d e t e r m i n e d by drawing a smooth line through the p a i n t s d i p l a y e d in f i g u r e 17,
PfGfJRE 19 : The compliance-torque curves for different sessions and at different j o i n t a n g l e s f o r s u b j e c t AC,
F I G U R E 20 : The compliance-torque curves for different sessions and a t d i f f e r e n t j o i n t a n g l e s for subject HW,
I NTROD K T I O N
A g r e a t d e a l of t h e knowledge c o n c e r n i n g m u s c u l a r
c o n t r a c t i o n B a s b e e n d e t e r n t i n e d i r o m e x p e r i n t e n t s w i t h i s o l a t e d
muscl e p r e p a r a t i o n s . T h e s e p r e p a r a t i o n s were d e s i r a b l e b e c a n s e
variables s u c h a s ~ u s c l e l e n g t h and a c t i v a t i o n conld be
c a r e f u l l y c o n t r o i l e d , B h i l e t h e s e s t u d i e s were used t o examine
t h e tnechanisrrrs of c o n t r a c t i o n i n frog ntusc les t h e r e s u l t s c o u l d
be a p p l i e d t o i n t a c t huaan ~ u s c l e s , In t h i s manner a c o m p o s i t e
p i c t u r e of muscu la r a c t i v i t y c o u l d be o b t a i n e d ,
Hany i n v e s t i g a t o r s h a v e used c o n c e p t u a l ntodels t o d e s c r i b e
t h e ph y s i a f o g i c a l e v e n t s s n s r o u n d i n g muscula r c o n t r a c t i o n * A
c ~ n c e p t u a P s o d e l h a s b e e n d e v i s e d which d e s c r i b e s q u i t e
s a t i s f a c t o r i l y t h e phenoaena a s s o c i a t e d w i t h @ u s c u f a r
c o n t r a c t i o n , ~ i g o r o u s a p p l i c a t i o n of this @&el t o d e s c r i b e
more c o a p f e x s y s t e m s , e , g , i n t a c t h u m n a u s c u f a r c o n t r a c t i o n ,
has p f o s e n t e d so&@ problleas, For exarttple, W i L k i e (1950) u s e d a
c o n c e p t u a l mdef t o d e s c r i b e f l e x o r a c t i v i t y i n human s u b j e c t s -
C h a p ~ a a (1973) h a s shown t h a t W i l k i e t s c o n c l u s i o n s were
p a r t i c u l a r t o one e l b o u position o n l y and t h a t t h e r e were
c h a n g e s i a some o t h e r factors v h i c h p r e v e n t e d the s x t r a p o l a t i o n
from W i l k i e J s d a t a t o o t h e r e l b o w p o s i t i o n s , B rstodel which is
a p p l i c a b l e t o one set of c o n d i t i o n s o n l y is n o t a s u s e f u l a s
o n e v h i c h d e s c r i b e s activity u a d e r a wiae r a n g e of c o n d i t i a a s .
B major problem associated w i t h p r e c i s e d e t e r m i n a t i o n of
- t h e c h a r a c t e r i s t i c s o+ intact musc le is a t t r i b u t a b l e t o t h e
complerit'y i n t r o d u c e d by c o n s i d e r i n g t h e ~ n s c l e a s p a r t of a
such l a r g e r corapfex sys t em, It is d i f f i c u l t t o q u a n t i f y , and i a
sofae cases q u a l i f y , t h e invo1vttrrteu-t of e x t r a n e o u s factors s o a s
t o t a k e their a f f e c t i n t o a c c o u n t , T h i s is e s p e c i a l l y e v i d e s t
when one h a s t o c o n s i d e r t h e c o n s c i o n s s u b j e c t i v e c o n t r o l of
t h e human subject o v e r his a c t i o n s ,
T h e present e x p e r i r a e n t s exaa t ine t h e dependaacy of t h e
t o r q u e - a n g u l a r v e l o c i t y c u r v e f o r huloan l t rusclufar
c o n t r a c t i o n on t h e t e c h n i q u e u s e d t o d e r i v e t h a t c u r v e - The
c h a r a c t e f i s t i c s o f t h e CC depend upon whether t h e e x p e r i m e n t a l
c o n d i t i o n s required i s o m e t r i c c o n t r a c t i o s j l s or u h e t h e r t h e
c o n d i t i o ~ s r e q u i r e d dynamic contractions (ParlrtJeg, Yeatman and
S o n n e n b l i c k , 1970)- I f t h e b e h a v i o u r of a n i s o l a t e d musc l e
depends upon t h e t y p e of r e s i s t a n c e encauntered then one
c a n o n l y wonder a t what c o n s t i t u t e s t h e r e a l c h a r a c t e r i s t i c s o f
e a c h c o ~ p o n e n t , I s o n i e t r i c and dynamic c o n t r a c t i o n s w i l l b e
etllployed i n t h i s s t u d y t o d e r i v e t h e t o f q n e - a n g u l a r v e l o c i t y
curve which should p r o v i d e a weans of c o f p a r i n y t h e
c h a r a c t e r i s t i c s of the nauscle u n d e r d i f f e r e n t a x p ~ r i r i t e n t a l
c o n d i t i o n s ,
T h e f o l l o u i n g s e c t i o n o u t l i n e s sonm of t h e h i s t o r i c a l
d e v e f o p ~ e n t of r e s e a r c h i n t h i s area, T h i s s e c t i o n is followed
by t h e d e s c r i p t i o n 02 an e x p e r i n e n t d e s i g n e d t o i n v e s t i g a t e
sortie o f t h e areas a s s o c i a t e d w i t h human muscuXar c o n t r a c t i o n -
The i m p l i c a t i o n s of t h e s e f i n d i n g s are d i s c u s s e d i n t h e f i n a l
s e c t i o n s ,
HPLWTED LITEXRTUW E
H i s t o r i c a l D e v e l o p m e n t
I n a n a t t e ~ p t t o u n d e r s t a n d t h e m e c h a n i s ~ s of g r o s s
m u s c u l a r a c l x v i t y i n v e s t i g a t o r s h a v e u s e d m e c h a n i c a l a n a l o g u e s .
They attempted t o d e s i g n ~ e c h a n i c a l m o d e l s t h a t a d e q u a t e l y
d e s c r i b e d t h e many c h a r a c t e r i s t i c s o f t h i s p h y s i o l o g i c a l
a c t i v i t y , E a r l y s t u d i e s ref i c d u p n o b s e r v a t i o u s on t h e
m e c h a n i c a l o u k p u t of a ruuscie , l a t e r , m e a s u r e s o d t h e h e a t
r e l e a s e d d u r i n g a c o n t r a c t i o n &ere used a s i u d i c a t o r s of any
i n t e r n a l c h a n g e s ~ e s u f t i n g i n that a e c h a n i c a l a u t p u t ,
T h e o b s e r v a t i o n t h a t a m u s c l e moved f i g h t e r l o a d s a t a
h i g h e r v e l o c i t y t h a n i t aoved h e a v i e r faads i n i t i a t e d
c o n s i d e r a b l e r e s e a r c h into t h e subject of t h e aechanica l
f e a t u r e s of m u s c u l a r c o n t r a c t i o n , E a r l y i n v e s t i g a t o r s
(f ick,lY82; Blix, 1 8 9 3 ) represented t h e ~ l u s c f e a s a s p r i n g
m o v i n g t h r o u g h a v i s c c u s a e d i u m a n d t h e y o b s e r v e d t h a t a
t e t a n i z e d m u s c l e d i d less work i f a l l o w e d t o shorten quickly
a g a i n s t a small mass, T h i s o b s e r v a t i o n % a s c o n s i d e r e d
i n d i c a t i v e o f t h e s u ~ p o s i t i o n that vhen s h o r t e n i n g much of t h e
m u s c u l a r e n e r g y was degsaded i n t o h e a t vhen o v e r c o m i n g t h e
i n t e r n a l o r v i s c o u s r e s f s t a n c e , T h i s i n t e r n a l r e s i s t a n c e was
g r e a t e r t h e more r a p i d t h e movement [ F i c k , 7893)-
L a n l a i n e (3905) was arrtong t h e first t o r e c o g n i z e
e x p l i c i t l y t h a t i n human m u s c u l a r movement t h e e f f i c i e n c y
( w o r k / t o t a l energy used) v a r i e d w i t h the s p e e d of c o n t r a c t i o n .
The e x i s t e n c e o f s u c h a r f l a t i o n s h i ~ i n v i t e d s t u d i e s i n t o t h e
possibiiitj uf a r z i a t i 6 a s k i . p b e t w e e n s h o ~ t e f l i n g s p e e d and
force e x e r t e d , S u r p r i s i n g l y , t h i s l i n e o f i n v e s t i g a t i o n was n o t
u n d e r t a k e n u n t i l H i l l ( 1 9 2 2 ) r e i n t r o d u c e d t h e i d e a o f 3 m u s c l e
v i s c o s i t y 8 t o a c c o u n t *or t h e d e c r e a s e i n f o r c e u i t h a n
i n c r e a s e i n t h ~ s p e a of s h o r t e n i n g o b s e r v e d d u r i n g e x p e r i m e a t s
o n t h e e l b o w f l e x o r s , He s h o w e d that t h e w o r k done i n c r e a s e d
r a p i d l y a t f i r s t d u r i n g a s i n g l e c o n t r a c t i o n a n d t h e n B o r e
s l o w l y b e c o n i n g a s y m p t o t i c w i t h time r e a c h i n g a t h e o r e t i c a l
maximum, T h i s o b s e r v a t i o n i d e n t i f i e d t h e a m o u n t of e n e r g y
d e g r a d e d t o h e a t u i t h v i s c o u s r e s i s t a n c e v i t h i n t h e m u s c l e , T h e
a m o u n t of e n e r g y d i s s i p a t e d i n o v e r c o m i n g t h e f r i c t i o n a f
r e s i s t a n c e was p s o p o r t i c n a l t o t h e s p e e d cf t h e c o n t r a c t i o n
( L u p t o n , 1 9 2 2 ) -
G a s s e r a n d H i l l ( 1 9 2 4 ) r e p e a t e d H i l l i s e a r l i e r w o r k Iro
e x a m i n e w h e t h e r t h e r e c o u l d h a v e b e e n a n y r e c i p r o c a l
i n n e r v a t i o n t h a t wouPa h a v e d i s t o r t e d HillSs s t u d i e s ( i-e, t h e
r e s u l t s m i g h t h a v e b e e n t h e c o n s e q u e n c e o f n e r v o u s a c t i v i t y
r a t h e r t h a n m u s c l e a c t i v i t y a l o n e ) , T h e y were a b l e t o c o n f i r m
E[ii19s c o n c i u s i c n s , h o w e v e r , u s i n g i s o l a t e d I r a g muscles, T h e y
c o n c l u d e d t h a t ,, t h e ~ h e n c m e n a i n v e s t i g a t e d a r e n o t d u e
p r i m a r i l y t o a n i n k e r v e n t i o n o f t h e n e r v o u s s y s t e m , b u t t o some
f u n d a m e n t a l c h a r a c t e r ot t h e a u s c l e f i b r e i t s e l f - 8 * { G a s s e r a n d
H i 1 1, ? 9 2 q ) , The q u e s t i o n ok w h e t h e r t h e r e l a t i o n s h i p was t h e
c o n s e q u e n c e of a v i s c o s i t y t a c t o r r e m a i n e a t o b e d e t e r m i n e d ,
I n 1 3 2 7 E e v i n a n d Wyman s t u d i e a q u i c k s t r e t c h e s a n d
releases i n c o n t r a c t i n g m u s c l e , They c b s e r v e d t h a t t h e t e n s i o n
n e v e r r e sponded i n s t a n t a n e o u s 1 y t o t h e s t r e t c h o r f e l e a s e ,
secondly, the c l a s s i c a l i y proposed l i n e a r r e l a t i o n s h i p between
force and v e l o c i t y o f t h e t h e o r e t i c a l v i s c o u s model was found
instead t o be a n o n - f i n e a r one,
To account f o r these d i f f e r e n c e s L e v i n and Pyman s u g g e s t e d
solncz n t tod i f i ca t ions t o t h e s i n g l e s p r i n g rsodel p r e x i o u s l y
p o s t u l a t e d , They p r o p o s e d a d d i n g an undamped s p r i n g i n series
w i t h t h e damped s p r i n g . This la t te r m d e l s a t i s f a c t o s i l g
described t h e i r data,
The i n v e s t i g a t i o n s of Boukea r t , Cape l f en and d e Blende
(1930) a l s o c o n f i r a e d t h e m o d i f i c a t i o n s o f L e v i n and gyman-
T h e c o a c l u s i o n s t h e y r e a c h e d fsoa s t n d i e s o n i s o l a t e d Erog
muscle, were t h a t H , , , t h e r e was no d o u b t t h a t t h e auscfe
behaves as a v i s c o u s elast ic sys te ln o f t h e darttped undamped two
s p r i n g type, '* ( M u k e a - f t e t al,, l93Q), The i n v e s t i g a t i o n s d u r i n g
t h i s era s u p p o r t e d t h e v i s c o u s h y p o t h e s i s which was considered
a p p l i c a b l e t o a wide v a r i e t y o f musc fe s from d o g f i s h
{Burs h, 1938) t o t o r to i ses (kyraan, 3926), Houever, Fenn i n
c o o p e r a t i o n with Harsh produced soae c a n t r a v g r s i a l f i n d i n g s
t h a t demanded l n o d i f i c a t i o n of the viscous node1 IPenn and Barsh,
1935) ,
Fenn a n d Har sh 11935) e x a ~ i n e d t h e rauscular force a t
d i f f e r e n t s p e e d s of s h o r t e n i n g u s i n q i s o l a t e d frog a n d ca t
Bustles by s t u d y i n g t h e mechanical p r o p e r t i e s of muscle
d e p r i v e d of any p a r t i c i p a t i o n By p o s s i b l e &on-v i scous e l a s t i c
e lements , T h i s was done by o b s e r v i n g t h e s p e e d of s h o r t e n i n g
Under d i f f e r e n t i s o t o n i c l o a d s v a r y i n g froftl zero t o the ~laxiretuoa
w h i c h cou ld b e L i f t e d .
They f o u n d that t h e f o r c e - v e l o c i t y c h a r a c t e r i s t i c s o f t h e
i s o l a t e d c o n t r a c t i l e element d i d n o t follow t h e e q u a t i o n
d e r i v e d b y H i l l ( l 9 2 2 ) , They r e - e x p r e s s e d t h e r e l a t i o n s h i p
r e f e r r i n g to a c o e f f i c i e n t c f t e n s i o n l o s s , rather t h a n a
c o e f f i c i e n t 02 v i s c o s i t y , a s b e i n g a major f a c t o r i n
d e t e r ~ i n i n g t h e f o r c e - v e l o c i t y c h a r a c t e r i s t i c s of a m u s c l e ,
This claim was s u p p o r t e d b y t h e o b s e r v a t i o n of t h e
n o n - l i n e a s i t y of t h e f o r c e - v e l o c i t y r e l a t i o n s h i p , " - - * t h i s
e x p o n e n t i a l r e l a t i o n was c o n c e r n e d i q solne way w i t h t h e p r o c e s s
of d e v e l o p i n g e x t r a e n e r g y f o r t h e work of shortening and t h a t
a m u s c l e c a n n o t properly be t r ea t ed as a s i m p l e m e c h a n i c a l
s y s t e n , * * ,
T h r e e years l a t e r H i l l (1938) d e v e l o p e d t h e f o r c e - v e l o c i t y
r e l a t i o n s h i p i n t h e course of e x p e r i m e n t s examining t h e h e a t
I p r o d u c t i o n of i s o l a t e d f r o g a u s c l e , T h i s c u r v e was s i a i l a r t o
that of P a n and B a r s h (7935) but o b e y e d a s i a a p l e r a n d more
I c o n v e n i e n t r e l a t i o n s h i p : [
j ( P + a ) V = { P o - P ) b 1
1
i
", w h e r e P is t h e iorce, V t h e v e l o c i t y of s h o r t e n i n g , and Po t h e 1 1 isoaetr ic maximum force d e v e f o ~ e d , T h e v a l u e s f o r a a n d b were I t 1 c h o s e n t o g i v e the best f i t of t h e e q u a t i o n t o a series of i E observed values of V and P a n d the c o n s t a n t s * b f and *ag h a v e I 6
I t h e d i i a e n s i o n s of v e l o c i t y and Eo rce r e s p e c t i v e l y ,
This study u e a l t t h e f i n a l b l c v t o t h e viscosity
h y p o t h e s i s which h a d h e l d s c i e n t i s t s c a p t i v e f o r so l o n g , "The
f ac t t h a t a ~ u s c l e s h o r t e n s m o t e s l o w l y u n d e r g r e a t e r force was
d u e , n o t to a~<scositp* h u l as F e n n h s s claimed, t o the nanner
i n w h i c h energy l i b e r a t i o n gas r e g u l a t e d , A l a r g e force c a u s e s
a 10% energy ra te , xhich r e s u l t s i n a l o w s p e e d , * j [ H i l l 4 9 3 8 ) ,
The ~ u s c l e was sti l l d e s c r i b e d a s a t w o - c o ~ p o n e n t s y s t e m with
a n undamped e l a s t i c e l e m e n t and a c o n t r a c t i l e e l e m n t i n
series, T h e characteristic e q u a t i o n 2or t h e f o r c e - v e l o c i t y
r e l a t i o n s h i p d e s c r i b e d t h e a c t i v i t y of t h e c o n t r a c t i l e e l e m e n t .
The c h a r a c t e r i s t i c e q u a t i o n 11) and ntodel s u f f e r e d some
l i m i t a t i o n s i n t h a k they were e s s e n t i a l l y e m p i r i c a l arad aade n o
s t a t e m e n t s ahout t h e m e c h a n i s a s u n d e r l y i a g the p r o p e r t i e s of
t h e contractile componsu t, They d i d d e s c r i b e a c c u r a t e 1 y t h e
p h e n o m e n o l o g i c a l r e l a t i o n s h i p s a n d ia doing so p r o v i d e d a
c o n v e n i e n t m e c h a n i s m by w h i c h one c o u l d study m u s c l e a c t i o n ,
T h e r e h a v e been o t h e r e q u a t i o n s d e r i v e d t o describe t h e
f o r c e - v e l o c i t y r e i a t i o n s b i ~ [Fenn a n d Harsh ,1935; P o l i s s a r , l 9 ! i L ;
Bbbott a n d % i l k i e , 1 9 5 3 ) b u t t h e y were i n no f u n d a ~ a e n t a l c o n f l i c t
w i t h H i l l ' s d e r i v a t i o n , L a t e r s t u d i e s c o n f i r m e d t h e
a p p i i c a b i l i t y 0 2 H i f 1's c h a r a c t e r i s t i c 2 o r c e - v e l o c i t y
r e l a t i o n s h i p t o severa l m u s c l e t y p e s w i t h o u t excluding t h e
o t h e r p o s s i k l e e q u a t i o n s (Katz, 1939; Abbott and Lowy, 1952;
R i t c h i e , 1954) ,
C h a r a c t e r i s t i c s o f isolated m u s c l e
T h e f o r c e - v e l o c i t y r e l a t i o n s h i p adequately d e s c r i b e s t h e
a c t i v i t y of t h e c o n t r a c t i l e c o m p o n e n t (CG) of skeletal m u s c l e ,
Nabtever, t h e r e are & h e r s t r u c t u r e s u h i c f t a l s o c o n t r i b u t e t o
t h e ~echanicaE o u t p u t o f t h e ~uscle, f n v e s t i g a t i o n s into t h e
p r o p e r t i e s of l e n g t h and t e n s i o n o f a n u s c l e b e g a n as e a r l y a s
1893 (Blix), S t u d i e s c o n d u c t e d t h r o u g h t h e f s l l o n i n g years
p s o d u c e d some c o n f l i c t i n g r e s u l t s concerning t h e l e n g t h - t e n s i o n
r e l a t i o r a s h i p a n d i ts a n a t c r a i c a l b a s i s , gamey a n d Street (7940)
a t e r i b u t e d t h e s e conflicts p r i m a r i l y t o d i f f e r e n c e s i n
e x p e r i m e n t a l t e c h n i q u e and, as a c o n s e q u e n c e , t o t h e m a g n i t u d e
of the r e s t i n g t e n s i o n ,
To s e t t l e t h e s e d i f f e r e n c e s RaBsey a n d S t r e e t f1940)
e x a m i n e d t h e i s o a e t r i c l e n g t h - t e n s i o n d i a g r a m of i s o f a e e d f r o g
semi- t e n d o n o u s m u s c l e f i b r e s , T h e l e n g t h - t e n s i o n curve t h a t
they d e v e l o p e d c o m p r i s e d t h r e e s u b c o ~ p s n e n t s , one b e i n g t h e sum
of t h e o t h e r %no- T h e c u r v e r i n f i g u r e 1 reprgsented t h e
p a s s i v e l e n g t h - t e n s i o n r e l a t i o n s h i p d e v e l o p e d f o r i s o l a t e d
muscle, The m u s c l e was s t r e t c h e d i n s t a g e s a n d t e n s i o n recorded
a t each i n c r e m e n t of s t r e t c h , H a v i n g n o t e d t h i s c u r v e the n e x t
s t e p was t o i d e n t i f y t h e a n a t o a i c a l co~ re fa t e s , T h e
i n v e s t i g a t o r s d e v e l o p e d a technique t h a t a l l o w e d them t o
des t roy t h e m u s c l e f ibtares a l o n e w i t h o u t a l t e r i n g t h e e x t e r n a l
sascotrilarnma, f s o l a t e d s a r c c l e m m a from s u c h a p ~ e p a r a t i o n
p o s s e s s e d a c a r v e f o r t h e p a s s i v e s t r e t c h i d e n t i c a l t o intact
a u s c f e i n d i c a t i n g t h a t t h e safcolem~a gas r e s p o n s i b l e f a r t h e
p a s s i v e l e n g t h - t e n s i o n c u r v e f o r w h c l e m u s c l e w h i l e t h e
c o n t r a c t i l e material contributed n o t h i n g to this t e n s i o n ,
T h e a c t i v e t e n s i o n curve a i n figure 1 was o b t a i n e d by
s e t t i n g t h e initial muscle l e n g t h and stinulating t h e m u s c l e
t e t a n i c a l f y , T h e r e l a t i o n s h i p b e t w e e n f o r c e and l e n g t h i n t h i s
F I G U R E 1 : The l e n g t h - t e n s i o n c u r v e f a r i so lated frog m u s c l e w h e ~ e : curve XI-- p a s s i v e s t r e t c h of the ~ u s c l e c u r v e a - maximally a c t i v a t e d muscle c u r v e d - the difference between c u r v e s p. )r
and a
a d a p t e d from W i P k i e , 1958,
c a s e a p p e a r e d i n d e p e n d e a t of t h e sarcolema t e n s i o n and seemed
t o act i n p a r a l l e l t o the p a s s i v e tension, T h i s a c t i v e c u r v e
was a c t u a l l y the c o n s e q u e n c e a l t h e i n t e r a c t i o n of t ~ o
components , t h e a c t i v e c o n t r a c t i f e c o ~ p o a e n t { C G ) a n d the
p a s s i v e p a r a l l e l e last ic component [PECf , X t is e v i d e n t
froa f i g u r e 1 that t h e PEC c o n t r i b u t e s t o the o v e r a f l t e n s i o n
o n l y after a s p e c i f i c length h a s been o b t a i n e d , T h i s ' t h f e s h o f d
l e n g t h * is a c h a r a c t e r i s t i c o f e a c h individual muscle- If the
p a s s i v e c o n t r i b u t i o n f c u r v e r ) was s a b t r a c t e d f ro& t h e active
c u r v e (a) t h e r e renraiaed a b e l l shaped curve, Xt was t h o u g h t
t h a t t h i s c u r v e r e p r e s e n t e d the true f e n g t h - t e n s i o n carve f o r
t h e c o n t r a c t i l e cornponeat [ c u r v e d ) ,
B wide variety of musc le s h a v e been i n v e s t i g a t e d i n t h i s
Banner { s e e Ciose,1972), T e c h n i c a l limitations d e l a y e d t h e
d e t e r ~ i n a t i o n oE t h e real l e n g t h - t e n s i o n c u r v e of the
c o n t r a c t i l e c o a p s n e n t , These l i a i t a t i o n s sere overcome i a 3366 I
I when Gordon, Huxley and J u L i a a 11966f elrarained t h e e f f e c t of
changes i n length of a s i n g l e s a r c o m e r e on t h e force deve loped
o v e r a r a n g e of l e n g t h s of 130% of the resting l e n g t h Lo- T h e
f n v e s t i g a t o r s found a length-tension r e l a t i o n s h i p that Mas
s i a i l a r t o t h a t of Ramsep e t al, f f 9 4 0 ) -
The e o n t r a c t i f e c o a p o n e n t h a s two c h a r a c t e r i s t i c s t h a t
d e s c r i b e i ts a c t i v i t y t These a r e t h e f o r c e - v e l o c i t y
r e l a t i o n s h i p a n d t h e isctw tr ic l e n g t h - t e n s i o n r e l a t i o n s h i p , It
gas p e r t i n e n t , t h e r e f o s e , t o observe v b e t h e r there was any
i n t e r p l a y between t h e s e which would a f f e c t t h e d e v e l o p ~ e n t of
force or t b e s h o r t e n i n g o f t h e a u s c l e -
Hill (1950) stated that ,_, ?he e x p e r i m e n t a l r e l a t im
b e t w e e n s p e e d of s h o r t e r i n g a n d load could be e x p r e s s e d by a
f a m i l y of c u r v e s , e a c h for a g i v e n r n u s c l e l e n g t h o v e r a
c o n s i d e r a k f e r a n g e ,,, it was g i v e n m a t h e m a t i c a l l y by t h e
s i n g l e c h a r a c t e r i s t i c e q u a t i o n , . , ",
r3sing f r o g s a r t o r i o u s utuscPe A b b o t t and W i l k i e j1953)
e x a m i n e d t h e s e l a t i o n s h i p b e t w e e n t h e v e l o c i t y of shortening
and muscle l e n g t h t o v e r i f y w h e t h e r R i l l ' s characker i s t i c
e q u a t i o n f i t t e d a t o t h e r w u s c l e l e n g k h s , T h e y f o u n d t h a t i f t h e
i s o m e t r i c maximum f o r c e f a r tha t m u s c l e l e n g t h aas u s e d a s Po
t h e n t h e e q u a t i o n f i t t e d v e r y w e l l , I n o t h e s words , there was a
r a n g e o f f o r c e - v e l o c i t y c u r v e s each a c h a r a c k e r i s t i c of s o B e
~ a l u e of P o which c o u l d b e a t t r i b u t e d t o the r e s t i n g a u s c l e
l e n g t h ,
Bahler, Fales a n d Zierler 11 968) e x a ~ i n e d t h e
i n t e r r e l a t i o n s h i p of force, v e l o c i t y and m u s c l e l e n g t h $',-,of
t h e c o n t r a c t i l e coiriponent of t e t a n i c a l l p s t i m u l a t e d i n t a c t
mannal iaa s k e l e t a l m u s c l e , t he r a t g r a c i l i s antic~s,~. The
r e s u l t s were d i s p l a y e d a s a t h r e e d i m e o s i c n a l r e p r e s e n t a t i o n of
t h e f a m i l y o r f o r c e - v e l o c i t y c u r v e s w i t h r e s p e c t t o m u s c l e
l e n g t h [ f i g u r e 2 ) . It may ke s e e n t h a t t h e i n s t a n t a n e o u s l e n g t h
t h r o u g h u h i c h the m u s c l e s h o r t e n e d a • ’ f e c t e d b o t h t h e v e f o c i t y
o•’ s h o r t e n i n g a n d t h e force d e v e l o p e d ,
T h e d e v e l o p m e n t of the l e n g t h - t e n s i o n r e l a t i o n s h i p , t h e
f o r c e - v e l o c i t y r e l a t i o n s h i p a n d t h e i n t e r r e l a t i o n s h i p of all
t h e s e f ac tors on i s o l a t e d p r e p a r a t i o n s h a s b e e n c o n s i d e r e d , The
next issue r e q u i r Zng i n v e s t i g a t i o n was w h e t h e r t h e same
ref a t ionships h e l d for i n t a c t hunan ~ u s c f es-
F I G U R E 2 : The f o r c e - v e l o c i t y - l e n g t h c u r v e for i s o l a t e d rat g r a c i l u s a n t i c u s m u s c l e
a d a p t e d fro^ B a h l e r , %a le s and Zierler, 6958
Character istics of i n t a c t n u s c l e
T h e problems of d e t e r m i n i n g the c h a r a c t e r i s t i c s of i n t a c t
human m u s c l e s are n u n e r o u s due t o t h e c o n c e r n for t h e well
b e i n g of t h e s u b j e c t , Rafston, Znrrtan, S t r a i t , and S h a f f r a t l h
17947) a t t e m p t e d t o f i n d t h e l e n g t h - t e n s i o n r e l a t i o r a s h i p for
i n t a c t human m u s c l e s , T h e i r s u b j e c t s were v e t e r a n s w i t h
a m p u k a t e d f o r e a r m s , E x p r i ~ e n t a l P y they were f i t t e d c i n e p f a s t i c
t u n n e l s c o n n e c t & t o a t e n s i o n r e c o r d i n g device so that t h e
m u s c l e t e n s i o n at d i f f e r e n t lengths c o u l d be e x a a i n e d .
T h e s e d a t a showed a r e l a t i o n s h i p s i n i l a r tc t h a t p r o p o s e d
by Ramsey and Street [ l 9 4 0 ) , However , t h e r e were some problems
i n c o r r e l a t i n g t h e two s t u d i e s b e c a u s e i n the study oZ RaSston
g& a l , 11947) t h o muscles were n o t * n o r m a l a m u s c l e s i n t h e
o r d i n a r y s e n s e , T h e y oere n c t a t t a c h e d to t h e f o r e a r i a a s t h e y
would be i n t h e intact s u b j e c t and it was n o t clear v h e r e t h e s e
data of R a l s t o n g& &, 37947) Lay o n t h e t o t a l l e n g t h - t e n s i o n
c u r v e of normal subjects. hlso, t h e aaximula . tensions recorded
were y u i t e low % h e n compared t o o t h e r s t u d i e s p d i l k i e , IgSO).
T h a t t h e r e gas a t f e a s t a s i m i l a r i t y i n t h e two c u r v e s
{ i s o l a t e d and intact) was e n c o u r a g i n g since it i l a d i c a t e d a
p o s s i b i l i t y of c o n p a s a b l e l e n g t h - t e n s i o n r e f a t i u n s h i p s f o r
i n t a c t human ~ u s c l e s , I I 1 Anather a p p r o a c h t o studying the a p p l i c a b i l i t y of the
a l e n g t h - t e n s i o n c u r v e derived by W a l s t o n et a& (1940) t o intact
human m u s c l e s h a s b e e n o u t l i n e d b y S t o l c v and W e i l e p p (1965) - T h e y c i t e d s i x a n a t o m i c a l dements p o s s i b l y c o n t s i b u t i n y t o t h e
p a s ~ i v e l e n i j t h - t e n s i o n c u r v e , T h e s e were; 1, t h e ou te r
t i s s u e s h e a t h ; 2, t h e perlirttysiutr! a n 3 e n d o n t y s i u ~ ;
3. the s a r c o f e m a a ; 4, the i n d i v i d u a l f i b r e c o n t e n t s ; 5, t h e
t e n d o n s a t origin and i n s e r t i o n ; a n d 5 , a d h e s i o n s t o
n e i g h b o a r i n g s t r u c t u r e s , A l t h o u g h t h e e x a c t c o n t r i b u t i o n of
each of t h e s e f a c t o s s remained unknown t h e a u t a o r s suggested
that e a c h & u s t b e t a k e n into c o n s i d e r a t i o n when exaa in ing t h e
PEC a n d i ts c o n t r i b u t i o n t o t h e tension developed,
Dern, L e v i n e and S l a i r (1947) a t t e ~ l p t e d t o d e f i n e t h e
f o r c e - v e l o c i t y r e l a t i o n s h i p in human ~ u s c l e s a b o u t t h e e l b o g
joint, B o u e v e r , t h e i ~ r e s u l t s were n o t d e s c r i b e d by t h e
c h a r a c t e r i s t i c e q u a t i o n , The a u t h o z s d o c u m e n t e d sowe
a n t a g o n i s t i c m u s c u l a r a c t i v i t y a n d s u g g e s t e d t h a t t h i s was o n e
source ol d i s c r e p a n c y , L a c k o f c o n s i d e r a t i o n far t h e
a c c e f @ r a t i o n of t h e arm v o u l d have l e d t o f u r t h e r error. The
a u t h o r s did n o t s u g g e s t t h a t the c h a r a c t e r i s t i c e q u a t i o n was i n
f u n d a m e n t a l error, only t h a t f u f t h e r s t u d y of its g e n e r a l
a p p l i c a b i l i t y was r equ i r ed ,
W i i f r i e 11 950) p r o p c s e d t h e f i rst s i g n i f l c a n t a t t e ~ p l t o
a p p l y the model t o i n t a c t human m u s c l e s , H e d e v e l o p e d a
force-velocity r e l a t i o n s h i p for a t a u - c o ~ p o n e n t XCC p l u s S E G )
s i n g l e e q u i v a l e n t ~ u s c l e , p a r a l l e l t o t h e u p p e r arm, a c t i n g a t
t h e h a n d ( f i g u r e 3 ) - T h i s model r e p r e s e n t e d t h e c o m b i n e d effect
of all t h e elbow f l e x o r m u s c i e s , I ts f o r c e - v e l o c i t y
r e l a t i o n s h i p was a c c u r a t e l y d e s c r i b e d by t h e c h a r a c t e r i s t i c
e q u a t i o n , after j u s t i f i a b l e c o r r e c t i o n s for t h e a c c e l e r a t i o a of
t h e i n e r t i a of t h e f o r e a r n ,
P I G U S E 3 : The linear h o r i z o n t a l e q u i v a l e n t B O & ? ~ used by H i i k i e (1950) to d e s c r i b e ef bow f l e x i o n f - h o r i z o n t a l force recorded L - torque produced 8 - e f b o w angle
CC - contractile coaponent S E C - series elastic component
adapted fssm i i i l k i e , 1950,
Aovever , a t t e m p t s to generalize from g i l k i a + s model to thc
r a n g e o f m o v e n e n t f r o m a h o r i z o n t a l p o s i t i o n t o coraplete
f l e x i o n of the e.fbors raet w i t h d i f f i c u l t y , Chapman 11973) h a s
s h o w n w i d e v a r i a t i o n i a h o r i z o n t a l force d e v e f o p e c i t h r o u g h a
r a n q e of flexion o f the e l b o w (30 o f the g r e a t e s t i s o a e t r i c
force), B i l k i e showed a 2 0 % v a r i a t i o n o v e r 90 degrees of
f l e x i o n , On the b a s i s o f t h e s e o b s e r v a t i o n s , i t w u l d seem t h a t
t h e s i n g l e e q u i v a l e n t h o r i z o n t a l usa ale way be a f a i r
r e p r e s e n t a t i o n of a ~ u s c l e o v e r a small r a n g e o f l e n g t h s o n l y ,
Between e l b o w - a n g l e s of 0 d e g r e e s a n d 20 d e g r e e s [ l o n g m u s c l e
P e n q t h s ) , changes i n force t a k e p l a c e v h i c h are Ear t o o g r e a t
t o be c o m p a t i b l e w i t h those p r e d i c t e d from t h e relationship
b e t w e e n isometric t e n s i o n a n d l e n g t h of a * rea lg m u s c l e ,
Chapman I1 973) s u q g e s t e d t h a t a g e o m e t r i c a l . correction may h a v e
t o be a p p l i e d a s t h e t e n d o n s of t h e b i c e p s b r a c h i i and
b r a c h i a l i s p a s s o v e r t h e c a p i t u l u m a n d t r a c h l e a of t h e h u m e r o u s
r e s p e c t i v e l y , T h i s f a c t o r would a l t e r t h e aagfe of p u l l of t h e
t e n d o n s a n d i n d o i n g s o a l t e r t h e t o r q u e d e v e l o p e d a b o u t t h e
ef bow- j o i n t ,
T h e e x a m i n a t i o n p r e s e n t e d t h u s f a r h a s c e n t e r e d o n t h e C C =
There is a l s o a SEC w h i c h a f f e c t s t h e t r a n s m i s s i o n of t h e force
d e v e l o p e d b y t h e CC t o t h e i n s e r t i o n of t h e m u s c l e , T h e
p r e s e n c e of s u c h a c o m p o n e n t h a s b e e n evident f rom some o f t h e
earliest s t u d i e s ( L e v i n and Wyrnan, 1927)- T h e s e a u t h o r s c o n s i d e r e d
t h e SEC a s a n undamped s p r i n g i n series w i t h t h e c o n t r a c t i f e
c o m p o n e n t a n d a s s u c h t h e SEC m o d i f i e d t h e r a t e of change of
t h e e x t e r n a l t e n s i o n r e c o r d e d a s se l l a s t h e v e l o c i t y of
movement,
Shiie the SEC h a s b e e n s h e w n to b e a p a s s i v e eleaent
t h r o u q h o u t c o n t r a c t i o n I n i l k i e , 7 956) i t does i n t r o d u c e p e a k i n g
a n d ~ s c i l l a t i o n i n t h e v e l o c i t y - t i m e c u r v e d u r i n g f l e x i o n of
t h e f o r e a r m f P i l k i e , 1950 ) - A c c u r a t e d e t e r m i n a t i a n of t h e
v e l o c i t y o t s h o r t e n i n g of t h e CC is d e p e n d a n t upon t h e
d e t e r m i n a t i o n of t n e v e l o c i t y of m o v e ~ e n t a t t h e h a n d a s a
f u n c t i o n of b a t h the c h a n g i n g f e n g t h e o f t h e SEC a n d t h e
v e l o c i t y of a o v e m e n t of t h e CC, If the v e l o c i t y of s h o r t e n i n g
of t h e CC is r a p i d t h e n the v e l o c i t y of f l e x i o n of t h e hand
w i l l b e d i f f e r e n t b y an amount e q u i ~ s a l e n t t o t h e v e l o c i t y of
movement of t h e SEC,
T h e l o c a t i o n OF the SEC h a s n o t been c o n c l u s i v e l y
d e t e r m i n e d , It seems l i k e l y t h a t some resides i n the tendons
( W i l k i e , 7950) a n d c o n n e c t i v e tissue, It has a l s o b e a n I
s u g g e s t e d t h a t some can be a t t r i b u t e d to the c o n t r a c t i l e f material i tself, I n a n y case, i t is n o t p o s s i b l e to r e m o v e t h e
S E C from i n t a c t m u s c h e s and t h e r e f o r e some v i g i l a n c e w i l l h a v e
t o b e m a i n t a i n e d on t h e effect of t h e c h a n g i n g l e n g t h o f t h e
S E C ,
One f a c t o r w h i c h a f f e c t s s t u d i e s of i n t a c t h u a a n a u s c l e s
i s t h e degree of v o l u n t a r y m u s c u l a r a c t i v a t i o n , T h i s p r o b i e m
was most t r o u b l e s o m e when r e p e a t a b l e maximal v o l u n t a r y
c o n t r a c t i o n s are r e q u i r e d , I n i s o l a t e d ~ u s c f e p r e p a r a t i o n s the
a c t i v a t i o n o f t h e m u s c l e would be very c a r e f u l l y r e g u l a t e d , I n
human m u s c l e s this r e g u l a t i o n is not q u i t e a s s i m p l e , Factors I
s u c h a s f r e q u e n c y of s t i m u l a t i o n and t h e number of active motor
u n i t s affect t h e rise of force ( B a h l e r e t a t , 1 9 6 8 ) , T h e r e is
also t h e possibility of inkcrackion cf a n t a g o a i s t i c units
r e s u l t i n q i n r e f l e x c o n t r o l @ern et a,, 1947)- I n s t u d i e s
d e a l i n g w i t h intact human muscles t h e s e factors raus t be taken
i n t o account a n d c o r r e c t e d f o r where p o s s i b l e , H e w
i n v e s t i g a t o r s h a v e matie r e p e t i t i v e s t u d i e s t o confirm t h e
achievement 02 r e p e a t e d ~ a x i m a l a c t i v a t i o n o r w h e t h e r i t h a s
b e e n a c h i e v e d e v e n o n c e ,
E l e c t r o ~ y o g r a p h y ( E R G ) , a s a t e c h n i q u e t o explore t h e
e v e n t s o c u r r i n g within a muscf e, h a s r e c e i v e d much a t t e n t i o n .
U s e o f s u r f a c e electrodes p r o v i d e s a simple n o n - i n v a s i v e
t e c h n i q u e f o r a o n i t o r i n g internal e l ec tr i ca l a c t i v i t y *
However , t h e r e are a n u m b e r of p r o b l e m s associa ted w i t h t h e
q u a n t i f i c a t i o a of t h e EEG signal [ B a l s t o n , 1967) a n d
c o n s e q u e n t l y there has n o t been any s n c c e s s f u f a t t e n p t a t
r e f a t i n y t h e E a G s i g a a l , b e it unprocessed os q u a n t i f i e d i n
soae fashion, to the e v e n t s l e a d i n g t o a c t i v a t i o n o f t h e
a u s c l e . The p u r p o s e of this t h e s i s i s n o t i n a n y way t o a t t e m p t
t o d e v i s e s u c h a r e l a t i o n s h i p n o r w i l l any a t t e m p t be made t o
use E%G,
T h e p r o b l e m s of d e t e r m i n i n g the effect of a c t i v e state o n
t h e rise i n force cannot be i g n o r e d , J e v e l l and W i l k i e (1958)
h a v e shown t h a t t h e t h e o r e t i c a l rise i n force derived frog
i s o t o n i c force velocity r e l a t i o n s h i p s @as q u i c k e r t h a n recorded
e x p e r i r s e n t a f iy, Parmiey, Yeatmasl a n d S o n r a e n b l i c k ( 7 970) h a v e
d e r i v e d f o r c e - v e l o c i t y elations ships from i s o t o n i c and
isometric c o n t r a c t i o n s , Their results show that t h e r e was a
c o n s i s t e n t d i f f e r e n c e i n t h e two c u r v e s , B o t h g r o u p s 02
iavestiyatars argued t h a t t h i s azcmaly c s u l d S e attcibuted to
d i f f e r e n c e s i n the active state of t h e muscle,
P r i n g l e (1859) postulated a d i E f e r e n t v i e % of t h e active
s t a t e t o e x p l a i n these o b s e r v a t i o n s . R a t h e r t h a n h y p o t h e s i z e a n
a c t i v e s t a t e a s being u n a f f e c t e d b y guick s t r e t c h e s o r g u i c k
releases '* , , ,oue m i g h t p c s t u l a e e a p r o p e r t y called, s a y
a c t i v a t i o n , which was i n c r e a s e d by t e n s i o n a n d which c o n t r o l s
velocity of shortening at a g i v e n t e n s i o n , " , Using this
definition Pringfe was able t o d e s c c i b e the o r i g i n of t h e
\ differences be tween isotcnhc and isometric derivations of t h e
\ f o r c e - v e l o c i t y r e l a t i o n s h i p , T h e force-velocity relationship
now r e p r e s e n t e d the combined action of t e n s i o n and a c t i v a t i o n
a n d t h e o b s e r v a t i o n s of J e w f l . a, (1958) a a d Parntley at AS
(1970) c o u l d be e x p l a i s e d , Whether t h i s vLew is i n greater
harmony vith the underlying mechano-elecitrical-chemical events
than the t r a d i t i o n a l v i e w , p o s t u l a t e d by H i l l (3949), remains
presently u n d e t e r a i n e d ,
S i n c e t h i s thesis is ccncerned vith t h e r a t e of rise i a
force measured under isoirietric c o n d i t i o n s t h e above c o ~ m e n t s of
Jewel1 & a, (3958 ) and Parmley et af- g1970) are i ~ p o r t a n t - -7-
I f s u c h dramatic differences were shoan i n i s o l a k e d
p r e p a ~ a t i a n s , e q u a l l y p r c n o u n c e d v a r i a t i o n s B a y well be
o b s e r v e d i n intact p r e p a r a t i o n s , O b v i o u s l y , extreme vigilance
%ill have to be aaiutained on ail factors a f f e c t i n g the rise i n
force,
P a r a l e y ~t d, (1970) have s h o w n t h a t t h e f o r c e - v e l o c i t y
c u r v e c a l c u l a t e d f r o m iscmetric c o n t r a c t i o n s o f i s o l a t e d
p r e p a r a t i o n s uas d i f f e r e n t from t h a t d e r i v e d • ’ s o n t h e same
p r e p a r a t i o n s u s i n g d y n a m i c c o n t r a c t i o n s . Tt would be
i n t e r e s t i n g t o see whether t h e same o b s e r v a t i o n s w o u l d be made
o n intact human muscles. To c o t a p l e t e t h i s t a s k r e q u i r e d the
development o f two t e c h n i q u e s , one u s i n g isowetric c o n t r a c t i o n s
a n d one u s i n g d y n a t a i c c o n t r a c t i o a s , W h i l e t h e s e t e c h n i q u e s a r e
d i s c u s s e d e x t e n s i v e l y i n the s e c t i o n t i t l e d E e t h o d of A n a l y s i s
t h e y w i l l b e o u t l i n e d briefly h e r e ,
To d e r i v e a f o r c e - v e l c c i t y c u r v e from isometric
c o n t r a c t i o n s B a c P h e r s o n (1953) d e v i s e d a t e c h a i g u e t h a t re l i ed
o n t h e d e v e l o p m e n t cf farce u n d e r two conditions, In the f i r s t
c o n d i t i o n t h e m u s c l e c o n t r a c t e d i s o m e t r i c a l l y a g a i n s t a force
t r a n s d u c e r and the rise i n force was recorded, A c o m p l i a n t
s t r u c t u r e f a s p r i n g ) was t h e n f i x e d be tween t h e muscle and t h e
t r a n s d u c e r and the m u s c l e was s t i ~ u l a t e d a g a i n - I n b o t h
c o n d i t i o u s t h e s t i m u l a t i c n ~ r o d u c e d a maximal isometric
c o n t r a c t i o n b u t t h e r i se in force in t h e s e c o n d instance was
sloves t h a n in the f i rs t i n s t a n c e , The m a g n i t u d e of t h e
c o m p l i a n c e h a d to b e f a r g e e n o u g h t o p e r m i t t h e s e p a r a t i o n of
t h e tuo force-time c u r v e s b u t not sa f a r g e as to p e r m i t gross
c h a n g e s o f t h e r n u s c l e l e n g t h , M a c P h e r s o n assunted o n l y t h a t t h e
velocity of s h o r t e n i n g was a f u n c t i o n of t h e force d e v e l o p e d ,
With t h i s a s s u m p t i o n h e was a b l e t o u s e the d i f f e r e a t i a l of t h e
~ i s e in farce in t h e + u o c c n t r a c t i o n s and t h r o a g h a series of
m a t h e m a t i c a l m a n i p u l a t i c n s determine t h e v e l o c i t y of s h o r t e n i n g
05 t h e cou t rac t i l e c o m p o n e n t , This method is very aes i rabfe a s
it permits t h e d e t e r m i n a t i o n o f t h e f o r c e - v e l o c i t y curve of the
contractile cowponent fro^ t u o c o n t r a c t i o n s usnaffected b y t h e
s e x ies e l a s t i c component. T h e SEC m o d i f i e s t h e v e l o c i t y o f
shortening o f the CC a s i t t r a n s m i t s t h a t v e l o c i t y t o t h e
i n s e r t i o n of the m u s c f e , I f t h i s effect caa be b y p a s s e d t h e n
the d e t e r m i n a t i o n of t h e f o r c e - v e l o c i t y curve of t h e CC is v e r y
m c h s i m p l i f i e d ,
The m e t h o d of u e v e f o p i n g a f o r c e - v e l o c i t y c u r v e for h u ~ a n
m u s c l e s from dynamic c o n t r a c t i o n s i s not q u i t e a s s t r a i g h t
f o r v a r d a s when i t is d e v e l o p e d i s o n t e t r i c a l l y . T h e rotation of
t h e elbow, t h e i n t e r a c t i o n of t h e series e l a s t i c cowponent i n
the m o d i f i c a t i o n of t h e v e l o c i t y of s h o r t e n i n g of ad j o i n i n g
s t r u c t u r e s and the i n t e r a c t i o n of t h e subjectJs c o n s c i o u s
a w a r e n e s s of the r e q u i r e d m u s c u l a r activity a l l affect t h e
fofce r e c o r d e d , B e z o r e one c a n i s o l a t e the force developed and
v e l o c i t y of shortening p r o d u c e d b y t h e c o n t r a c t i l e c o m p o n e n t
a l o n e , the m a g n i t u d e uf t h e i u v o l v e a e n t of t h e i n t e r f e r i n g
factors must he assessed and s u b s e q u e n t f y reatoved, f deal1 y, for
the determination of the v e l o c i t y of s h o r t e n i n g of t h e CC the
r a t e of c h a n g e n Z t o rque m u s t be zero. A t this point the
veZocity of the hand is t h e s a m as the v e l o c i t y of shortening
of t h e CC, However , this restricts t h e s e l e c t i a m of p o i n t s f o r
t h e d s v e i o p m e n t of a t o r q u e - a n g u l a r v e l o c i t y c u r v e and i t Bay
b e d e s i r a b l e t o select a range of t o r q u e s where the change is
sma l l ~ n n u g h to F n t m d u c c a n e g l i g i b l e e r r o r i n the c a l c u l a t i o n
of the v e l o c i t y of s h o r t e n i n g of the CC. T h i s p o s s i b i l i t y will
be explored i n the s e c t i o n titled 'Hethod of A n a l y s i s * ,
Once the two methods Tor development of the torque-a~gular
velocity curve are devehuged the study proposes to exa~inz the
f o l l o w i n y ;
1, Is there a difference i n the t o r q u e - a n g u l a r v e l o c i t y
c u r v e derived from iso~etric c o n t r a c t i o n s when co~pared
to a torque-angular v e l o c i t y c u r v e derived from dynamic
c o n t r a c t i o n s ?
2, T h r o u g h t h e r a n g e of e x c u r s i o n of t h e e l b o w - j o i n t is
these s u f f i c i e a t l e n g t h e n i n g o f t h e Ct t o c h a n g e t h e
force produced b y the muscle? 1 3 , Do t h e p r o p e r t i e s of t h e series elastic c o a p a n e n t is
c h a n g e d u r i n q a maximal c o n t r a c t i o n a t d i f f e r e n t j o i n t
posit i o n s ?
4, Does W l f k i e g s s i n g l e equivalent model adequately
describe the c h a r a c t e r i s t i c s of human muscular
c o n t r a c t i o n ?
T h e s e were two grouFs of subjects i n this study, The
embers of each group were h e a l t h y male university personelf
and their aqes, w e i g h t s and s t a t u r e s were l i s t e d i n Appendix I ,
A l l s u b j e c t s were r i g h t handed and although some exercised
r e q u l a r i l y n o n e were e n g a g e d i n p r o g r e s s i v e resistance
exercises, I n g r o u p o n e there were n iue subjects and in g ~ o u p
two there vers two subjects,
a) The apparatus u s e d f o r the n c a s u r e m e n t of torque, d i s p l a c e m s n t a n d a c c e i e r a t i o n
T h e a p p a r a t u s [ f i g u r e 4 ) e s s e n l t i a l l y comprised the rear
a x l e of a n au tomobi le w h i c h %as s u p p o r t e d w i t h i t s o u t e r c a s i n g
r i g i d l y f i x e d i n a wooden tressle and a l i g n e d parallel t o t h e
s a g i t t a l a x i s of -the s u b j e c t , T h e t w o half-shafts, c o r a p l e t e !
with h e a r i n g s , remained w i t h i n t h e c a s i n g of t h e a x l e and a s
t h e d i f f e r e n t i a l h a d been removed, t h e t u o opposinq eads of the
ha12 s h a % & s %ere j o i n e d w i t h a mila steel collar, To the collar
was a t t a c h e d a s p r i n g which c o u l d b e so a r r a n g e d t o p r o v i d e a
~ o r n p f iant connection b e t r e e n the tuo h a l f s h a f t s [f i c ju rs , 5 ) -
A t one end of this a p p a r a t u s were l o c a t e d t h e to rque , 11 111
acceleration and d i s p f a c e m e a t transducers and t h e a e c h a n i s m for
a l i g n i n g t h e s u b j e c t w i t h the a p p a r a t u s , The subject was
s e a t e d i n a n a d j u s t a b l e cha i r w i t h t h e right arm elevated so
that t h e u p p e r arm was h o r i z o n t a l i n t h e c o r o n a l plane, T h e r e
was a v c r t i c a l suppcrt for the elkow a s well as a c h e s t s u p p o r t
to s t a b i l i z e t h e subjectrs p o s i t i o n , T o m a i n t a i n t h i s p o s i t i o n
safety belts were passed around t b e s u b j e c t s chest and t h i g h s
a n d a t t a c h e d t o the a p p a r a t u s ,
At t h e o t h e r e n d of t h e a p p a r a t u s was l o c a t e d a b o a r d that
was u s e d t o f i x t h e p o s i t i o n of t h e axles for the isometric
p u l l s a s w e l l a s provide a convenient place to hang the weights
f o r the dynamic p u l l s ,
F I G U R E 4 : The a p p a r a t u s used i n the p r e s e n t s t u d y , (see text f o r a complete d e s c r i p t i o n )
F I G U R E 5 : T h i s s p r i n g p r o v i d e d a coap l iaa t connection between t h e t w o half s h a f t s ,
F I G U X E 6 : This shows t h e two h a l v e s oP the c a s t used to p r e s e n t v s i s t f l e x i o n during cantractiora-
FfCUBE 7 : This i l l u s t r a t e s a schematic of the dynamometer used in the experiment, T h e various transducers were a t t a c h e d to this dynamolrte t er , The ditnensions of t h e beam {in cms) are as follows;
Tc l i ~ i t t b e flexion cf tZz f o r z a r m 2 f i b r e g l a s s cas t was
t a p e d to the s u ~ j e c t s foream, T h i s c a s t c o n s i s t e d of t s o s i d e s
a n d e x t e n d e d from the fingertips to the elbow, It d i d n o t iirait
elbow f l e x i o n b u t it d i d p r e v e n t wrist f l e x i o n , On the pafwer
s i d e awl l oca t ed i n t h e c e n t r e of t h e pa lm a b l o c k of % ~ 0 0 d was
f i x e d w i t h a t h x e a d e d b o l t which could b e a t t a c h e d t o the beam
[ f i g u r e 6 ) -
b] The dynaraorae te r for t h e t r a n s d u c t i o n o f t o r q u e ,
displacement and a c c e l e r a t i o n
The dyn~rnometer ( f i g u r e 7) was required t o r e g i s t e r
t o r q u e , d i s p l a c e m e n t and a c c e l e r a t i o n w i t h ref ererice k o t h e
a x i s af r o t a t i o n of t h e efbcer j o i n t , Xn order to keep c o m p l i a r t t
connections t o a miniaum, a beam, t o w h i c h t h e f o r e a r i a cast
c o u l d b e bolted, was c h o s e n a s t h e b a s i c u n i t of the
d y n a n o m e t e r , T h i s beam o r l e v e r had t o b e c o n s t r u c t e d i n such a
m a n n e r t h a t i t a l l o w e d t h e i n d i v i d u a l t r a n s d u c e r s to operate
without i n t e r f e r e n c e , W h i l e rigidity was i m p o r t a n t a certain
a m o u n t of bend was n e c e s s a r y t o e n s u r e a n output from the
strain guage t r a n s d u c e r s , T h i s c r i t e r i o n was determined by the
c h a r a c t e r i s t i c s o f the strain guages which h a d a l i n e a r range
of r e s i s t a n c e in r e s p o n s e t o strain between zero and 1/1000 of
t h e i r u n s t r a i n e i i l e n g t h , T c meet these specifications a beaw
was c h o s e n t h a t w o u l d bend 20 more t h a n ,00125 r a d i a n s a t i t s
o u t e r end ( 4 0 c n from the a x i s of r o t a t i o n ) ,
T h i s t r ansauc t ion was c o a p l e t e d by f o u r strain gauges
( t y p e MA-0b-250BG- 120 , manufacused b y Eicro C e a s u r e r n e n t s ,
~ i c h , ) a t t a c h e d t o t h e beam, their l o n g axes c o i n c i d e a t a l t o
t h e l o n g a x i s of t h e beam, 10 c n s from the c e n t r e of the axle,
The four s t r a i n gauges were w i r e d t o g e t h e r as t h e a c t i v e arBs
of a Whea t s tone b r i d g e { f i g u r e 8 ) - T h e u s e o f f o u r g a u g e s
minimized t h e e i f e c t o f t e m p e r a t u r e [all four uould be a f f e c t e d
thereby i n c r e a s i n g t h e stability) and a l l o w e d for greater
r e s o l u t i o n of t h e a p p l i e d to rque as two of t h e g a u g e s wers
s u b j e c t t o s t r a i n while the o t h e r t w o were s u b j e c t t o
c o m p r e s s i o n .
ii) Transduction of d i s p l a c e a e n t
T h e t r a n s d u c e r f o r r e c o r d i n g d i s p l a c e m e n t was a wire wound
p o t e n t i o m e t e r w i t h a r e s i s t a n c e w h i c h varied from O ohms t o 10
ki lohrns ( t y p e 153-585313, manufactured by TRC, St, P e t e r s b u r g ) ,
T h e a x l e of t h i s p o t e n t i o m e t e r was fixed t o t h e o e n t r e o f t h e
h a l f shaft closest to the subject, The t r a n s d u c t i o n o f the
a n g u l a r d i s p l a c e m e n t of t h e D e a ~ f rom t h e h o r i z o n t a l i iepended
upon t h e f inear r e l a t i e n s h i p between angular d i s p l a c e ~ e n t of
the s h a f t a n d t h e electrical resistance of t h e p o t e n t i o m e t e r -
FIGURE 8 : T h e circuit of t h e W h e a t s t o n e B r i d g e f R 1 t o 8G) a l o n g w i t h t h e power s u p p l y (2 -5v) a n d t h e b a l a n c i n g r e s i s t o r {Rd) u s e d f o r t h e t r a n s d u c e r s of t a f q u e and a n g u l a r a c c e l e r a t i o n , T h e b r i d y e u s e d f o r t h e t r a n s d u c t i o n of t o r q u e i n v o v l e d R 3 a n d R 3 i n c o m p r e s s i o n and $2 a n d BY i n t e n s i o n o r v i c e v e r s a d e p e n d i n g u p o n t h e d i r e c t i o n of t h e t o r q u e , The b r i d g e u s e d f o r the t r a n s d u c t i o n of a c c e l e r a t i o n i n v o l v e d R 2 i n c o n p r e s s i o n and B& i n t e n s i o n o r vice versa d e p e n d i n g upon the d i r e c t i o n of t h e a c c e l e r a t i o n while E l and R 3 remained f i x e d i n v a l u e , T h e n o m i n a l v a l u e s f o r t h e resistors f i n ohms) ace a s f o l l o w s :
T o r q u e a c c e l e r a t i o n b o t h 31-R4 = 120 v a r i a b l e E l a n d 2 3 = 320 f i x e d R 6 = 1 0 K
R 5 = O •’32 an4 R 4 = 3 2 0 v a r i a b l e X 7 = 1 0 R 25 = 1 K R8 = I D K
H 9 = 1 M
FIGUBE 9 : This s h o w s t h e main a m p l i f y i n g u n i t o
iii j Thc f r a n s d u c t i c n of a c c e f c r a t i o n
This was p e r f o r m e d b y a m i n i a t u r e a c c e f e r ~ ~ e t e r { t y p e
i3LA2, m a n u f a c t u r e d b y Pye Dyn., London) moun ted o n a rigid c l i p
f i x e d t o the o u t e r end of the beam, T h e sensitive a x i s o f t h e
a c c e l e r o a e t e r was o r i e n t e d with t h e s e n s i t i v e a x i s of t h e beare,
A smal l i n e r t i a a f f e c t e d the o u t p u t of t h e s t r a i n g a u g e s v i t h i n
t h e accelerometer when t h e t r a n s d u c e r was s u b j e c t t o
a c c e l e r a t i o n , T h e s e two s t r a i n g a u g e s were c o u p l e d w i t h two
f i x e d r e s i s t o r s w i t h i n t h e amplifier tc f o r m a Wheats tone
b r i d g e c i r c u i t ,
T h e power s u p p i y tc each t r a n s d u c e r and a ~ p i i f i c a t i o n of
i ts o u t p u t v o l t a g e was c e n t r o l l e d by s e p a r a t e s t r a i n g a u g e
a m p l i f i e r s { t y p e A D 6 ) mounted i n a s i n g l e i n t e q f a t e d unit [ t y p e
T E 4 , manufactured b y T e c a , G h i t e P l a i n s , N, ]I,), See f i g u r e 9-
c) C a l i b r a t i o n of t h e t r a a s d u c e r s
i) Sta t ic p r o p e r t i e s
T o assess t h e h i d i r e c t i o n a l i t g of t h e t o r q u e t r a n s d u c e r a
series o f w e i g h t s were h u n g from the s l o t when t h e lever was
h o r i z o n t a l o n e i t h e r s i d e of t h e v e r t i c a l , A p l o t of t h e
r e l a t i o n s h i p b e t w e e n t h e known a p p l i e d t o r q u e s a n d t h e
c a l c u l a t e d t o r q u e s , b a s e d cn t h e o u t p u t of t h i s t r a n s d u c e r ,
s h o w e d t h a t t h e torque t r a n s d u c e r e x h i b i t e d a l i n e a r r e s p o n s e
b i d i r e c t i o n a U y , T h e r e was n o m e a s u r e a b l e v a r i a t i o n from t h i s
expected f o r e v e n the s t r o n g e s t c t f s u b j e c t s .
Since t h e accelerometer a n d t o r q u e t r a n s d u c e r w e E e s u b j e c t
t o t h e e f fec ts o f q r a v i t y t h e o u t p u t for t h e full r a n g e o f
p o s i t i o n s was e x p e c t e d t o b e p r o p o r t i o n a l t o the c o s i n e of the
a n g l e o f t h e beam, T h i s a n g l e was d e t e r m i n e d by a l i g n i n g t h e
d i s p l a c e r t t e n t t r a n s d u c e r s o t h a t a t a n g l e 0 ( f e v e r h o r i z o n t a l )
i : t h e o u t p u t voltage was 0 and the o u t p u t v o l t a g e was f u l l s c a l e p
(1 .25 V) a t t h e a n q l e 1 8 0 d e g r e e s , B y k n o w i n g the a n g l e a n d
r e c o r d i n g t h e c u t p u t from t h e o t h e r two t r a n s d u c e r s a p l o t of
and t o r q u e t r a n s d u c e r s f o l l o w e d a cosine c u r v e ,
iif ~ y n a m i c p r o p e r t i e s
k h The d y n a m i c p r o p e r t i e s 0% the t r a n s d u c e r s were assessed a s 5 t
f ollorsrs:
1, T h e a n g l e m e a s u r e d from t h e o u t p u t v o l t a g e of 'the
d i s p l a c e m e n t t r a n s d u c e r was c o m p a r e d w i t h i h e a n g l e d e t e r m i n e d
ky r a p i d l y m t a t i n y t h e lever as i t was i l l u m i n a t e d w i t h a
s t r o b o s c ~ p i c l i g h t and p h o t o g r a p h e d , T h e r e was n o d e t e c t a b l e
d i f f e r e n c e b e t w e e n t h e results obtained f r o m t h e two ~ e t h o d s of
d e t e r m i n a t i o n of t h e a n q l e ,
2, T h e f r e q u e n c y respcnse o f t h e t o r q u e t r a n s d u c e r was
d e t e r m i n e d b y e x a m i n i n g i t s o u t p u t f o - l l o w i n g a s t e p i n p u t - The
o u t p u t of t h e t r a n s d u c e r was e x p o n e n t i a l i n f o r m w i t h a
t i m e - c o n s t a n t of 10 msecs i n d i c a t i n g t h a t i t w o u l d f a i t h f u l l y
rep r35uce t h e s i s n a l s slcgfr than t h i s , Thc time c o n s t a n t f o r
a n i s o m e t r i c p u l l h a s b e e n estimated t o be near 50 msec w h i c h
is well w i t h i n t h e c a p a b i l i t i e s of t h e a p p a r a t u s ,
3, T h e r e s p o n s e o f t h e a c c e l e r o m e t e r was assessed by
o s c i l l a t i n g the l e v e r from the o p p o s i t e e n d o f t h e a p p a r a t u s , A
b o l t was fixed t o t h e s l o t i n the beam so t h a t a l a r g e r o u t p u t
f r o m t h e t o r q u e t r a n s d u c e r c o u l d b e a c h i e v e d , B e c a u s e t h e
i n e r t i a of & h e bolt a n d beam was constant t h e r a t i o o f t h e
t o r q u e t o t h e a c c e l e r a t i o n s h o u l d a l s o h a v e b e e n c o n s t a n t , A
v a r i a t i o n of 2 % was o b s e r v e d i n the r e s p o n s e of t h e s e
t r a n s d u c e r s , T h i s v a r i a t i o n was a t t r i b u t e d t o t h e f r e q u e n c y
r e s p o n s e of e a c h t r a n s d u c e r , This was not a s s r i o u s d e f f i c i e n c y
s i n c e the s i g n a l s sere filtered p r i o r t o a n a l y s i s o r s t o r a g e as
d e s c r i b e d b e l o w , H e n c e , t h e signals were a t t e n u a t e d t o t h e same
level,
d ) F i l t e r i n g t h e o a t p u t of t h e t r a n s d u c e r s
E l e c t r o n i c f i l t e r i n g of t h e o u t p u t from each t r a n s d u c e r
permitted t h e r e m o v a l of n o n p h y s i o l o g i c a l d i s t u r b a n c e s , s u c h a s
t h e n a t u r a l f r e q u e n c y of t h e bean ( 3 6 f i a , ) , and matchinq the
S r e y u e r x q r e s p o n s e of t h e a c c e l e r o n e ter and t o r q u e t s a n s d u c e r . T h e output from t h e a c c e l e r o m e t e r c o n t a i n e d t h e h i g h e s t
f r e q u e n c y c o m p o n e n t s anrd h e n c e , t h e u n f i l t e r e d o u t p u z from t h i s
t r a n s d u c e r was r e c o r d e d a n d s u b s e q u e n t l y p l a y e d back t h r o u g h a n
ad j u s t a b h e a n a l o g u e f i l t e r , T h e band u i d t h o r f r e q u e n c y
r e s p o n s e was d e t e r a i n e d b y narrowing the width u n t i l t h e s i g n a l .
was a t t e n u a t e d 3db, T h e r e c o r d i n g s demonstrated t h a t t h e s i g n a l
became a t t e n u a t e d below f r e g u e n c i e s of f 2Hz f-3db), The c u t o f f
f r e q u e n c y was c h o s e n t o be 35Hz 4-3db) t o r a a i n t a i n a a a r g i n of
s a f e t y .
ef Permanent r e c o r d i n g of t h e o u t p u t f ro~tt t h e t r a n s d u c e r s
i) The fregueaep a o d u l a t e d (FE4) t a p e - r e c o r d e r I$+
An f t a p e r e c o r d e r { t y p e 309Q&, n a n u f a c t u r e d by H e v i e i t
Packard, C o l o r a d o USA) was used t o store t h e o u t p n k frortl the
t r a n s d u c e r s , T h i s recorder has Eouf s e p a r a t e channels e a c h w i t h
a n i n p u t and o u t p u t a m p l i f i e r , Each a i n p l i f i e r h a s a g a i n
c o n t r o l which a f L o u e d the n s e r t o m a i n t a i n t h e i n p u t and o u t p u t
f ~ l t a g e s v i t h i n the iifiear response range of the a m p l i f i e r s
{f u3.f scale 0-2.5 8 ) - The t a p e u s e d was low noise P h i f l i p s
X n s t r u a e n t a t i o n t a p e { a a n u f a c t u r e d i n Vancouver Canada) - 535 ca
i n w i d t h , T h e r e c o r d a n d p l ayback s p e e d gas 38- 1 can/sec, The
c e n t r e f r e q u e n c y of wodufa t ion was 27KHz a n d t h e s i g n a l to
n o i s e r a t i o was 48db-
T h e i n p u t s i g n a l s sere f i l t e r e d t o and f roa the t a p e
r e c o r d e r t h r o u g h t h e saw filters, T h i s served t o r e a o v e any
h i g h f r e q u e n c y n o i s e g e n e r a t e d by the t a p e - r e c o r d e r d u r i n g
e i t h e r t h e r e c o r d i n g or r e t r i e v a l p r o c e s s ,
. XL) Anal o ~ u c tc d i g i t a l c o n v e r s i o n
I n o ~ d e r to u s e a c o m p u t e r f o r t h e c o m p u t a t i o a i t was
necessary t o t r a n s f e r t h e a n a l o g u e s i g n a l o n t h e F2 tape
r e c o r d e r t o t h e c o m p u t e r , P h i s was c o m p l e t e d b y t r a n s f e r i n g the
d a t a t h r o u g h a 10 b i t , 10000 s a m p l e s p e r s e c o n d a a a l o g u e t o
d i g i t a l c o n v e r t e r { t y p e BDC, m a n u f a c t u r e d b y D i g i t a l E q u i p m e n t
Corp , , sass. USA) w h i c h was a p e r i p h e r a l u n i t t o a m i n i c o m p u t e r
w i t h 12K l o c a t i o n s o f 1 2 b i t s each ( t y p e PDP-8e, a a u f a c t u r e d by
D i g i t a l E g u i p , C o r p , , Bass, U S A ) , A l l s i g n a l s were c o n v e r t e d a t
a s a m p l i n g r a t e o f 200 s a m p l e s p e r second, T h i s was c h o s e n a s
t h e minimum ra te w h i c h w o u l d a c c u r a t e l y r e p r o d u c e t h e inp t rL
s i g n a l , A co rnp ro rn i se between the i d e a l s a a t p l e rate a n d
a v a i l a b l e storage space v i t h i n t h e c o i a p u t e r was n e c e s s a r y and
t h e r e f o r e a h i g h e r s a m p l i n g r a t e c o u l d n o t b e u s e d a s i t v o u l d
r e s u l t i n a n o v e r f i l l i n g of t h e s t o r a g e ,
T h a p r o c e s s of c o n v e r s i o n was c o n t r o l l e d b y m a c h i n e
l a n g u a g e (BAT, 111) while t h e i n i t i a l i z a t i o n was c o n t r o l l * d by
the o p e r a t o r t h r o u g h a c o n v e r s a t i o n a l l a n g u a g e FOCAL, A c o n t r o l
s w i t c h was u s e d t o i n i t i a t e t h e a c q u i s i t i o n and t o reset a f t e r
c o m p l e t i o n of one p a s s , PC a c q u i r e + h e d a t a t h e o p e r a t o r p l a y e d
t h e o u t p u t from t h e t a p e r e c o r d e r t o a n o s c i l l o s c o p e w i t h
s t o r a g e f a c i l i t y ( t y p e 1201 A , ~ a n u f a c t u r e d by Heslett Packard,
C o l o r a d o USA) and t h e n r e p l a y e d t h ~ o u t p u t w i t h t h e i r a a g e
r e m a i n i n g o n t h e s c r e e n , As t h e i m a g e moved across t h e screen a
s e c o n d time the u p e r a t c r i n i t i a t e d t h e A-D with t h e c o n t r o l
switch a t t h e a p p r o p r i a t e t i m e ,
S t o r a g e of LX+= d a t a was conrpli;ted i n G i y i t i a e d f o r a ou
~ a g n e t i c tape (type DECTAPE, z t a n u f a c t u r e d b y Digital Equip ,
Corp- Eass USA) through a t a p e d r i v e sys ter t l i n t e r z a c e d with t h e
compute r .
iiif R e c o r d i n g O s c i l l o g r a p h
A i n u f t i - c h a n n e l oscillcgraph {type 5-127, m a n u f a c t u r e d b y
Bell and Howell, Basingstoke, Eng,) was u s e d t o record t h e rise
in t o r q u e in a series of of isometric contractions, These d a t a
were u s e d i n the d e t e r m i n a t i o n of t h e compliance of the SEC a s
well a s i n t h e determination of the time-constants of the rise
in torque, T h i s o s c i l l c g r a p h was connected o n - l i n e w i t h the
t r a n s d u c e r s e l i r n i n a t . i n q i n t ~ r l m s to r i tqe or! F % e ??PI
t a p e - r e c o r d e r .
PROCEDURES
T h i s s t u d y c o m p r i s e d two segaf a t e experiments, The
e g u i p a e n t used was t h e salne b u t t h e p r o c e d u r e s fo r each
experiment d i f f e r e d g r e a t l y ant3 sill b e i t i s cussed separately,
i be aim of the first e x p e r i n e n t uas t o o b t a i n a torque-angular
velocity r e l a t i o n s h i p f roa isometric c o n t r a c t i o n s w h i l e
t h a t of t h e s e c o n d e x p e r i ~ e n t r a s d e t e r m i n a t i o n of t h e same
r e l a t i o n s h i p from dynamic c o n t r a c t i o n s ,
A ) P r o c e d u r e s - Experimenk 1
Subjects attended e x p e r i m e n t a l s e s s i o n s a t t h e i r
conven ience , 811 s u b j e c t s a t t e n d e d t h r e e such s e s s i o n s e a c h
session being s e p a r a t e d from the others B y no less t h a n one
week, These s e s s i o n s w i l l be t e r m e d u o r k - s e s s i o n 1, 2 and 3-
The purposes of this s e s s i o n were t o locate accurately the
subject within the a p p a r a t u s , t o determine t h e m a e n t sf
i n e r t i a o f t h e forearm and t o fami l iar i ze t h e subject w i t h t h e
e x p a r i ~ e n t a l procedu~es o f t h e study-
T h e first s t e p was t o a t t a c h t h e cast t o t h e forear% A
l i g h t uadeswrap was used to ease t h e c o a t a c t bstween f i b r e g l a s s
and skin when t h e cast was at tached t o t h e f o r e a m , The w r a p
was t i g h t l y compressed and c o n t r i b u t e d a n e g l i g a b l e a m u n t t o
t h e c o m p l i a n c c 2 of the f o r e a r m . T h e cas t w a s p l a c e d o n + E e
f o r e a r m , s d j u s t e d t o its most c o m f o r t a b l e p o s i t i o n a n d s eca ro ly
w r a p p e d w i t h t a p e in order t o p r e v e n t wrist f l e x i o n w i t h o u t
res t r ic t i nq bloc4 flow,
T h e s u b j e c t was t h e n p l a c e d i n t h e c x p e r i m e n t a f p o s j +.;on
and t h e a p p a r a t u s a d j u s t e d t o ~ a k e t h e a x i s nf t h e qik~%-inin+
c o i n c i d e n t a l with t h e a x l e a n d + o position t h e uppnr a r m
h o r i z o n t a l l y , A s a f e t y s t r a p f r o 3 a n a i ~ t o m r t b i l n was p l aczd
a r o u n d t h e c h e s t a n d another a r o u n d t h e +kiqhs t o e l i m i n a * ~
gross c h a n g e s i n the e x ~ e r i m e n t a l p o s i t i o n , T o c h e c k tht?
l o c a t i o n o f t h o e l b c w - j o i n t a p e n c i l was a t t a c h e d t o t h e cay+
a n d t h e s u h j e c t was i n s t r u c t e d t o f l e x the e l b c u - j o i n t s? t h ? *
a n a r c was d r a w n o n p a p e r p l a c e d v e r A i c a l l y i n t h e f r o n t a l
plane of t h ~ sukiect,
T h i s procedure was r e p e a t e d s e v e r a l t imes a n d t h e
p e s p e n d i c u l a r t i sec tors n f two c h o r d s d r a w n o n these arcs
intersected at the l o c a t i c n of t h e a x i s of r o t a t i o n o f t h e
efkoa-jaint, Any n e c e s s a r y a d j u s t a e n t was made t o t h e e l 5 n w
a n d c h e s t s u p p n r t s t o a l j g n t h e a x i s c-E r o t a t i o n of t h e elbow
with t h a a x l e , The i n d i v i d u a l p ~ s i t i o n cf s u p p c r t s f o r t h ~
chest a n d e l b o w were n o t e d so t h a t t h e y could b e replicated i n
a l l f u r t h e r experiments.
With + h e s u b j e c t f i x e d i n t h e a n g a r a t u s t h e n e x t s t e p ~ 3 5
to d e t e r m i n e t h e moment cf i n e r t i a o f t h e l i ~ h . T h e mi?thod
d e s c r i b e d in C h a p , IV, a (iif was u s e d , Yhen t h i s was
complete t h e s u b j e c t p r a c t i c e d some t r i a l c c n t r a c t i 3 n s w i t h
c a r e f u l o b s s r v a t i o n by t h e i n v e s t i q a t o r a n d s u k s e q u e n t
5 0
s u g g e s t i o n s f o r i m p r o v e ~ e n t s h o a l d t h e y b e required , T h e
s u b j e c t gas n o t i n f o r m e d about t h e a im of t h e stud?, However,
t h e i ~ p o r t a n c e oE ~ a x i m a l a c t i v a t i o n was s t r e s s e d ,
ii) VJork-Session 2
3n t h i s s e s s i o n d a t a needed t o derive the t o rque -anyu lax
v e l o c i t y r e l a t i o n s h i F %as c o l l e c t e d , Upon arr i oaf t h e subject
was p l a c e d i n the a p p a r a t u s a c c o r d i g g t o p r e v i o u s m e a s u r e a e n t s
taken d u ~ i n g ~ i o r k - s e s s i o n 7, O n a l l o c c a s i o n s t h e s u b j e c t was
i n s t r u c t e d to p r o d u c e maxi~al voluntary c o n t r a c t i o n s a b o u t t h e
e lbow j o i n t as r a p i d l y a s p o s s i b l e , The v e r b a l s t i m u l u s fro&
the i s r r e s t i g a t o f was t h e comaand * p u l l @ ,
F i v e s t a r t i n g posit i o n s were c h o s e n f o r t h e d e v e f a p r w n t of
the torque-angular veic;ci i;g c u r v e , These H e r e 0-5, 0-8, 1-0, 5 - 5 ,
and 2-0 r a d i a n s where 0-0 r a d i a n s r e g r e s e n q e d f u l l ex teas ion o f
t h e elbow, The beam was set a t t h e r e q u i r e d p o s i t i o n by a
- chain a t t a c h e d a t t h e o t h e r ernd o f the a x l e , A t each p o s i t i o n
t h e s u b j e c t aade e i g h t s e p a r a t e p u f l s , The first, t h i r d , f i f t h
an8 s e v e n t h pulls were c o a p l e t e k y i s s~e t r i c , T h e r e was no added
c o ~ p l i a n c e and the i n v e s t i g a t o r e n s u r e d t h a t t h e r e s i s t i n g
c h a i n had no s l a c k , The second , f o u r t h , s i x t h and e i g h t h p u l l s
were not c o a p l e t e f y isoaetric i n t h a t t h e y were made a g a i a s t
t h e spring, wkich was naw p a r t of the sys t em- The spsing
uncoi led b y aa a ~ o u n t r e f a t e d to t h e t e n s i o n e x e r t e d and t h e
co iap f i ance of t h e s p r i n g ,
The d a t a were c o l l e c t e d on a n FR t a p e - r e c o r d e r , The s u b j e c t
raz a l P c ~ s d tit rc ta te his a r a f r z b i y tetueen each conttackioit
t o e a s e a n y stress l n d ~ c e d by t h e c o n t r a c t i o n , E a c h p u l l l a s t e d
no n o r e than 1 - 5 s e c o n d s ,
Upon c o m p l e t i o n of a l l t h e p u l l s t h e c a l i b r a t i o n f o r t h e
effect of g r a v i t y {Chap, IV, a (iii)) was c o l t l p l e t e d , The s u b j e c t
was removed fro^ t h e appara tus and t h e calibration
[Chap, IV, a l i ) ) o f t h e t r a n s d u c e r s was c o ~ ~ l e t e d -
iii) W o r k - S e s s i o n 3
T h i s s e s s i o n was a r e p e a t of w o r k - s e s s i o n 2 and served to
p r o v i d e a c h e c k on the repeatability of t h e p r e v i o u s l y
c o l l ec tea data , T h e i n t e r s e s s i o n a l t i m e - i n t e r v a l was no l e s s
t h a n o n e w e e k ,
After a l l t h e d a t a f r o m e a c h v o r k - s e s s i o n bad been
collected on a t a p e - r e c o r d e r it was t r a n s f e r r e d to a c o n p u t e r
DECTBPE i n p r e p d r a t i o n f o r a n a l y s i s , A n a l y s i s of t h e o r i g i n a l
d a t a s h o w e d t h a t i t d i d n o t e x h i b i t the e x p e c t e d form* T h e
rise of t o r q n e d u r i a g a c o ~ p i i a a t p u l l was f a s t e r t h a n i n a
n o n - c o n p l i a n t p u l l , As t h e c o n v e r s e o f t h i s observation was a
necessary c o n d i t i o n of t h e a n a l y s i s a n u s i d e n t i e i e d phenomenon
was judged to h a v e been c c n t r i b u t i n g t o t h e d i f f e r e n c e between
rise-time of t h e c o m p l i a n t a n d n o n - c o m p l i a n t p u l l s ,
C o n s e q u e n t l y , a new a p p r o a c h t o t h e d e d u c t i o n of t h e
t o r q u e - a n g u l a r v e l o c i t y c a r v e was r e q u i r e d ,
w i l k i e 11950) was a b l e t o e l i c i t a r e s p o n s e front i n t d c t
human m u s c l e s s i a i i l a r t c t h a t r e p o r t e d by M a c P h e r s o n (1953),
wilkie's siltjtxt~ & e r e p r e s e n t e d u i t h Bare coa t r ac t io t t s t o
c o m p l e t e t h a n i n the p r e s e n t study. T h e r e f o r e t h e u n u s u a l
s e s u l t s o b t a i n e d here may h a v e b e e n d u e t o a lack of p r a c t i c e
o r s k i f f i n r e c r u i t i n g ~ u s c u l a r a c t i v i t y a s r a p i d l y a s p o s s i b l e
on a l l o c c a s i o n s , I t was ' t h o u g h t t h a t p e r h a p s a p e r i o d of
t r a i n i n g n a s r e q u i r e d , C o n s e q u e n t l y t w o s u b j e c t s were c h o s e n
a n d p e r f o r m e d a series of e x p e r i m e n t a l s e s s i o n s f r o m which
t h e i r d a t a was a n a l y s e d p r o g r e s s i v e l y , T h e r e was no t r e n d i n
t h e d a t a t h a t i n d i c a t e d a n e f f e c t w h i c h could b e a s s o c i a t e d
w i t h p r a c t i s e , The subjects d i d make s o B e coraments on how t h e y
f e l t d u r i n g e a c h t y p e of c o n t r a c t i o n , Both s a i d t h a t t h e y felt
more s a t i s f i e d w i t h t h e c o m p l i a n t p u l l t h a n w i t h t h e
n o n - c o m p l i a n t p u l l and a t t s i b u t e d t h i s f e e l i n g t o t h e f a c t that
t h e y had a c c o a p l i s h e d s o m e t h i n g hy m a k i n g t h e h e a ~ move a
c o n s i d e r a b l e amoun t . In the case of t h e n o n - c o m p l i a n t p u l l t h e
e x t e n t of movement was s o smal l t h a t t he re was l i t t l e f e e d b s c k
t o t h e s u b j e c t i n terms cf how t h a t p e r s o n had done,
On t h e b a s i s of these c o m m e n t s i t s e e m e d t h a t t h e r e was
p e r h a p s some form of p h y s i o l o g i c a l f e e d b a c k t h a t a f f e c t e d t h e
p e r f o r m a n c e sf the s u b j e c t s , W i t h t h i s i n mind i t s e e m e d
r e a s o n a b l e t o t r y a s e s s i o n d u r i n g w h i c h t h e subjects u o u l d n o t
b e informed of t h e n a t u r e of t h e c o n t r a c t i o n t h a t would be
r e q u i r e d , T h e m o t i o n s t h e i n v e s t i g a t o r w e n t through d u r i n g a
r e c o r d i n g s e s s i o n were s t a n d a r d i z e d so a s n o t t o p r o v i d e a n y
h i n t s , T h e o n l y coiiiment d u r i n g t h i s s e s s i o n was the command t o
p u l l , .
Zn s p i t e 02 tts a t t e a p t s to aask t h e a p p d r a t u s t h e data
were a t v a r i a n c e w i t h the i n t e n t i o n of t h e s t u d y , I t was
decided a t t h i s s t a g e t o a b a n d o n t h i s a p p r o a c h a n d c o n c e n t r a t e
o n t h e s e c o n d p a r t of t h e s t u d y ,
It should be n o t e d t h a t t h e r e s p o n s e of t h e a p p a r a t u s was
c h e c k e d t o e n s u r e t h a t the problem was n o t a f u n c t i o n of s h e
a p p a r a t u s , Po do t h i s t h e i n v e s t i g a t o r a t t a c h e d a w e i g h t [32 ,15
Kg) b y a r o p e t o the lever i n t h e h o r i z o n t a f p o s i t i o n ,
Initially t h e i n v e s i g a t o ~ s u p p o r t e d t h e weight so the r o p e was
s l a c k b u t released the weight a p p l y i b g a s u d d e n i n p u t t o the
l e v e r , This p r o c e d u r e was compf e t e d under bokb experiments l
c o n d i t i o u s , T h e r i se 02 t o r q u e i n t h e c o n t r a c t i o n w i t h t h e
added compliance was s l o w e r than w i t h o u t t h e a d d e d c o m p l i a n c e ,
T h e a p p a r a t u s gas n o t the s o u r c e of %he v a r i a t i o n i n t h e d a t a
w i t h t h a t r e p o r t e d e l s e w h e r e ,
B) Procedures-Experiment 2
A s b e f o r e t h i s q r o u p came a t t h e i r c o n v e n i e n c e and since
t h e d y n a m i c c o n t r a c t i o n s were n o t a s d e m a n d i n g a s i s o m e t r i c
cane a s f r e g u e n t l y a s orice a day , One s u b j e r k canie o n l y s i x
t i ~ e s b u t the o t h e r s u b j e c t was a b l e to a t t e n d s e v e n s e s s i o n s ,
A s e s s i o n s i m i l a r t o w o r k - s e s s i o n 1 i n e x p e r i ~ e n t 1 was
c o m p l e t e d b e f o r e %he a c t u a l da t a c o l l e c t i o n began , The s u b j e c t
was c a r e f u l l y fitted intc the a p p a r a t u s a n d t h e a o ~ e n t of
i n e r t i a of t h e liab w a s d e t e r m i n e d ,
. . TCe method o f d c t c r m l n n g t h e t o r q u e - a u y u 2 a r v e l o c i % j
c u r v e froin dyuainic c o n t r a c t i o n s r e q u i r e d t h e s u b j e c t to
c o n t r a c t a g a i n s t a variety of o p p o s i n g l o a d s , The opposing
l o a d s were a series of w e i g h t s t h a t c o u l d b e fixed t o any o n e
of t h r e e p o s i t i o a s o n the h a r d a t t h e e n d of the a p p a r a t u s
o p p o s i t e t h e s u b j e c t , The b a r d was f i x e d off centre t o t h e
a x l e , Two of t h e holes i n t h e b o a r d were o n one side o f t h e
1
axle a n d one o n t h e o t h e r side, Using d i f f e r e n t weights a n d
h o l e position p r o d u c e d a range of torques t h a t the s u b j e c t had
t o overcome, To e n a b l e a c h i e v e m e n t of h i g h v e l o c i t i e s o f
~ o v e m e n t t h e t h e i n v e s t i g a t o r a i d e d iaoveaent b y r a p i d l y
r o t a t i n g t h e the board i n the d i r e c t i o n o f f l e x i o n ,
It was d e c i d e d t o deter~ine torque-any u l a r v e _ l o c i t y c u r v e s
for f i v e e l b o w positions, 0-5, 0-8, 3-0, 1-5, and 2-0 r a d i a n s ,
where 0,0 r a d i a n s r e p r e s e n t s full e x t e n s i o n of t h e e l b o w - j o i n t ,
T o c o m p l e t e t h e torque-aagular v e l o c i t y c u r v e s it was n e c e s s a r y
t o r e c o r d t h e i s o m e t r i c t o r q u e s f o r each of t h e s e p o s i t i o n s . A
t o r q u e - a n g l e c u r v e was d e v e l o p e d by r e q u e s t i n g the s u b j e c t to
c o n t r a c t i s o m e t r i c a l l y f o u r times d u r i n g each e x p e r i ~ e n t a l
s e s s i o n . T o maintain t h e p o s i t i o n o f the beam d u r i n g an
isometric c o n t r a c t i o n a c h a i n was used to f i x the board to t h e
f loor , The i n v e s t i g a t o r ensured t h a t t h e r e was n o slack i n % h e
c h a i n d u r i n g t h e c o n t r a c t i o n ,
The e x p e r i a e n t a l situations were the same f o r t h e k i r s t
f o u r s e s s i o n s for subject o n e ana first t h r e e for s u b j e c t t u o -
Upon a r r i v a l the s u b j e c t was fixed within the a p p a r a t u s i n
a c c o r d a n c e with the m e a s u r e s n o t e d d u r i n g t h e trial sess ion-
D u r i n g thcsc a x p z r i i f i e r t a l s s s s i o n s t i id first a n d l a s t two
c o n t r a c t i o n s were i s o m e t r i c w h i l e the r e ~ a i n i n g e i g h t e e n were
dynamic, B d y n a m i c c o n t r a c t i o n r e q u i r e d t h a t the i n v e s t i g a t o r
f u l l y e x t e n d t h e r e l a x e d r i g h t arm cf the subject, A t the
command *PULLq the s u b j e c t m a x i m a l l y a c t i v a t e d the flexors of
t h e elbow and f l e x e d h i s a m a s q u i c k l y a s p o s s i b l e , T h e
f l e x i c a was arres ted b y a mechan i sm of rope t h a t p r e v m t e a t h e
s u b j e c t h i t t i n g h i m s e l f , F o r each w e i g h t and h o l e p o s i t i o n two
p u f ls were c o n p i e l e d , T h e e t h e r f o u r p u l l s were c o m p l e t e d , two
of u h i c h were d o n e when t h e r e %as no l o a d o n t h e b o a r d a n d t h e
o t h e r two were d o n e w h i l e t h e i n v e s t i g a t o r assisted t h e
r o t a t i o n , T h e latter f o u r p r o v i d e & t o r q u e s t h a t sere low with
h i g h v e l o c i t i e s ,
I n t h e r e m a i n i n g t h r e e s e s s i o n s t h e c o n t r a c t i o n s were
isometric only, T h i s data was used i n the d e t e r a i n a t i o n of the
c o m p l i a n c e of t h e S E C d u r i n g a n i s o n e t f i c c o n t r a c t i o n and i n
.the c a l c u l a t i o n of the, time-constant of t h e rise i n t o r q u e . I n
the f i r s t t v o of t h e s e s e s s i o n s t h e s u b j e c t p u l l e d o n c e a t each
of t h e f i v e elbow p o s i t i c n s d e s c r i b e d a b o v e , A t h i r d s e s s i o n
was completed d u r i n g which t h e s u b j e c t s c o m p l e t e d t h r e e p u l l s
a t e a c h of t h e s e elbow p o s i t i o n s ,
The data to be used in t h e d e t e r m i n a t i o n of t h e
t o r q u e - a n g u l a r v e l o c i t y c u r v e were c o l l e c t e d o n t h e Ff!i
t a p e - r e c o r d e r , The data t o b e u s e d f o r t h e c a l c u l a t i o n of the
c o n p l i a n c e of the S E C a n d the t i ~ e - c o n s t a n t of t h e rise i n
t o r q u e d u r i n g a n isometric c o n t r a c t i o n were c o l l e c t e d o n t o t h e
r e c o r d i n g o s c i l l o y r a p h ,
The prigaary aim of t h i s s t u d y was t o derive a
torque-angular v e l o c i t y r e l a t i o n s h i p for huaan ~ u s c u f a r
c o n t r a c t i o n , Two different etethods have been developed t o
a c h i e v e t h i s aim, S i n c e j o i n t - a n g l e ref Zeets auscfe-length
then t h e i n t e r r e l a t i o n s h i p of three variabf es cou ld be s t u d i e d ,
During t h e e x p e r i ~ o n t al process e a l i b r a t i o e ua s perf orated t o
f a c i l i t a t e q u a n t i f i c a t i o n of the ref a t i o n s h i p s i n a b s o l u t e
uni is,
a) C a l i b m t i o n dur ing t h e e x p e r i ~ e n t s
i) C a l i b r a t i o a c o n s t a n t s
410 determine a b s o l u t e u n i t s f o r the d a t a i t was n e c e s s a r y
to use a ca l ibrat ioa procedure t h a t vould canver t the o u t p u t
v o l t a g e from t h e transducers to a b s o l u t e u n i t s . The procedure
was as foliaws (see DBCAL-SV in Appendix 2). The lever was
placed in five different positions, In the f i r s t p o s i t i o n t h e
lever was placed v e r t i c a l and i n the other p o s i t i o n s t h e l e v e r
was p l a c e d h o r i z o n t a l a l t e r n a t i n g from side t o s i d e of t h e
sertical , These p o s i t i o r n s were nuxibered s e q u e n t i a i l y froia o n e
to five,
I n p o s i t i o n one the lever was v e r t i c a l a n d there was no
torque r e c o r d e d by the s t r a i n gauges, T h e o u t p u t fro& t h i s
position was oiased to 50% oaf f u l l scale to facilitate
r e c ~ r d i n ? b i p k a s i c s i g r t a l s , T o cafcuLate the torque f a c t o r a
known torque was a p p l i e d i n p o s i t i o n s f o u r a n d f i v e , T h e t o r q u e
* s e e n g by t h e t r a n s d u c e r when t h e fever was h o r i z o n t a l % i t h no
l o a d , p o s i t i o n s 2 a n d 3 , was t h a t t o r q u e a t t r i b u t a b l e t o t h e
e f f e c t of g r a v i t y o n t h e l e v e r , T h e d i f f e r e n c e i n o u t p u t
b e t w e e n p o s i t i o n f o u r and two a n d p o s i t i o n f i v e and t h r e e uas
t h e c o n s e q u e n c e of t h e known a p p l i e d t o r q u e s , C a l c u l a t i o n of
two t o r q u e f a c t o r s served t o c h e c k t h e l i n e a r i t y of t h e
r e s p o n s e of t h e t r a n s d u c e r i n t h e e a r l y s t a g e s of t h e
e x p e r i m e n t ,
O n c e t h e i n v e s i g a t o r %as s a t i s f i e d w i t h t h e r e s p o n s e
c h a r a c t e r i s t i c s o f t h e t o r q u e t r a n s d u c e r t h e b i a s l e v e l was
s h i f t e d t o a v a l u e slightly h i g h e r t h a n z e r o v o l t s , This shift,
c o n c o m i t a n t w i t h a n i n c r e a s e i n t h e g a i n of t h e t h e a m p l i f i e r ,
p e r m i t t e d a n i n c r e a s e i n the r e s o l u t i o n of the d a t a c o l l e c t e d
from t h i s t r a n s d u c e r ,
T o c a l c u l a t e t h e accelerometer factors ( i n r a d i a n s p e r
sec, p e r sec,) t h e d i f f e r e n c e s i n o u t p u t b e t u e e n p o s i t i o n two
a n d o n e a n d p o s i t i o n three a n d one were d e t e r m i n e d , The
a c c e l e r o m e t e r r e c o r d e d zero a c c e l e r a t i o n when t h e lever was
vertical, A t e ach of t h e h c r i z o n t a l p o s i t i o n s the a c c e l e r o m e t e r
recorded o n e g or 9 - 8 1 m Jsec/sec of t a n g e n t i a l a c c e l e r a t i o n ,
T h e r e l a t i o r i s h i p b e t w e e n t a n g e n t i a l a c c e l e r a t i o n " F A a a n d
a n g u l a r a c c e l e r a t i o n & A A * is;
TB = AA * B 2
Mhere * K g was t h e d i s t a n c e k e t w e e n t h e a x i s o f r o t a t i o n
a n d t h e acceierorrletrtr, T h i s e q u a t i o n was s o l v e d for t h e a n g u l a r
accel~zation ~ A i c h %as t Z e n G i v l d e d by t b ~ o u t p u t f r o a
p o s i t i o n s 1 and 2, A s e c o n d accelercmeter f a c t o r was d e t e r n i n e d
u s i n g t h e o u t p u t from p o s i t i o n s o n e a n d three, T h e e f fec t of
g r a v i t y on the accelerometer was a s s e s s e d b y c a l c u l a t i n g the
d i g f e r e n c e b e t w e e n t h e o u t p u t f r o @ p o s i t i o n t w c a n d t h r e e a n d
d i v i d i n g by 2 ,
T h e d i s p l a c e n e n t or p o s i t i o n of t h e l e v e r was c o n s i d e r e d
i n r a d i a n s , F u l l e x t e n s i o n of t h e e l b o w was considered t o
o c c u r a t 0 - 0 r a d i a n s , T h e r e l a t i o n s h i p b e t w e e n r a d i a n s an3
d e g r e e s was d e s c r i b e d a s 1.90 d e g r e e s b e i n g e q u i v a l e n t t o 3,1&15
r a d i a n s , F r o m t h i s r e l a t i o n s h i p t h e r a d i a n factor was
d e t e r m i n e d , The d i f f e r e n c e i n t h e o u t p u t frcm g o s i t i o n s tuo and
t h r e e (lever h o r i z o n t a l on o p p o s i t e s i d e s of t h e v e r t i c a l ) was
e q u i v a l e n t t o a d i s p l a c e m e n t of 3 , 3 4 1 6 r a d i a n s or 180 d e g r e e s ,
T h e r a d i a n factor [ r a d i a a s / u n i t ) was d e t e r m i n e 4 by d i v i d i n g
3,1416 r a d i a n s b y t h e d i f f e r e n c e s i n t h e o u t p u t f r o m the lever
when h o r i z o n t a l oa o p p o s i t e s i d e s ,
T o m a i n t a i n a safety m a r g i n i n case of drift u i t h i n t h e
a m p l i f i e r s a small v o l t a g e above zero was i n c l u d e d i n t h e
determination of the r a d i a n f a c t o r , To a a j u s t t h e l e v e l s t o
a b s o l u t e zero a r a d i a n r e m a i n d e r ( u n i t s ) was d e t e r m i n e d b y
c a L c u P a t i n y t h e d i f f e r e n c e s between t h e o u t p u t when the l e v e r
was h o r i z o n t a l f o r f u l l e x t e n s i o n and real zero v o l t s - T h i s
r a d i a n r e m a i n d e r was subtracted fro@ t h e c a l c u l a t e d p o s i t i o n s -
t o a s s u r e t h e calculation of a n g l e i n a b s o l u t e u n i t s -
59
iif D e t e r a i o a t i o n of thc moment of i n e r t i a of t h e Emeara
The s t r a i n g a u g e s were f i x e d to t h e l e v e r b e t w e e n t h e a x l e
and t h e slot w h e r e t h e cas t was a t t a c h e d , A c o n s e q u e n c e of t h i s
a r r a n g e m e n t vas t h a t t h e t o r q u e r e c o r d e d by t h e s t r a i n g a u g e s
only r e p r o d u c e d the t o r q u e d e v e l o p e d b y t h e ~ u s c l e when t h e
mass l y i n g b e t w e e n t h e elbow-joint a n d s t r a i n g a u g e s was not
a c c e l e r a t i n g , Under c o n d i t i c n s o f a c c e l e r a t i o n of t h i s mass t h e
torque r e c o r d e d v a s less t h a n t h e t o r q u e d e v e l o p e d by a n a m o u n t
e q u a l t o t h e t o r q u e r e q u i r e d t o a c c e l e s a t e t h e m a s s , T h e t o r q u e
r e c o r d ~ d was t h a t t o r q u e a v a i l a b l e t o b e n d t h e f e v e r and t h e
added c o a t p l i a n c e ,
If a n i a p u l s e was a p p l i e d t o t h e a x l e s f r a ~ t h e o p p o s i t e
e n d of the apparatus then the torque recorded is that torzue
u h i c h a c c e l e r a t e s t h e t h e B a s s d i s t a l t o t h e s t r a i n g a u g e s ,
C o n s e q u e n t l y , t h i s t o r q u e c a n be used t o d e t e r m i n e the i n s r t i a
of t h e f o r e a r m dnd casts, This r e c o r d e d t o r q u e is e q u a l t o t h e
a c c e l e r a t i o n of t h e i n e r t i a of the forearm a n d cast m u l t i p l i e d
b y t h e i n e r t i a ,
T h e t e c h n i q u e d e v e l c p e d r e q u i r e d t h e i n v e s t i g a t o r ta a p p l y
a r a p i d p o s i t i v e a n d n e g a t i v e torque t o t h e subject*^ forearm
v i a the a x l e s l i n k i n g e a c h e n d o f t h e a p p a r a t u s w h i l e the
subject uas at rest, T h e a p p l i e d i ~ p u f s e was of s h o r t d u r a t i o n
i n o r d e r t o exclude i n v o l u n t a r y a c t i v i t y b y the s u b j e c t and o f
small d i s p l a c e m e n t t o e x c l u d e t h e e f f e c t s of g r a v i t y , T h e
a c c u r a c y of this t e c h n i q u e was d e t e r a i n e d b y fixing known
i n e ~ t i a s t o t h e beam a n d p e r f o r m i n g t h e e x p e r i m e n t . T h e r e was
l i t t l c 5 i f Z e r c n c e b e t w e e n thc c a m p u t c d vafues dfiJ t h e k n o ~ n
v a l u e s of i n e r t i a ,
four t r i a l s were u s e d and the mean o f v a l u e of these f o u r
es t imat ions was c h o s e n a s t h e f i n a l v a l u e . Tis data a n d the
c a l i b r a t i o n d a t a vas a c q u i r e d d i r e c t l y by t h e c o m p u t e r - A
p r o g r a m [see 3EWflfS,SV i n Appendix 2) d e t e r l a i n e d the a b s o l u t e
v a f u e s o f t o r q u e and a c c e l e r a t i o n frcm w h i c h the value of
i n e r t i a %as d e t e r m i n e d , T h e final v a l u e s were typed oa p a p e r
a n d t h e Bean v a l u e c a l c u l a t e d ,
iii) E s t i m a t i c - n of t h e g r a v i t a t i o n a l effects on t h e l e v e r w i t h the subjects arm a n d c a s t a t t a c h e d
The efteet of gravity on t h e lever was seen t o modify t h e
o u t p u t of t h e t r a n s d u c e s s with r e s p e c t to a n g u l a r : p o s i t i o r t , Kt
was necessary t o r e m o v e t h i s effect when d e t e r m i n i n g t h e
a b s o l u t e v a l u e s of t o r g u e , For t h i s reason, hhe o u t p u t o f t h e
t o r q u e t r a n s d u c e ~ was m e a s u r e d for eighteen different a n g u l a r
positions with t h e subject i n the e x p e r i m e n t a l p o s i t i o n , B
program (see GBAV.SV i n a p p e n d i x 2 ) p r i n t e d out the a s s o c i a t e d
p o s i t i o n s and t o r q u e s a n d t h e n s u b ~ i t t e d the e i g h t e e a p a i r s t o
a p o l y n o m i a l c u r v e - • ’ it t i n g prograa {see CURFIT, S V i n a p p e n d i x
2) whica predicted t o r q u e a t a n y g i v e n axlgle by a p o l y n o m i a l
e q u a t i o n , This e q u a t i o n c o u l d t h e n b e subtrac ted f rom t h e
o b t a i n e d v a l u e s o f torque t o reiuove the e f f e c t due t o g r a v i t y ,
bj E x p c r i n c c t 1 - D e t c m i n a t i c n of t h e t o c y u e - a n g u l a r v e l o c i t y r e l a t i o n s h i p f r o m two isometric c o n t r a c t i o n s
I t iacPherson (9953) d e v i s e d a t e c h n i q u e w h i c h a l l o w e d the
d e r i v a t i o n of the f o r c e - v e l o c i t y r e l a t i o n s h i p of t h e CC
u n a f f e c t e d b y t h e SEC, T h e m e t h o d e s s e n t i a l l y c o m p r i s e d t h e
mnscfe c o n t r a c t i n g i s o ~ e t r i c a l P y a t o n e time and t h e n
c o n t r a c t i n g a g a i n v i t h a c o m p l i a n t c o n n e c t i o n b~tweea t h e
~ u s c f e a n d the r e c o r d i n g t r a n s d u c e r s , By examining t h e
d i f f e r e n c e s b e t u e e n t h e f o r c e - t i m e curves i n t h e two c o n d i t i o n s
h e was a b l e t o derive t h e f o r c e - v e l o c i t y r e f a t h o a s h i p - T h i s
method is o u t l i n e d b e l o w a s %elf a s t h e m o d i f i c a t i o n s necessary
f o r a s i t u a t i o n w i t h i n t a c t human m u s c l e ,
I n d e v e l o p i n g t h i s method of a n a l y s i s Mac Pherson assu@ed
t h a t the force d e v e l o p e d b y t h e CC v a r i e d o n l y wi th the
v e l o c i t y of s h o r t e n i n g . G i v e n two c o n d i t i o n s of f o r c e v h i c h
rose t o t h e same i s o a e t r i c l e v e l v i t h l i t t l e or no c h a n g e i n
l e n g t h , a n y p o i n t o f f o r c e o n these c u r v e s i n d i c a t e d e q u a l
v e l o c i t i e s of s h o r t e n i a q of the cC, T o create tuo d i f f e r e n t
c o n d i t i o n s E a c P h e r s o n i n s e r t e d a c o i n p l i a n c e betueen t h e n u s c f e
and t h e r e c o r d i n g transducers, This c o m p l i a n t c o n n e c t i o n c o u l d
b e e i t h e r i s o l a t e d f r o m the e x p e r i m e n t , a l l o w i n g for a n
i s o m e t r i c c o n t r a c t i o n , or i n c l u d e d , which p r o d u c e d a slower
r a t e of r ise of f o r c e , From the t w o d i f f e r e n t r a tes of r ise of
F f G U B E 10 : T h i s is a drawing oE the system d e s c r i b e d b y E a c P h e r s o n ,
a) this describes t h e s i t u a t i o n without t h e a d d e d c o m p l i a n c e ,
b) this r e s p r e s e r i t s t h e situation with t h e added as a paht of t h e t o t a l system
P = t h e force d e v e l o p e d by t h e CC F = t h e force r f c o r d a d b y the transducers x = t h e l e n g t h e n i n g of the SEC y = the l e n g t h e n i n g of t h e a d d e d
c o m p l i a n c e
SEC \. \
CC P
\ \ SEC added compliance
CC
.
force h e C C ~ S S q u s 1 v a l u e s of force a n d , therefore, e q u a l
c a l c u l a t e d v e t o c i ties, Figure 10a illustrates t h e experimental
conditions and the f aliouiny is t h e mathematiczil manipulation
r e q u i r e d to achieve t h e d r i n a l results- When the contraction is
total1 y isometric,
and
where (iitr/d%) o is t h e v e l o c i t y of t h e CC, The s u b s c r i p t l o i
d e n o k e s the coolidition without: t h e addzd compliance, Figut's 10b
shows t h e s i t u a t i o n w i th t h e added c o m p l i a n c e , Now,
This reduces to
Now v e l o c i t y of t h e CC is f d [ x + y ) / d t ) c w h e f e t h e subscript 'ci
denotes the condition with t h e a d d e d compliance, S i n c e , a t a n y
i n s t a a t velocity depends upcn force then for a n y equal
values o f P the velocities could he equated, Thus, equating
e q u a t i o n s 4 a n d 6 ;
T h e v a l u e of dx/dP is t h e c o m p l i a n c e of t h e SEC and can b e
s u b s t i t u t e d i n t o e q u a t i o n 4 which is s o l v e d for the v e l o c i t y
of s h o r t e n i n g 0% t h e CC,
ii) f l a d i f i c a t i o n s tc f i t r o t a t i o n a l system
T h i s above a n a l y s i s u a s d e v e l o p e d f cr l i n e a r s y s t e m s a n d
befare i t was u s e d cat r c t a t i o n a l s y s t e m s (human movement) some
m o d i f i c a t i o n s were a a d e , Tbs m e a s u r e m e n t s were made i n a n ~ u l a r
terms, such a s moment of i n e r t i a , angular v e l o c i t y etc-
S e c o n d l y , i t was not p o s s i b l e t o c o u p l e a n a d d e d compliance
d i r e c t l y t o t h e S E C o f i n t a c t human m u s c l e s , T h e r e was a n
inertia between the SEC and t h e added c o m p l i a n c e , n a m e l y t h e
arm, casts and beaai, D u r i n g c o n t r a c t i o n w i t h t h e added
c o m p f i a n c e t h i s i n e r t i a gas accelerated and, h e n c e , t h e t o rque
r e c o r d e d was less t h a n t h e t o r q u e d e v e l o p e d by a n a m o u n t equal
t o t h a t required t o accelerate the arm, casts and beam* If P
was t h e t o r q u e d e v e l o p e d by t h e CC a n d T was t h e to rque
recorded t h e n ;
P = T + f 6
where 10 was t h e t o r q u e r e q u i r e d t o accelerate t h e i n e r t i a -
T h i s m a n i p u l a t i o n v a s c o m p l e t e d p r i o r t o t h e a p p l i c a t i o n of
M a c P h e r s o n s s analysis, O n c e T was corrected v e r y l i t t l e
FEGUXE 11 : This is a drawing of the s y s t e m d e s c r i b e d i n f i g u r e 10 a s modified to suit the needs of the p r e s e n t s t u d y ,
a) t h i s d e s c r i b e s t h e situation without the a a d e d c o m p l i a n c e ,
b ) this r e s p r e s e n t s t h e s i t u a t i o n w i t h the added a s a p a r t of the total s y s t e m
P = t h e t o r q u e deve loped by the CC T = the t o r q u e r e c o r d e d by t h e t r a n s d u c e r
i3, = t h e a n g u l a r d i s p l a c e m e n t of t h e SEC 8, = t h e a n g u l a r d i s p l a c e m e n t of t h e
added ccmpl iance T = the inertia of the forearm, cas t
a n d outer p o r t i o n of t h e l e v e r
Ln added ,.'f?fl compliance
f ollowirlq presen t s t h e modified analysis (see figure 11).
a n d
W i t h t h e a d d e d c o ~ p l i a a c e
and
E q u a t i o n o f t h e a n g u l a r velocities and r e d u c t i o n g i v e s ;
The value f o r the corngfiance of t h e SEC, de , / d ~ , was
substituted i n t o e q u a t i o n f l which was solved f o r t h e v e l o c i t y
of s h o r t e n i n g of t h e CC, This t e c h n i q u e a l l o w e d one t o arr ive
at a t o r q u e - a n g u l a r v e l o c i t y r e f a t i o a s h i p for the c o n t r a c t i l e
component a s well as c h e c k on c h a n g e s i n the c o m p l i a n c e of t h e
SEC, When the analysis was done a t a series of different muscle
lengths one was a b l e examine t h e effect of c h a n g e s i n l e n g t h on I
the torque-angular v e l o c i t y relationship for i n t a c t human auscfe.
iii) Data m a n i p u ~ a t i o a
When t h e o p e r a t o r was r e a d y t o b e g i n t h e f i n a l computation
t h e da ta set % a s t r a n s f e r r e d f r o m t h e DECTAPE t o core meaory,
The p s o g r a a u s e d t o w a n i p u l a t e t h e d a t a gas c a t a l o g u e d a s
D A V E P 2 , S B a n d a l i s t i n g a n d t y p i c a l p r i n t o u t is shown i n
Append ix 2,
The p r o g r a a i n i t i a l f l y r e q u i r e d t h e o p e r a t o f t o e n t e r t h e
c a l i b r a t i o n c o n s t a n t s , c o e f f i c i e n t s f o r t h e c o r r e c t i o n o f
t o r q u e d u e t o g r a v i t y a n d t h e momeat o f i n e r t i a o f t h e t o r e a r m
a n d cast, T h e s e v a l u e s were u s e d i n t h e c o m p u t a t i o n o f a b s o l u t e
u n i t s from arbitrary c o m p u t e r units, T o make u s e of t h e f u l l
c a p a b i l i t i e s of t h e c o m p u t e r t h e c a l c u l a t e d v a l u e s were scaled
b y t h e use of m u l t i p l i c a t i o a c o n s t a n t s , Uhen d a t a was d i g i t i z e d
t h e r a n g e i n v a l u e s was O t o 102Y u n i t s b u t t h e c o m p u t e r nas
t h e c a p a c i t y t o d e a l w i t h n u m b e r s r a n g i n g from 0 t o 4095 u n i t s -
I n t h e c a s e of d i s p l a c e m e n t , t h e l a r g e s t p o s s i b l e v a l u e gas
3,142 r a d i a n s , Hence, t h i s number was m u l t i p l i e d b y 1000 t o
i n c r e a s e t h e r e s o l u t i o n , When t h e r e s u l t s were p r i n t e d o u t t h e
a u l t i p l y e r becaw t h e d i v i s o r a n d 3 1 4 2 was r e t u r n e d t o 3.142.
Additive c o n s t a n t s were a l s o used t o a a k e a l l n u ~ b e r s p o s i t i v e .
Because o f t h e d i s c r e t e i n c r e m e n t s i n the a a t a r e s u l t i n g
from t h e d i g i t a l . c o n v e r s i o a a method o f d i g i t a l smoo th ing was
employed to smooth these i n c r e m e n t s , A utethod desc r ibe t l b y
L a n c z o s f1956) was errrpfoyed, T h i s method e n t a i l e d t h d a v e s - a g i n j
o f f i v e s u c c e s s i v e p o i n t s a n d d e p o s i t i n g t he in here the? t h i r d
p o i n t i n t h e a r r a y gas l o c a t e d , The n e x t series of p o i n t s t o b e
averaged F c c l u d e d t h i s t h i r d , now szoothed, po ic r , T h e p r o c e s s
of s m o o t h i n g included t h r e e p o i n t s t h a t had b e e n s m o o t h e d and
two, a s yet, u n p r o c e s s e d ~ c i n t s ,
Upon c o m p l e t i o n of these s t e p s a s u b r o u t i n e w i t h i n t h e
p r o g r a m displayed t h e da t a on a n o s c i l l o s c o p e i n t e r f a c e d w i t h
t h e c o m p u t e r , In t h i s f a s h i o n a v i s u a l check was r ~ a i n t a i n e d o n
t h e p r o y r a B a s i t p r o c e s s e d t h e d a t a , % h e n t h i s step was
c o m p l e t e t h e actual a n a l y s i s was begun, The p r o g r a i a d e t e r m i n e d
t h e n u m e f a t c t r f o r e q u a t i c n 14, This r e d u c e d t o t h e v e l o c i t y a t
t h e hand and its d e t e r m i n a t i o n was dons b y d i f f e r e n t i a t i n g t h e
a r r a y o f d i s p l a c e m e n t , T h i s s t e p was c o m p l e t e d a n d t h e array of
velocity was s t o r e d in t h e i o c a t i o n p r e v i o u s l y held by
a c c e l e r a t i o n , "fe a r r a y o f acce le ra t ion was n o t r e q u i r e d a f t e r
t h e a r ray of torque had been c o r r e c t e d f o r a c c e l e r a t i o n o f t h e
mass discussed a b o v e , T h e v e l o c i t y %as s c a l e d b u t n o t s m o o t h e d
a s one had no weans of a s s e s i n g what was s i g n a l a a d w h a t zaay
h a v e been aoise.
Xt s h o u l d be p o i n t e d o u t t h a t t h e r e were kwo m e t h o d s
egp loyed to calculate t h e v e l o c i t y o f wovement of t h e hand
d u r i n g t h e c o m p l i a n t p u l l . One me thod a s s u n e d t h a t t h e r e was no
wovement d u r i n g t h e isometric c o n t r a c t i o n a n d t h e r e f o r e a n y
a o v e m e n t i n t h e c o m p l i a n t cont rac t ion was a t t r i b u t e d t o t h e
spring, T h e o t h e r me thod was n o t to a s s u a e zero movment i n the
f i r s t p u k l a u d t o c a l c u l a t e t h e d i f f e r e n c e i n v e l o c i t i e s a s a
resul t of moyemect i n both p u l l s , In this f a s h i o n t h e v e l o c i t y
t h a t arose s t r i c t l y frcm t h e added c o m ~ l i a u c e was d e t e r m i n e d -
U s i n g two methods p r o v i d e d s o a e f u r t h e r i n f o r m a t i o n t h a t Bay
have b e e n u s e f u l ,
rrr l i n 2 n e x t step st;.qsir&d the i ie . t+ra inat ion 5LZ t h e
d e n o m i n a t o r i n e q u a t i o n 14, T h e d e n o m i n a t o r c o a s i s t e d o f two
c o m p o n e n t s , t h e a i f f e r e n t i a f s o f t h e rise i n t o r q u e from two
c o n t r a c t ions, The v a l u e s f o r t h e s e d i f ferent iaf s were
d e t e r m i u e d , t h e i r d i f f e r e n ~ e c a l c u l a t e d and d i v i d e d i n t o t h e
n u a e r a t o r , T h e v a l u e w a s d e p o s i t e d i n care f o r l a t e r
a c q u i s i t i o n , T h i s s t e p was c o m p l e t e d f o r t h e array o f t o r q u e
v a l u e s a l r e a d y p r o c e s s e d a n d s t o r e d i n core, f f the difference
b e t w e e n t h e d i f f e r e n t i a l s was zero o r n e g a t i v e e x e c u t i o n of t h e
p r o g r a m was s t o p p e d .
H a v i n q c a f c u f a t e d t h e s o l u t i o n t o e q u a t i o n 14 a n d t h e
v a l u e s s t o r e d a s a n array i n t h e Deu io ry t h e p r o g r a a i n i t i a t e d
t h e c a l c u f a t i o n o f t h e v v e l c c i t y f r o & e q u a t i o n 9, These v a l u e s
were a l s o d e p o s i t e d f o r l a t e r a c q u i s i t i o n , T h e p l o t t i n g
s u b r o u t i n e was e m p l o y e d uFcn completion t o p e r m i t v i s u a l
i n s p e c t i o n o f t h e r e s u l t s ,
A s e p a r a t e p r o g r a a , P L O T D B - S V , was l o a d e d t o p l o t t h e
f i n a l results on h a r d copy, T h i s p rog ran t p i c k e d u p t h e a r r a y s
oE v e l o c i t y , t o r q u e , and c o m p l i a n c e and plotted t h e a on a
p l o t t e r w h i c h was a peripheral. d e v i c e t o t h e PBP-8e-
c) Sxperimenk-2 The d e t e r m i n a t i o n o f t h e t o r q u e - a n g u l a r v e l o c i t y r e l a t i o n s h i p Ercw dynamic c o n t r a c t i o n s
The data r e q u i r e d f o r t h i s a n a l y s i s was t h e t o r q u e
d e v e l o p e d a t a n y t i a e d u r i n g a d y n a m i c c o n t r a c t i o n and t h e
72
v e l o c i t y at t h a t same i c s t m t i n t i a e , l o d e t s r a i n e t h e
v e l o c i t y it was n e c e s s a r y t o d i f f e r e n t i a t e t h e output froin the
d i s p l a c e m a n t t r a n s d u c e r , T h i s was t h e v e l o c i t y a t t h e h a n d a n d
how a c c u r a t e l y it was a m e a s u r e o f t h e v e l o c i t y o f the
c o n t r a c t i l e c o m p o n e n t d e p e n d e d upon how q u i c k l y t h e t o r q u e n a s
c h a n g i n g , U n d e r c o a d i t i c n s of h i g h r a t e of c h a n g e of torque the
5 E C was e i t h e r l e n g t h e u i n g o r s h o r t e n i n g a n d t h i s c h a n g e i n
l e n g t h in the SEC a f f e c t e d t h e v e l o c i t y r e c o r d e d a t t h e hand ,
When t h e ra te of c a a n g e of t o r q u e was low t h e n t h e SEC was
s t a b l e and t h e v e l o c i t y a t t h e h a n d a c c u r a t e l y r ep roduced t h e
v e l o c i t y of s h o r t e n i n g of the c o n t r a c t i l e c o m p o n e n t ,
An a t t e m p t was inade t o assess t h e a f k e c t s o f t h e ra te of
change of torque on t h e s t r e t c h o f the SXC, S u b j e c t 2 h a d b e e n a
s u b j e c t i n a n o t h e r e x p e r i m e n t the aim of which was to estimate
a l i n e a r c o a p f i a n c e f o r t h e SEC, T h a t e x p e r i m e a t h a d d e t e r m i n e d
t h i s v a l u e t o b e ,004 Nw/radian. W i t h t h i s estimate i t nas
p o s s i b l e t o correct t h e o b s e r v e d v e l o c i t i e s t o t a k e i n t o
a c c o u n t c h a n g e s i n l e n g t h of t h e SEC, However, t h i s m e t h o d o f
c o r r e c t i o n p roduced a n o v e r c o r r e c t i o n when t h e t o r q u e s were low
and a n u n d e r c o r r e c t i o n when t h e torques were h i g h . Xt was
d e c i d e d not t o p e r s u e this thought as t h o s e p o i n t s v h i c h rere
a f f e c t e d , and c o n s e q u e n t l y f u f t h e r d i s p l a c e d f r o m the bulk of
t h e d a t a , could b e i g n o r e d ,
The a n a l y s i s p r o g r a m p r i n t e d t h e v a l u e s of t o r q u e , a n g l e ,
a n d angu l a r v e l o c i t y f o r t h e w h o l e c o n t r a c t i o n , S i n c e f i v e
p o s i t i o n s %ere c h o s e n a s s u i t a b l e fo r t h e d e v e l c p m e n t of t h e
t o r q u e - a n g u l a r v e l o c i t y curve t h e o p e r a t o r had t o select t h e
p o i n t s from t h e p r i n t o u t ,
i j s a t a m a n i p u l a t i o n
T h i s proqrdm was c a t a l o g u e d a s DFV-SV and a l i s t i n g
is contained i n A p p e n d i x 2, T h e progrsia i ~ i i t i a l l y
r e q u i r e d t h e o p e r a t o r t o load the c a l i b r a t i o n f a c t o r s , moment
of inertia a n d c o e f f i c i e n t s f o r the c o r r e c t i o n of gravity p r i o r
t o beginning t h e a n a l y s i s , W i t h t h e s e c o n s t a n t s the p z o g r a a
\ d e t e r m i n e d t h e a b s o l u t e v a l u e s f o r e a c h of a c c e l e r a t i o n , t o r q u e
a n d d i s p l a c e m e n t , s m o o t h e d t h e s e by t h e 5 p o i n t mov ing a v e r a g e
t e c h n i q u e a n d s t o r e d t h e % , T h e a r r a y of torque was corrected
last b e c a u s e t h e a r r a y o f a c c e l e r a t i o n was r e q u i r e d t o c o r r e c t
f o r a c c e l e r a t i o n o f the limb, V e l o c i t y was c a l c u l a t e d from t h e
a r r a y of d i s p l a c e m e n t a n d t h e n s t o r e d i n t h e l o c a t i o n
previously h e l d b y a c c e l e r a t i o n , Wben +he prcgxam gas f i n i s h e d
t h e a n a l y s i s and i t p u n c h e d the d a t a on h a r d c o p y f o r t h e
o p e r a t o r , A d x s p l a y p r o g r a m was b u i l t i n t o t h e o v e r a l l p r o g r a w
a n d a l l t h e v a l u e s were d i s p l a y e d f o r v i s u a l e x a m i n a t i o n a s the
p r o g r a m p r o g r e s s e d ,
ii) D e t e r m i n a t i o n of t h e tirne c o n s t a n t of t h e r ise i n t o r q u e
Houk ( 1 9b3f l i n e a r i z e d t h e r e l a t i o n s h i p s of f o r c e - v e l o c i t y
for the CC a n d the l e n g t h - t e n s i o n f o r t h e SEC and d e v e l o p e d a
t r a n s f e r function t h a t d e s c r i b e d the rate o f r i se i n f o r c e ,
T h i s d e s c r i p t i o n was e x p o n e n t i a l i n n a t u r e and f o l l o w e d c l o s e l y
t h e r i se i n f o r c e d e t e r m i n e d e x p e r i n e n t a l l y , C h a p ~ a n 33973)
3 l s o u s e d t h i s d e t z r a i n a t i c n sf f i n e a r p r ~ p e r t i e s of c o n p a n c n t s
of the m o d e l t o examine some effects of l e n g t h o n t h e aodel,
S i n c e t h e ra te of rise i n f o r c e could b e d e s c r i b e d as a n
e x p o n e n t i a l i t was p o s s i b l e t o d e t e r l n i n e t h e time c o n s t a n t of
t h e rise i n force, This d e t e r m i n a t i o n ~ e r m i t t e d the
e x a m i n a t i o n s f t h e r a t e o f a c t i v a t i o n of t h e m u s c l e ,
T h i s r i s e i n torque i n the p r e s e n t study was considered t o
b e n e a r l y e x p c 6 e n t i a l i n nature and t h e following a n a l y s i s
a p p l i e d t o d e k e s m i n e t h e t i w - c o n s t a n t of t h e r ise i n t o r q u e ,
The i n t i a l slow r i s i n g p o r t i o n of t h e c u r v e was i g n o r e d as
being d u e t o t h e c o m p r e s s i o n of t h e s o f t tissue (Chapman,
1973), T h e c u r v e was; e x t r a p o l a t e d t o t h e zero level, The time
c o n s t a n t of an e x p o n e n t i a l curve was d e f i n e d a s t h a t time
r e q u i r e d t o a t t a i n 6 3 % o f the i a a x i m u ~ v a l u e , The maximum value
f o r the i s o a e t r i c c o n t r a c t i o n s o b t a i n e d i n t h i s s t u d y were
d e t e r m i n e d and t h e n t h e time r e q u i r e d t o a t t a i n 53% of t h i s
value, These d a t a were e x a m i n e d to see w h e t h e r the change i n
e l b o w - p o s i t i o n a f f e c t e d the r i se in t o r q u e ,
iii) D e t e r a i n a t i o n of t h e c o m p l i a n c e of t h e SEC
The r a t e of r i s e i n t c r q u e d u r i n g a n i s o m e t r i c c o n t r a c t i o n
is d e p e n d e n t upon the t o r q u e - a n g u l a r v e l o c i t y relationship o f
t h e CC a n d l e n g t h - t e n s i o n c u r v e o f t h e SEC, Knowing the
f o r c e - v e l o c i t y curve a n d the r a t e of c h a n g e o f f o r c e d u r i n g a n
iso~etric c o n t r a c t i o n o n e n a s a b l e t o d e t e r m i n e t h e c o ~ p l i a n c e
o f t h e sec.
d y n a m i c c o n t r a c t i o n s , T o f a c i l i t a t e t h e d e r i v a t i o n of the
c o m p l i a n c e of t h e 5 E C a s m o o t h l i n e was d r a m t h r o u g h t h e
m i d d l e of t h e p o i n t s o n a t o r q u e - a n g u l a r v e l o c i t y c u r v e , T h e
c a l c u l a t i o n of the c o m p l i a n c e was done b p hand and therefore a n
equation d e f i n i n g t h e t o r q u e - a n g u l a ~ v e l o c i t y curve was
c o n s i d e r e d u n n e c e s s a r y ,
T h e d a t d d o l l e c t e d f roiu t h e i s o a e t r i c c o n t r a c t i o n s were
d i s p l a y e d on the p a p e r r e c o r d i n g o s c i l l o s c o p e a t a p a p e r s p e e d
o f 16 cm/sec, The c a l i b r a t i o n d a t a was d i s p l a y e d i n t h e same
fashion, The i n v e s t i q a t o r s e f e c k e d p o i n t s o n t h e rise i n torque
c u r v e on t h i s r e c o r d i n g and d e t e r m i n e d t h e a b s o l u t e t o r q u e , A
g e o m e t r i c a l t a n g e n t was d r a m t o t h e c u r v e a t t h e s e p o i n t s a n d
the v a l u e of r a t e of z i s e i n t o r q u e d e t e r m i n e d i n tlm/sec, T h e
r e l a t i o n s h i p b e t w e e n rise i n t o r q u e a n d v e l o c i t y o f s h o r t e n i n g
is d e p e n d a n t upon t h e e x t e n s i o n of t h e SEC [ d e t e r m i n e d by its
s t i f f n e s s ) a n d the velocity of s h o r t e n i n g of t h e CC (see e q u a t i o n
3 ) - T h i s r e l a t i o n s h i p was u s e d t o c a l c u l a t e the c o m ~ l i a n c e of
t h e SEC ( t h e i n v e r s e ot t h e s t i f f n e s s o f t h e SEC)
T h e p o i n t s o n t h e rise i n to rque c u r v e were transferred t o
t h e t o r q u e - a n g u l a r v e l o c i t y c u r v e d e t e r m i n e d i n e x p e r i m e n t 2
a n d t h e v e l a c i t i e s f o r t h a t t o r q u e r e c o r d e d , S u l t i p l y i n g t h e
v e l o c i t y b y t h e i n v e r s e of t h e rate of rise i n t o r q u e p r o d u c e d
t h e compliance a t t h a t p o i n t d u r i n g the c o n t r a c t i o n , T h e
c o m p l i a n c e d a t a gas d i s p l a y e d a s a f u n c t i o n of t o r q u e -
T h e s e were a number o f factors w h i c h c o u l d h a v e affected
t h e o u t c o m e of t h e e x p e r i m e n t a l r e s u l t s , A p r i m a r y s o u r c e
a r i s e s from t h e c o n s c i o u s a w a r e n e s s o f t h e s u b j e c t ,
T h e method of a l i g n i n g t h e s u b j e c t with t h e a p p a r a t u s was
made carefully c o n s i s t e n t w i t h e a c h s e s s i o n , A s was s t a t e d
e a r l i e r the p c 6 i t i o n of each s u p p o r t was r e c o r d e d a n d t h e
s u p p o r t s r e t u r n e d to t h a t s a a e p o s i t i o n e a c h t i m the s u b j e c t
was i n t h e e x p e r i m e n t , The a p p l i c a t i o n o f t h e c a s t s was a l s o
kept e x a c t l y t h e s a m e s o t h a t t h e n e c e s s a r y c o n s i s t e n c y o f f i t
was m a i n t a i n e d , D u r i n g She experiment t h e s u b j e c t was
i n s t r u c t e d t o l o o k s t r a i g h t a h e a d a t a b l a n k wall and n o t t o
move d u r i n g t h e c o n t r a c t i o n s , T h e chest a n d thigh s u p p o r t s a n d
s a f e t y straps m a i n t a i n e d t h e e x p e r i m e n t a l p s i t i o n t h r o u g h o u t
t h e e x p e r i m e n t ,
With these p r e c a u t i o n s t h e i n v e s t i g a t o r was a s s u r e d t h a t
the s u b j e c t was i n t h e same p o s i t i o n e a c h time h e was a l i g n e d
w i t h the a p p a r a t u s , The oniy area where t h e i n v e s t i g a t o r had
no c o n t r o l #as the a r e a of a c t i v a t i o n of t h e m u s c l e , R e p e a t a b l e
~tlaximum a . c t i v a t i o n was a n e c e s s i t y of t h e exper iaen ta l
technique, T h e s e h a s n o t b e e n a methcd d e s i g n e d t h a t w i l l
p e r m i t the e s t i m a t i o n of a c t i v a t i o n i n i n t a c t a u s c l e s , The
i n v e s t i g a t o r bad t o r e l y o n the s u b j e c t a p p r e c i a t i n g t h e
importance o f c o n s i s t e n t a c t i v a t i o n and a t t e ~ p t i n g t o r e s p o n d
a p p r o p r i a t e l y , It was p o s s i b l y t h i s item which f e d to t h e
d i s c r e p a n c i e s o b s e r v e a d u r i n g e x p e r i m e n t 1,
T h c responsz charac te r i s t ics of t h e transducers has been
describes f u l l y e l s e w h e r e a n d i t was evident that t h e y were
n i t h i n t h e r e q u i r e m e n t s of this s t u d y , No d e t e c t a b l e d i f f e r e n c e
could be a s s e s e d in t h e static or d y n a m i c r e s p o n s e o v e r a
number of t r i a l s , F i l t e r i n g to 15 Hz p r o v i d e d a wide aargin fo r
r e s p o n s e of each t r a n s d u c e r a s well a s a a t c h i n g the upper l i a i t
of t h e frequency r e s p o n s e cf e a c h transducer,
The filkering of t h e s i g n a l from t h e t a p e recorder removed
aost o f the n o i s e i n h e r e n t i n t h a t form of r e c o r d i n g , F u r t h e r
d i g i t a l smoothing renoved a n y n o i s e r e s u l t i n g from t h e
d i y i t i z a t i o a of t h e a ~ a l o g u e i n p u t s i g n a l from the
tape-recorder,
On t h i s b a s i s , then, there does n o t a p p e a r t o be any ~ a j o r
source of error In the experimental procedure,
T h i s s e c t i o n p r e s e n t s t h e d a t a as t h e y %ere c o l l e c t e d
d u r i n g t h e s t u d y , T h e s e da ta a re p r e s e n t e d p r i a a r i l y i n
g r a p h i c a l . f o r m , The i m p l i c a t i o n s of t h e d a t a w i l l b e d i s c u s s e d
i n t h e f o l l o w i n g s e c t i o n ,
As d e s c r i b e d i n t h e s e c t i o n t i t l e d ' B e t h o d of A n a l y s i s 1
t h e s u c c e s s & - M a c P h e r s c n 9 s t e c h n i q u e r e l i e d on the rise of
t o r q u e i n t h e n o n - c o m p l i a n t p u l l being q u i c k e r t h a n t h e r i se i n
t o r q u e i n the c o m p l i a n t p u l l , However , i n t h i s s t u d y t h i s
c o n d i t i o n %as n o t me%, F i g u r e 12 i l l u s t r a t e s t h e rise i n t o r q u e
f o r a t y p i c a l p a i r of c o n t r a c t i o n s , I t is e v i d e n t t h a t t h e r i se
i n t o r q u e i n t h e n o n - c o ~ p l i n t p u l l is slower t h r o u g h a l a r g e
r a n g e of the c o n t r a c t i o n , T h i s p a i r were chosen a s t h e y were a
t y p i c a l e x a m p l e of t h e data observed d u r i n g t h e e x p e r i m e n t
r e g a r d l e s s of a t t e m p t s t o g a t h e r d a t a s imi lar t o t h a t r e p u r t e d
by H a c P h e r s o n ( l953), On t h e b a s i s o f t h i s i n a b i l i t y t o o b t a i n
a p p r o p r i a t e d a t a t h i s e x p e r i m e n t was a b a n d o n e d , The r e ~ a i n d e r
of t h e data p r e s e n t e d h e r e was d e r i v e d f r o m e x p e r i m e n t 2 u s i n g
d y n a m i c ~ o n t r a c t i o n s ,
F i g u r e s 1 3 a n d 1 4 p r e s e n t t h e p o i n t s d e s c r i b i n g t h e
r e l a t i o n s h i p f o r e a c h o f t h e sub jec t s i n g r o u p 2.
The v a r i a t i o n i n isometric torque w i t h e l b o w p o s i t i o n i n d i c a t e
t h a t a t l e a s t o n e p o i n t a n t h e t o x g u e - a n g u l a r v e l o c i t y curve i s
d e p e n d a n t u p o n j o i n t p o s i t i o n , T o d e t e r m i n e t h e isometric
/ t o r q u e for e a c h of the e x p e r i m e n t a l p o s i t i o n s a s m o o t h l i n e was
'drawn t h r o u g h t h e p o i n t s i n figures 13 and 74, T h e v a l u e of
t o r q u e was d e t e r m i n e d a t t h o i n t e r s e c t i . c n of t h i s l i n e with a
l i n e cirdwn rrom t h e d p p r o p r l a t e e l b o w p o s i t i o n ,
f i g u r e s 15a t o 15c and 17a t o 17e p r e s e n t t h e
i n t e r s e s s i o n a l da ta describing t h e r e l a t i o n s h i p between t o r q u e
d e v e l o p e d a n d a n q u i a r v e i c c i t y f o r each s u b j e c t a t each o f the \
f i v e e x p e r i a e n t a l p o s i t i o n s , It is e v i d e n t f r o m the scat ter of
t h e p o i n t s t h a t t h e d a t a f r o a e a c h s e s s i o n o v e r l a p s t h e c t h e r s ,
The o v e r i a p p i n g of t h e i n t e r s e s s i o n a l d a t a p e r m i t t e d t h e
d r a w i n g of a l i n z t h f o u y h t h e s e p o i n t s that w o u l d permit
c o n i p a r i s o n o t a mean 02 each c u r v e for each e i b c w p o s i t i o n
( F i g u r e s 16 a n d 1 8 ) - A i i a s s e s s m e n t of t h e c o m p l i a n c e cf t h e SEC
a n d the use of that a s s e s s m e n t to c o r r e c t t h e t o r q u e - a n g u l a r
v e l o c i t y c u r v e s d i d n c t d l t e r t h e c u r v e s t o a n y e x t e n t fsee
B e t b o d of A n a l y s i s ) ,
T h e c o m p f i a n c e o i the SEC was d e t e r m i n e d f r o m t h e rise i n
i s o m e t r i c t o r q u e a n d i s p r e s e n t e d a s a f u n c t i . c n of torque i n
f i g u r e s 1Ya-e and 20a -e f o r e a c h elbow p o s i t i o n , Trials 1 a n d 2
were o b t a i n e a o n aifferent d a y s w h i l e t r i a l 3 was c o n p l e t e d a t
o n e s e s s i o n , T r i a l 3 c o n t a i n s 3 c o n t r a c t i o n s f o r each p o s i t i o n
of t h e e l b o w - j o i n t ,
T a b l e 1 p r e s e n t s t t e t i m e - c c n s t a n t s f o r the rise i n torque
d u r i n g a n i s o m e t r i c c o n t r a c t i o n , T h e s e da ta were c o u i p u t e d Lrom
t h e d a t a c u l l e c t e u a s d e s c r i b e d i n Chap , IV, c f i i ) ,
F I G U R E 12 : The r i se in torque i n two con t rac t ions , one with t h e added conapfiance and one w i t h o u t t h e a d d e d compliance,
FIGURE 13 : The torque-angle c u r v e f o r subject BC,
0 I SPLRCEMENT (RFIOI FINS)
F I G U R E 34 2 T h e torque-angle curve f o r s u b j e c t HV,
PIGUEE 15 : T h e k o r y u e - a n g u l a r v e l o c i t y curve f o r d i f f e r e n t s e s s i o n s and at d i f f e r e n t joint a n g l e s for subject AC,
a) t o r q u e - a n g u l a r v e i o c i t y curve at 0- 5 radians b) t o r q u e - a n g u l a r velocity curve a t 0 - 8 radians c) torque-angular v e l o c i t y c u r v e a t 1 - 0 radians d) t o r q u e - a n g u l a r velocity curve a t 1-5 radians e) torque-aagulas velocity curve a t 2-0 r a d i a n s
x T / R V 8CO fl1 . 5 RRDS
0 T/flV 8Cl RT . 5 RRDS
X T/8V HC2 fiT . 5 flHOS
# T / B V flCU 8 1 . S RflDS
x T / R V SMOOTH . 5 AflDS.
I 0 I I I I
3 .00 61 4-30 12.00 I 15.00 VELOC I TO U?ADS. SEC. I
I I I I 8 00 3.00 6.00 9.00 12.00 15.00
VELOC 1 T Y ~ 6 R D S . / SEC. 1
x T/RV FICO FIT 1.0 AFlOS
+ T / W F l C l F I T 1 . 0 R F I O S
x T/AV B C 2 FIT 1.0 RflOS
x T/FIV flcu flT 1.0 RFIOS
T/FIV SnOOTH FIC
T / R V SMOOTH R C
%%y 3.00 6.00 9.00 12.00 15.00 VELOC I T Y (RFIDS. / SEC. 1
X T / R V flCO flT 2 . 0 RflOS
0 T / R V R C l FIT 2 .0 RRDS
x T / R V RC2 BT 2 .0 RBOS
# T / R V B C Y R T 2 .0 RROS
T / R V SHCJCJTH 2 . 0 AROS
0 0
0 o* .-I
Q 0 . 0- rC)
O m -0
t & LT-n- z Y
'% 30
f-
0 0 . Q, CV
0 0
'
18 4f m
W m m )It
f m m f Q m 6
*e"
X W
% m rn
%?OO 3 .00 I 1 I I I(c
6.00 9.00 12.00 15.00 VELOCITY (RRDS. / SEC. 1
FIGURZ 16 : The torque-angular v e l o c i t y c u r v e s de termined ky drawing a smooth line t h r o u g h the pciuts d i s p l a y e d i n figure 15,
93
x T / a V HC F1T .S RROS
0 T/FIV i92 FIT . 8 RHOS
x T/FIV FIC R T 1.0 HflUS
T / g V 41: FIT 1.5 ,911OS
T/CI'J 112 FIT 2 . 0 RRDS
FIGURE 17 : T h e t o r q u e - a n g u l a r veJ_ocity c u r v e f o r d i f f e r n n t sessions and a t d i f f e r e n t j o i n t angles f o r s u b j e c t HH,
a ) t o r q u e - a n g u l a r v e l o c i t y c u r v e a t 0-5 r a d i a n s b) t o r q u e - a n g u l a r velocity curve at 0 - 8 radians c) t o r q u e - a n g u l a r v e l o c i t y curve a t 1-0 r a d i a n s d ) torque-angular v e l o c i t y c u r v e a t 1-5 r a d i a n s e) t o r q u e - a n g u l a r v e l o c i t y c u r v e a t 2.0 radians
x T / f l V HW3 flT . 8 RROS
T/FIV HW4 FIT .B AFIOS
x T / R V HU5 flT .8 RflOS
# T/FIV SHOOTH - 8 AflOS
0
I I 1 9 3.00
I 6.00 9.00 12.00 15.00
VELOCITY I R R D S . / SEC. 1
9 7 x T/CIV Hh3 flT 1.0 flR0S 0 T/W Hull AT 1.0 RADS
x T / @ V HW5 fl7 1.0 RRDS
# T/FIV HU SHOOTH flT 1.0
I 1 I I 00 3.00 6.00 9.00 12.00 l$.OO
VELOCITY [RFIDS. / SEC.1
I 1 I f ,00 3: 00 6.00 9: 00 12.00 15.00
VELBC; I T Y (RFIQS. / SEC. I
F I G U R E 18 : The t o r q u e - a n g u l a r velocity c u r v e determined by drawing a s a o o t h fine t h r o u g h the points d i s p l a y e d in f i g u r e 17-
3 r 3
c
w c.3 I--
o t)
'3, N
-2 0 ,
m x 3€ X %
f x w
I s m 3 6
x )(li m W
31C W m
IY
0 1 I I I . O O 3.00 6.00 9.00 12.00 15.00
V E L O C I T Y (RHOS. / SEC, I
FIGUBE 19 : The compliance-torque curve for d i f f e r e n t sessions a n d a t d i f f e r e n t joint a n g l e s for s u b j e c t AC,
a) compl i ance - t o r q u e curve a t 0.5 r a d i a n s b) c o ~ p l i a n c e - t o r q u e c a r v e at 0-8 r a d i a n s c) cqmpliance-tcrque curve at 1 - 0 r a d i a n s d ) compliance- torque curve a t 1-5 r a d i a n s e) compliance-torque curve a t 2 - 0 r a d i a n s
I I I 1 4t 20.00 iSO.00 60.00 60.00 1QO.OO
TORQUE iNM1
0
4 0 0 I I I
1 V 20.00 qo. 00 60.00 BU, 00 100
TORQUE INM)
TORQUE [ N M I
x R C 1 1 . 5 R f l O S
RC2 1.5 RROS
x RC3 1.5 RRDS
FIGURE 20 : The compliance-torque curve for d i f f e r e n t sess ions a n d at d i f f e r e n t j o i n t a n g l e s for s u b j e c t BW,
a) colrrpliance- torque curve at 0 - 5 radians b) compliance-torque curve at 0-8 radians
< -, c) cotapfiance-torque c u r v e a& 9.0 r a d i a n s d) ~ o r a ~ l i a n c e - t o r q u e c u r v e at 1-5 radians e) compliance-torque curve at 2 - 0 r a d i a n s
I I I I P 20.00 110.00 60.00 80.Orl ld3.00
TORQUE INM)
I I I I V 00 20.00 40.00 60.00 80.00 100.00
TORQUE INM)
p o s i t i o n -5 - 3 1-0 1-5 2-0 t r i a l
T a b l e la: tirae-constants for rise in isoaetric torque subject AC (in ntlsecs,)
p o s i t i o n - 5 - 8 1-0 1-5 2- 0 t r i a l
fable Ib: the-constants for rise in isoaetric t o r q u e subject Hi4 (in Rtsecs,)
One o f t h e i n i t i a l aims of t h i s p r o j e c t was t o a d a p t - a a c P h e r s o n * s m e t h o d f o r d e t e r m i n a t i o n o f t h e f o r c e - v e l o c i t y
c u r v e oE t h e CC t o i n t a c t human m u s c l e s , T h e ~ e t h o d o u t l i u e d
by E a c P h e s s o n (1953) was d e v e l o p e d o a i s o i a t e d p r e p a r a t i o n s and
its simplicity a a d e i t a desirable me thod f o r u s e i n o t h e r
t y p e s o f p r epa ra t i ons , However , t h e method was f o u n d to b e
i n a d e q u a t e f o r u s e in i n t a c t h u a a n m u s c l e s i n t h a t i t p r o d u c e d
r e s u l t s that were inconsistent w i t h t h o s e d e r i v e d f r o n i so la ted
p s e p a r a t i o n s ,
T o r q u e d e v e l o p e d by tho CC is a f u n c t i o n of a t least t h r e e
f a c t o r s ; t h e v e i o c i t y of s h o r t e n i n g (Bill, 1938) , t h e a c t i v a t i o n
of t h e CC ( Y a h l e r e S 3 8 6 8 ) aaii t h e i n i t i a l l e n g t h of t h e
LnC ( B a h l e r et a&, 153683, T o e x a m i n e t h e r e l a t i o n s h i p b e t w e e n
t o r q u e d e v e l o p e d a n d velocity of s h o r t e n i n g e x t r a n e o u s f a c t o r s
m u s t be held constant, F a i l u r e t o m a i n t a i n the@ c o n s t a n t
p r e s e n t s p r o b l e m s i n t h e i n t e r p r e t a t i o n of the effect of
v e l o c i t y of s h o r t e n i n g a l o n e on force d e v e l o p e d by t h e CC- I n
expqriments on i s o l a t e d p r e p a r a t i o n s , such a s BacPherson's, the
l e n g t h of t h e i n u s c l e can b e m a i n t a i n e d f a i r l y e a s i l y a s can t h e
a c t i v a t i o n , I n human p r e ~ a r a t i o n s t h e s e f ac tors a re more
difficult to c o n t r o l a n d it is l i k e l y t h a t a t l e a s t one of
t h e s e v a r i a b l e s , v e l o c i t y of s h o r t e n i n g , a c t i v a t i o n o r i n i t i a l
l e n g t h , was not s l a y i a g c o n s t a n t i n t h e p r e s e n t s t u d y -
D u r i n q t h e p r e s e n k e x p e r i m e n t t5c subjects x@re i n f o r a e d
of t h e i m p o r t a n c e of a c t i v a t i o n and v e r e reques ted t o a c t i v a t e
max i r aa f iy e a c h time a s f a s t a s t h e y c o u l d , B l t h o u g h the
s u b j e c t s r e p o r t e d t h a t t h e y f e l t t h a t t h e y had done s o
t h r o u g h o u t t h e e x p e r i m e n t , a c t i v a t i o n was n o t well c o n t r o l l e d
as is e v i d e n t f r o m T a b l e 1, B e c a u s e o f t h i s d i f f i c u l t y
e x a m i n a t i o n was made of t h e p o s s i b i l i t y t h a t v a r i a t i o n s i n
a c t i v a t i o n were t h e s o u r c e of the p r o b l e m ,
W i P k i e (1950) eras a b l e t o o b t a i n r e s u l t s similar t o t h o s e
d e s c r i b e d by P I a c P h e r s o n ('1953) a n d d i d so o n i n t a c t Buoaan
i a u s c l e s , W i l k i e ' s d a t a was o b t a i n e d a f t e r a number of trials
and it seemed p o s s i b l e t h a t t h e r e was a t r a i n i n g e f f e c t , T o
e x a m i n e t h i s h y p o t h e s i s two s u b j e c t s were chosen t o perf or^ a
number of c o n t r a c t i o n s , T h e s u b j e c t s v e r e aware o f t h e need f o r
c o n s i s t e n t a c t i v a t i o n a n d t r i e d v e r y h a r d t o a c h i e v e t h a t ,
However , t h e r e was n o c h a n g e i n t h e d a t a t h a t would s u p p o r t t h e
c l a i n t h a t a p e r i o d o f t r a i n i n g was b e n e f i c i a l , T h e l a t e r
r e s u l t s were a s v a r i a b l e a s t h o s e p r o d u c e d earlier i n t h i s
s%udy ,
To e x p l o r e f u r t h e r t h e p o s s i b l e s o u r c e s of v a r i a t i o n i n
a c t i v a t i o n it was t h o u g h t t h a t p r e - k n o w l e d g e of t h e t y p e of
r e q u i r e d a f f e c t e d the a b i l i t y of t h e s u b j e c t t o c o n t r a c t
m a x i m a l l y , T h i s h y p o t h e s i s was based o n the c a m @ e n t s o f t h e
s u b j e c t s who r e p o r t e d t h a t t h e y felt b e t t e r after c o m p l e t i n g a
c o m p l i a u t p u l l rakher t h a t a n o n - c o m p l i a a t p u l l * H h i l e t h e s e
f e e l i n g s of a c c o m p l i s h m e n t c o u l d o n 1 y be r e a l i z e d a f t e r t h e
c o n t r a c t i o n was well u n d e r w a y t h e r e may h a v e been some
for t h e n s n - c ~ ~ p l i a n t p u l l was then m k n t s i n e d a t 1-0 r a d i a n s ,
T h e s t a r t i n g p o s i t i o n of t h e n o n - c o m p l i a n t pull was s e t a t o n e
of t h r e e l o c a t i o n s , F o r e x a m p l e , w i t h a d e v e l o p e d t o r q u e of 8 0
B m t h e s t a r t i n g p o s i t i o n o f o n e o f the c o m p l i a n t p u l l s was se t
-15 r a d i a n s b e f o r e the starting position of the n o n - c o m p l i a n t
p u l l , I n this c o n t r a c t i o n the t u o p u l l s f i n i s h e d at the s ane
p o s i t i o n , A n o t h e r p a i r of c ~ n t r a c t i o n s were o b t a i n e d by
s t a r t i n g t h e c o m p l i a n t p u l l - 0 8 r a d i a n s b e f o r e t h e
n o n - c o m p l i a n t p u l l . T h e t h i r d p a i r were o b t a i n e d rhea t h e
s t a r t i n g p o s i t i o n s were t h e same, However, t h e p r o c e d u r e
d e s c r i b e d d i d not produce d a t a which d i f f e r e d fro& t h a t
d e s c r i b e d i n i t i a l l y , It seems t h a t the range o f l e n g t h o f t h e
CG i n t h e s e c o n t r a c t i o n s was i n s u f f i c i e n t to affect t h e rate 02
d e v e l o p m e n t of t o r q u e ,
A s t h e p r e s e n t data are n o t s u b s t a n t i a l l y i a f l u e n c e d by
e i t h e r c h a n g e s i n a c t i v a t i s n o r c h a n g e s i n e l b o w - a n g l e , t h e
i n c o n s i s t e n c g w i t h t h e data of 'Miilkie (1950) is e v e n Bore
i n e x p l i c a b l e - H i s s t u d y e x a m i n e d t h e f o r c e - v e l c c i t y c u r v e of a
s i n g l e e g u i v a f e n t h o r i z o n t a l m u s c l e i n l i n e a r terms, The a d d e d
c o m p l i a n c e h e u s e d was a l m o s t 3 times a s l a r g e a s t h a t u s e d i n
t h e p r e s e n t s t u d y , G j i l k i e j u s t i f i e d t h i s s e l e c t i o n on t h e
g r o u n d s t h a t t h e h o r i a c n t a l force d e v e l o p e d by h i s s i n g l e
e q u i v a l e n t mode l was f a i r l y c o n s t a n t o v e r a v i d e r a n g e of elbow
f l e x i o n , T h e u s e o f a h i g h l y c o m p l i a s l t s t x u c t u r e a s the added
c o m p l i a n c e e n s u r e d that h i s r e s u l t s ZolZowed a f o r m a t s imi la r
to M a c P h e r s o n a s d a t a , The present s t u d y h a s shown h o % l a r g e is
t h e v a r i a t i o n i n t o r q u e w i t h respect t o j o i n t - a n g l e s o t h a t
cjross cbanges i n l e n g t h of t h e mnscle n a y render t h e use of
iYacPhersont s t e c h n i q u e i n v a l i d .
It i s e v i d e n t t h a t t h e v a r i a t i o n of the d a t a p r e s e n t e d
here f r o a the e x p e c t e d for^ ar ises frog t h e s u b j e c t r a t h e r than
from t h e a p p a r a t u s , T h e o r i g i n of t h e r n e c h a n i s g of response is
not o b v i o u s , A p o s s i b l e c a n d i d a t e is the c e n t r a l n e r v o u s
s y s t e m , F e e l i n g s of satisfaction r e p o r t e d b y t h e subjects arise
from h i g h e r o r d e r s of the CNS w h i c h e n h a n c e s t h e p o s s i b i l i t y
thaS this s y s t e m is somehow i n v o l v e d , However , r e s p o n s e from
the CNS requires t i ~ e a n d t h e contraction v o u f d most l i k e l y be
o v e r by t h e time t h e G N S h a d r e s p o n d e d , I n c t h e r words, t h e
c o n t r a c t i o n wou ld n a v e t o be c o m p l e t e b e f o r e oae c o u l d f e e l
s a t i s f i e d w i t h it, Even i f s a t i s f a c t i o n was b a s e d o u p r i o r
e x p e r i e n c e t h e c o n t r a c t i o n would be well o n the way b e f o r e the
s u b j e c t c o u l d be a w a r e of how h e naiqht feel a b o u t i t , T h i s
p o s s i b i l i t y i s r u l e d o u t , o f c o u r s e , b e c a u s e of t h e time i a c t o r
i n v o l v e d , Also, when t h e s u b j e c t s were unaware o f what t y p e of
c o n t r a c t i o n was to b e r e q u i r e d t h e y reacted i a t h e same m a n n e r
as when t h e y were aware o f what was c o m i n g next,
Activation of lower o r d e r s of the n e r v o u s s y s t e m (e ,g- the
s p i n a l r e f l e x Poop) a l s o r e q u i r e time and consideration o f
t h e s e m e c h a n i s m s s i l l not b e of i m p o r t h e r e , I t seems h i g h l y
l i k e l y t h a t some r e f l e x a c t i v i t y r e s u l t e d i n t h e s h a r p
c h a n g e i n t h e r a t e of rise i n t c r q u e p a r t nay t h r o u y k t h e
c o n t r a c t i o n w i t h the a d d e d c o m p l i a n c e ( f i g u r e 121,
Thefe is a n i n t e r a c t i o n b e t w e e n t h e m u s c l e s a n d t h e tendoa
a n d m u s c l e r e c e p t o s s , G u y t o n (1971) s t a t e d t h a t the m u s c l e
s p i n d l e s cac r e q o n d i n a f r a c t i o c of a m i l i i s e c o n d , if t h e i r
r e s p o n s e H a s q u i c k e n o u g h t h i s o rgan may have had a u effect on
t h e r i s e i n t o r q u e , T h e s e l e c t i o n of t h e s t a r t i n g p i n k f o r t h e
a n a l y s i s was d o n e by s e a r c h i n g f o r a c h a n g e i n t h e r e s t i n g
t o r q u e t h a t was l a r g e r t h a n t h e n o i s e , Iftlben t h e change was
l a r g e r t h a n t h i s l e v e l the program i n i t i a t e d and began t h e
a n a l y s i s , f f t h i s p o i n t vas p o o r l y c h o s e n t h e n ~ e r h a p s some
r e f l e x a c t i v i t y a i g h t h a v e been m i s s e d , T h i s is u n l i k e l y
b e c a u s e b e f o r e t h e s p i n d l e s c a n react t h e r e has t o b e t e n s i o n
d e v e l o p e d a n d once there was t e a s i o n it would b e recorded b y
the t r a n s d u c e r , T h e k b r c s h o l d level i n o u t p u t f o r t h e t o r q u e
t r a n s d u c e r was q u i t e small and t h e l i k e l y h o o d of m i s s i n g some
a c t i v i t y is v e r y small,
Similar c o n s i d e r a t i o n s e x c l u d e e x p l a n a t i o n s b a s e d on t h e
s tud ies of G o l l n i c k , P i e t i 1 a n d S a l t i n ( l 9 7 4 ) , T h e y have
s u g g e s t e d t h a t t h e r e i s scme s e l e c t i v e r e c u i t ~ e n t of d i f f e r e n t
f i b r e t y p e s d e p e n d i n g npon the t y p e o f c o n t r a c z i o n . W h i l e t h i s
is i n t e r e s t i n g t h e ~ e c h a n i s m of s e l e c t i o n of f i b r e t y p e s
u n d o u b t e d l y re l ies o n a c t i v a t i o n of some r e f l e x s y s t e m . T h e r e
may b e a new f a c t o r , a s y e t unknown, t h a t i s h a v i n g a s i g n i f i c a n k
e f f e c t nn t h e r ise i n tcrque d u r i n g iscmetric c o n t r a c t i o n s .
T h i s f a c t o r is n e i t h e r n e u r o ~ u s c u f a r nor m e c h a n i c a l i n o r i g i n but
rather m u s c u l a r o n l y * S p e c u l a t i o n r e g a r d i n g a f e e d b a c k system
i n v o l v i n g t h e g a i g i t e n d c n o r g a n , t h e m u s c l e s p i n d l e s and the
m u s c l e itself which b y p a s s e s t h e CNS are i m ~ f a u s a b f a s i n c e t h e y
u o u l d i m p l y a n i n t r a m u s c u l a r s y n a p s e which would p e r m i t a l m o s t
i n s t a t a n e o u s r e a c t i o n between t h e effectors a n d af fectors-
B nuzber of authors h a v e s u s g e s t e d t h a t t h e s e is soac
o t h e r f a c t o r w h i c h affects t h e t e n s i . c n produced i n c o n t r a c t i n g
m u s c l e ( P r i n g l e , 1959; H i l l , 1970) - T h e s e a u t h o r s s u g g e s t t h a t
t h e p r e s e n c e o f t e n s i o n a u g m e n t s t h e a c t i v e s ta te , It Bay be
p o s s i b l e , t h e n , f o r t h e t y p e of r e s i s t a n c e t o a f f e c t the r i se
of a c t i v e state, This s o r t of m e c h a n i s m would e x ~ l a i n the
f i n d i n g s h e r e a l t h o u g h t h e r e a s o n for s u c h a raecbanism is
not clear,
3) Experilneat 2
The i n i t i a l aim sf the whole s t u d y was to i n v e s t i g a t e the
d e p e n d e n c e of the t o r q u e - a n g u l a r v e l o c i t y c u r v e on its ~ e t h o d
of determination, The f i r s t e x p e r i m e n t d i d not produce t h e
e x p e c t e d r e s u i t s , t h e second e x p e r i m e n t assumed t h e t a s k of t h e
d e t e r m i n a t i o n of t h e t o r q u e - a n g u l a r v e l o c i t y r e l a t i o n s h i p a t
d i f f e r e n t j o i n t - a n g l e s ,
There a re some n o t i c a b l e d e f f i c i e n c i e s i n the d a t a a s
e x e a p l i f i e d i n f i g u r e s 15a, 15e, 17a a n d 17e, Xn f i g u r e s 1%
and 17e these is a d e f i n i t e a b s e n c e of p o i n t s i n some p o s t i o n s
of t h e t o r q u e - a n g u l a r v e l c c i t y c u r v e s , T h i s lack of p o i n t s was
t h e r e s u l t of s o a e i n a d e q u a c i e s i n t h e e x p e r i m e n a a l design,
Consequently, a line d r a w n t h r o u g h t h e s e p o i n t s , i n c l u d i n g t h e
i s o x t r i c p o i n t , passes t h r o u g h a n area ufiere there are no
guidelines f o r t h e s e l e c t i o n of its p a t h , T h e smooth f i n e s were
d r a w n on t h e b a s i s o f o b s e r v a t i o n s made i n other s t u d i e s a n d on
t h e assumption t h a t human s t r i a t e d m u s c l e ac t s i n a similar
f a s h i o 3 , T h i s s t s p is, p e r h a p s , o f q u e s t i o n a b l 2 v a l i d i t y Lor a s
was p o i n t e d out ear l i es t h e r e are d i f f e r e n c e s i n t h e
f o r c e - v e l o c i t y c u r v e s whfn d e t e r m i n e d b y d i f f e r e n t t e c h n i q u e s ,
f a f i q u r e s 15a a n d 1 7 a t h e s ~ o o t h c u r v e rises almost too
s h a r p l y t o b e c o n s i s t e n t vith o t h e r data, T h e p o i a t where
v e f o c i t y of s h o r k e n i n g was zero was d e t e r m i n e d from isometric
c o n t r a c t i o n s whereas t h e e t h e r p o i n t s o n the t o r q u e - a a q u l a r
v e l o c i t y c u r v e were d e t e r w i n e d Exom d y n a m i c c o n t r a c t i o n s , One
is led t o s p e c u l a t e that t h e r e may he t o t a l l y d i f f e r e n t
r e s p o n s e s o • ’ t h e t a u s c f e t o d i f f e r e n t t y p e s of loading ( P r i n g l e ,
IgTO), that is, a diffe~ent f o r c e - v e l o c i t y curve f o r dynaiaic
c o n t r a c t i o n s and a d i f f e r e n t c u r v e f o r i s o a e t r i c c o n t r a c t i o n s .
T h e s e c u r v e s m y h a v e the same s h a p e b u t w i l l v a r y i n a b s o l u t e
v a l u e ,
T h e d e t e r m i n a t i o n of t h e v e l o c i t y of s h o r t e n i n g of the CO
f r o @ data c o l l e c t e d a t t h e e l b o w - j o i n t i s s u b j e c t t o error when
t h e r a t e of c h a n g e of t o r q u e is n o t z e r o , This i s b e c a u s e t h e
SEC also c h a n g e s length d u r i n g a n i s o m t r i c c o n t r a c t i o n - The
v e l o c i t y o f iiiovement a t t h e e l b o w - j o i n t is t h e sum of the
v e l o c i t y o f s h o r t e n i n g of the CC and the r a t e o f c h a n g e o f
l e n g t h of the SEC, A m e t h o d for: estimating the e r r o r i n
v e l o c i t y 02 s h o r t e n i n g
of f o r c e is g u l t i p l i e d
r e s u l t i s t h e v e l o c i t y
h a d t o be d e v i s e d , If t h e r a t e of c h a n g e
by t h e c o i r i p l i a n c e of the SEC then t h e
o f c n a n g e i n l e n g t h of the SEC. This
f i g u r e c a n then b e added t o o r s u b t r a c t e d from t h e v e l o c i t y
r e c o r d e d a t the h a n d thereby c o r r e c t i n g t h e a n g u l a r v e f o c i t y a t
t h e h a n d t o p i e f d t h e v e l o c i t y of s h o r t e n i n g of tbe CC-
T o ~ e r f o r m t h i s c o s r e c t i o c an es t i ina t ion of t h e c o m p l i a n c e
of the SEC was r e q u i r e d . G i l k i e 41950) d e t e r m i n e d t h e
compliance of the sEC f o r a number of s u b j e c t s , T h e m o s t
c o a p f i a n t o f t h o s e p r o v i d e d b y Wilkie g a s a p p r o x i m a t e l y 0 - 0 3
f a d i a n s / N m , T h i s value was a u l t i p l i e d by t h e ra te of c h a n g e i n
t o r q u e t o g i v e a v a l u e of v e l o c i t y , T h e r a n g e of c o r r e c t i o n
y a l u e s d e t e r m i n e d i n t h i s manne r was fro@ ,001 r a d . / s e c - to -19
r ad . / s ec . T h e s e v a l u e s %ere n o t s u f f i c i e n t t o alter t h e s h a p e
of t h e c u r v e s p r e s e n t e d i n f i g u r e s 16 and 1 8 a n d so i t is
a s s u m e d t h a t t h e c u r v e s d o r e p r e s e n t t h e r e l a t i o n s h i p b e t w e e n
t o r q u e a n d a n g u l a r v e l o c i t y ,
T h e r e a re some d i f f e r e n c e s i n t h e t o r g u e - a n g u l a r v e l o c i t y
c u r v e v i t h e l b o w angfe t h a t i n d i c a t e s imi la r c h a r a c t e r i s t i c s to
i s o l a t e d m u s c l e s as r e p o r t e d b y B a h l e r et af, { l 9 6 8 ) , T h e
d i f f e r e n c e s i n the t o q u e - a n g u l a r v e l o c i t y curves with joint
a n g f e a r e most o b v i o u s upGn c o m p a r i s o n of d a t a c o l l e c t e d a t O a f
r a d i a n s w i t h t h a t c o l l e c t e d a t 1 - 5 r a d i a n s , T h e r e seem t o b e
t u o p o s s i b l e e x p l a n a t i o n s f o r t h e s e d i f f e r e n c e s , T h e r e may b e a
l e n g t h e n i n g of t h e CC t o a n e x t e n t w h e r e t h e t o r q u e g e n e r a t e d
was less a t the Bore a c u t e a n g l e s . T h i s effect h a s been
r e p o r t e d o n i s o l a t e d p r e p a r a t i o n s by Bahler et ua (1968) a n d
t h e e x t e a t o f t h e e f f e c t of l e n g t h e n i n g the a u s c l e o n the
p r o d u c t i o n o f t o r q u e b y t h e CC d e p e n d s upon t h e f o r c e - l e n g t h
c u r v e of t h e C C , A s e c o n d e x p f a n a t i o n n a y b e f o u n d i n the
s t r u c t u r e of the el bow- j o i n t , Chapman (1973) r e p o r t e d t h a t t h e
s h a p e a•’ t h e a r t i c u l a r s u r f a c e of t h e h u m e r u s a f f e c t s t h e a n g l e
o f p u l l o f the tendoas o f t h e f l e x o r s i n a f a s h i o n that
i n c r e a s e d the +orque a t l o n g e r muscle l e n c ; t h s , E c t h of -these
p o s s i b i l i t i e s w i l l b e d i s c u s s e d h e r e ,
T o e x a m i n e t h e e x t e n s i o n oE t h e f l e x o r muscles o v e r a
r a n g e of j o i n t a u g l e s u s e d i n t h i s s t u d y , w e a s u r e m e n t s were
made on a s k e l e t o n of t h e d i s t a n c e b e t w e e n the s h o r t bead of
biceps brachii a n d its i n s e r t i o n i n the r a d i u s - An e x c u r s i o n of
h e elbow j o i n t ffom 0 - 5 r a d i a n s t o 1.5 radians r e p r e s e n t s a
variation i n t h e i e n g t h of 21%. During p a s s i v e e x t e n s i o n t h i s
stretch would be a b s o r b e d p r i m a r i l y b y t h e c o n t r a c t i l e n ta tef ia l
for it w o u l d n o t resist s t r e t c h , a s would t h e t e n d o n s and t h u s ,
t h e f i g u r e of 21% is small, N o b l e ( p e r s o n a l c o n t m u n i c a t i o n ) h a s
c o n d u c t e d some m e a s u r e m e n t s on a s i n g l e cadaver a n d r e p o r t e d a
change i n l e n g t h of t h e m u s c l e Bass of t h e b i c e p s of up t o 6 0 %
of the r e s t i n g l e n g t h , T h i s r a n g e was e v i d e n t on f l e x i o n of t h e
el bow from f u l l e x t e n s i o n t o f l e x i o n of 2 - 4 r a d i a n s , W h i l e t h i s
r a n g e is l a r g e r t h a n t h e r a n g e u s e d i n the p r e s e n t s t u d y i t
i l l u s t r a t e s t h e r a n g e of c h a n g e i n l ~ n g t h a c h e i v e d b y f l e x i o n
of the elbow, T h e s e m e a s u r e a e n t s s u g g e s t that there is a
s u f f i c i e n t r a n g e of m o v e ~ e n t i n e l b o w f l e x i o n t o induce c h a n g e s
i n the o u t p u t of t o r q u e b y t h e CC, The m a g n i t u d e of t h i s c h a n g e
d e p e n d s u p o n t h e s h a p e of t h e f o r c e - l e n g t h c u r v e of the GC for
i n t a c t hu@an m u z z l e s which h a s y e t t o b e d e f i n e d ,
GJifisie (1950) c o n d u c t e d a s t u d y t o d e v e l o p a
f o r c e - v e l o c i t y curve f o r a h o r i z o n t a l l y e q u i v a l e n t muscle
a c t i n g a t the h a n d p a r a l l o l to the u p p e r ar@= H e r e p o r t e d t h a t
the h o r i z o n t a i force at, t h e h a n d was r e l a t i v e l y c o n s t a n t over a.
r a n g e of e lbow f l e x i o n , Chapman (1973) r e p o r t e d that t h e
h o r i z o n t a l force r n m a i n c d c o n s t a c t over a s ~ a l l c r r a n g e of
f l e x i o n a n d t h a t a s t h e a r @ became more e x t e n d e d t h e f o r c e r o s e
i n a f a s h i o n u n l i k e a r e a l m u s c l e - T h e f c r c e rose a s a f u n c t i o n
of t h e s i n e o f t h e a n g l e of f l e x i o n o f t h e e l b o w ( f i g u r e 3 ) -
W i l k i e assumed t h a t t h e f l e x o r s af t h e elbow a c t e d p a r a l l e l t o
t h e u p p e r arm a n d , h e n c e , was a p p r o p r i a t e o v e r a small r a n g e of
e lbow flexion o n l y, Chapman ( 1973) s u g g e s t e d t h a t t o c a l c u l a t e ' t h e c o r r e c t h o r i z o n t a l f o r c e one had to take i n t o a c c o u n t a
g e o a e t r i c a l f a c t o r , This f a c t o r r e s u l t e d f r o m t h e t e n d o n s o f
t h e f l e x o r s c u r l i n g over t h e humerus when t h e e l b o w was
e x t e n d e d p a s s e d a c e r t a i n angle , As a r e s u l t of this the a n g l e
o f p u l l of the tendon r e m a i n e d c o n s t a n t f o r c o n t i n u e d e x t e n s i o n
of t h e elbow,
C o n v e r s i o n o f the d a t a p r e s e n t e d i n t h e p r e s e n t s t u d y
if l u s t r a t e d s i ~ i l a f r e s u l t s . T h e h o r i z o n t a l f o r c e
gt t h e h a n d a t 0 - 5 r a d i a n s was 9 7 Neutons w h e r e a s i t was o n l y 84
M a t 1-5 f a d s fqr s u b j e c t BC, f o r s u b j e c t HW t h e d i f f e r e n c e s
were l a r g e r , 750 N a t 0-5 r a d s and 96 N a t 1-5 r a d i a n s ,
It is f a i r t o a s s u m e t h a t when t h e elbow is n e a r 90
degrees o f f l e x i o n t h a t t h e m u s c l e is n e a r its r e s t i n g l e n g t h
and t h e number of cross b r i d g e s f o r m e d d u r i n g c o n t r a c t i o n a t
t h i s l e n g t h would b e t h e g r e a t e s t (Gordon &* 1966) Idhen
t h e arm is e x t e n d e d t h e n t h e number o f cross b r i d g e s f o r m e d may
be less a s t h e ~ u s c l e is l e n g t h e n e d , Hence, t h e t o r q u e p r o d u c e d
a t t h e e x t e n d e d p o s i t i . c n s h o u l d b e less t h a n a t t h e i d e a l
f l e x e d p o s i t i o a , U h i l e i t Is l i k e l y t h a t t h i s o ccu r s the
p r e s e n c e o f s u c h h i g h h o r i z o n t a l c o m p o n e n t s , a s n o t e d h e r e ,
i ~ d i c a t e t h a t there is snae other factcr 3 f f e c t i n g t h e t o r q u e
recorded a t t h e hand, T h e most l i k e l y e x p l a n a t i o ~ is that t h e
t r a n s m i s s i o n o f t o r q u e t o t h e h a n d is a z f e c t e d b y t h e s t r u c t u r e
o f t h e j o i n t itself (Chapman, 1973) - T h e o v e r a l l effect is t o
p e r a i t t h e d e v e i o p m e n t of c o n s i d e r a b l e t o r q u e s a t a p o s i t i o n
which is mechanically i n e f f i c i e n t and when t h e r e are c h a n g e s i n
h e a b i l i t y of t h e CC t o d e v e l o p t o r q u e s ,
T h e s t r u c t u r e of t h e j c i n t a f f e c t s t h e t r a n s x i . s s i o n o f t h e
t o r q u e p r o d u c e d b y t h e CC t o t h e hand, Chapman (1973) h a s
s u g g e s t e d t h a t t h e e n d s of t h e h u ~ e r u s e f f e c t i v e l y f i x t h e
a n g l e o f i n s e s t i o n of t h e t e n d o a thus g a i n t a i n i n g a c o n s t a n t
moment arm a t t h a t p o i n t , This a c t i o n p r o d u c e s a p p a r e n t 1 y h i g h
t o r q u e s when t h e e l b o u i s e x t e n d e d , T h i s a l s o e x p l a i a s why t h e
h o r i z o n t a l Eosce is s o h igh , An overal l effect
wou ld be t o e n s u r e t h a t t h e r e is s u b s t a n s i a f torque a v a i l a b l e
ts l i f t l o a d s when the e f b c w i s e x t e n d e d ,
B pre l , j .mina ry s t u d y by t h i s author showed t h a t t h e torques
d e v e l o p e d by t h e arm a c t u a l l y i n c r e a s e d when the arm was
e x t e n d s d f u l l y , T h i s has b e e n s u p p o r t e d r e c e n t l y by t h e
p r e l i m i n a r y s t u d i e s of N o b l e [ u n p u b l i s h e d d a t a ) a n d l e n d s
f u r t h e r s u p p o r t t o t h e clainr of Chapman (3973) t h a t t h e
e l b o w - j o i n t ~odifies t h e t o r q u e s r e c o r d e d a t t h e hand, Such a
~ o d i f i c a t i o n is h a n d y , of c o u r s e , f o r i t p e r n i t s a p e f s o n t o
d e v e l o p a t o r q u e a b o u t t h e elbou- j o i n t a t a n y angle e v e n wher
t h e e l b o w - j o i n t is f u l l y e x t e n d e d , W i t h o u t t h i s effect t h e
l e v e r arm p e r m i t t e d b y t h e s p a c e b e t w e e n the t e n d o n a n d t h e
p o i n t of r o t a t i o n of t h e e l b o w - j o i n t would he so smal l t h a t t h e
t o r a u e s ;t this p o s i t i c c aould be smaP1,
A common me thod f o r d e t e r m i n i n g t h e c o m p l i a n c e of t h e SEC
is t o c a l c u l a t e t h e f o r c e - v e l o c i t y r e l a t i o n s h i p f r o m i s o t o n i c
c o n t r a c t i o n s , r e c o r d t h e r a t e of r i s e i n t o r q u e d u r i n g a n
i s o m e t r i c c o n t r a c t i o n a n d , f i n a l l y , s o l v e e q u a t i o n 3 a b o v e , T h e
r e c e n t o b s e r i s t i o n of P a r m l e y aJ, (IgTO), h o w e v e r , has s h o m ;,a a n error i d t h i s t e c h n i q u e , T h e r e a r e d i f f e r e n t f o r c e - v e l o c i t y
c u r v e s d e r i v a b l e for d i f f e r e n t t y p e s of c o n t r a c t i o n s , Hence , i t
is n o t r e a l l y correct t o u s e t h e d i f f e r e n t c o n t r a c t i o n s d u r i n g
t h e p r o c e s s o f c a l c u l a t i n g t h e c o ~ p l i a n c e of t h e SEC,
The error t h a t is i n t r o d u c e d , h o w e v e r , is n o t one of s h a p e
b u t r a t h e r o n e of ~ a g n i t u d e , W i t h t h e e x c e p t i o n of t h e h i g h e r
v e l o c i t i e s o f c o n t r a c t i o r a t h e two f o r c e - v e l o c i t y c u r v e s are of
t h e same shape, A s l o a g a s t h e d e t e f m i n a t i o n of t h e c o m p l i a n c e
o f t h e SEC is c o n f i n e d t o t h e m i d d l e and e n d areas of t h e
isornetsic c o n t r a c t i o n t h e n o n e c a n see t h e c h a n g e s u n d e r g o n e
d u r i n g t h a t c o r a t r a c t i o n , T h e e s t i m a t i o n s f o r the actual v a l u e
of t h e c o m p l i a n c e is, o f c o u r s e , s u b j e c t t o t h e error,
B e c a u s e of the c u r i o u s e v e n t s n o t e d d u r i n g e x p e r i m e n t 1
t h e c o m p l i a n c e of the 3 E C was d e t e r m i n e d i n the B a n n e r just
d e s c r i b e d , The t o r q u e - a n g u l a r v e l o c i t y c u r v e s were d e t e r m i n e d
f s o n d y n a a i c c o n t r a c t i o n s a n d t h e t o r q u e - t i m e c u r v e r e c o r d e a
d u r i n g a n i s o m e t r i c c o n t r a c t i o n , T h e c o i a p l i a n c e - t o r q u e c u r v e s
sere d e t e r m i n e d from t h e s e data,
T h e d a t a shown h e r e are s imi lar t o t h a t r e p o r t e d by W i l k i e
( 1 9 5 0 ) - T h e s h a r p swing u p w a r d s is d u e u s i n g t h e wrong
i t o r q u e - a n g u l a r v e l o c i t y c u r v e , f t is a l s o n o t e d t h a t t h e s h a p e 2,
of t h e ciirves does no t v a r y w i t h j o i n t ?aqfe+ 'This implies
t h a t the characteristics o f the S E C d o n o t c h a n g e w i t h joint
p o s i t i o n , T h e i n t e r s e s s i o n a l variation is m o s t l i k e l y d u e t o
t h e v a r a i t i o n i n a c t i v a t i o n n o t e d i n T a b l e 1, /
&he c h a r a t e r i s t i c s of the SEC a re u u i t e i m p o r t a n t i n the
d e t e r ~ i n a t i o n of t h e c h a r a c t e s i s t i c s of i n t a c t m u s c l e , T h e r e
h a s been some s u g g e s t i o n t h a t the SEC c a n n o t be represea ted a s
a s i a p l e a o n - l i n e a r s p r i n g b e c a u s e its c h a r a c t e r i s t i c s raay
c h a n g e a t v e r y h i g h tensions ( H i l l , 1970). T h i s issue needs
~ u c h more e x a m i n a t i o n b e f o r e t h e SEC is c o m p l e t e l y u n d e r s t o o d ,
A c o m p l e t e picture of the c h a r a t e r i s t i c s of huitian muscle v i U
have t o wait u n t i l this is c o m p l e t e ,
T h i s s t u d y e m b a r k e d upon a n i n v e s t i g a t i o n of five areas of
human ~ u s c u P a r c o n t r a c t i o n , T h e s e areas were d e s c r i b e d b y
q u e d i o o i o c h a p t e r 1. T h e c o n c l u s i c n s of the i a v e s t i g a t i o n are
pfesented here.
1. T h e q u e s t i o n of w h e t h e r t h e r e are d i f f e r e n c e s i n t h e
t o r q u e - a n g u l a r v e l o c i t y c u r v e of the CC that are a s c r i b a b l e t o
t h e method of d e t e r m i n a t i o n s e a a i n s u n a n s w e r e d , This was t h e
c o n s e q u e n c e of t h e k a i l u r e t o a d a p t BacPherson3s t e c h n i q u e t o
i n t a c t human m u s c u l a r c o n t r a c t i o n .
2. T h e r e was l i t t l e doubt t h a t t h e j o i n t - a n g l e affected
t h e p r o u u c t i o n o f t o r q u e a b o u t t h e e l b o v - j o i n t , It was n o t
clear whether t h e d i f f e r e n c e s i n t h e t o r q u e - a n g u l a r v e l o c i t y
c u r v e w i t h r e s p e c t t o e l b o w position were d u e t o t h e anatomy of
t h e elbow- j o i o t p e r se o r u h e t h e r the e x c u r s i o n of a n g l e was
s u f f i c i e n t l y l a r g e t o p r o v o k e a l e n q t h e n i n g of t h e @ C - If t h i s
coraponent was l e n g t h e n e d t h e n it gas likely t h a t the t o r q u e
p r o d u c e d w o u l d d e c r e a s e w i t h l e n g t h e n i n g i n a fashion s imilar
to t h a t d e sc r ibed by B a h l e r &, (1968) . It was c o n c f uded
t h a t t h e r e is a n i n t e r a c t i o n of t h e aena tomy of t h e e l b o w j o i n t
w i t h t h e t o r q u e - a n g u l a r v e l o c i t y c u r v e o b s c u r i a g any
l e n g t h e n i n g of the C C , I t was n o t p o s s i b l e to assess the effect
of l e n g t h e n i n g of t h e CC as t h a t l e n g t h e n i n g would depend u p o n
IU the t o r q u e - a n g l e c u r v e of t h e CC which has y e t to be d e s c r i b e d ,
r e g a r d l e s y of t h e p o s i t i o n of t h e e lbow- j o i n t , T h i s i s e v i d e n t
f r o m t h e f i g u r e s t h a t show l i t t l e c h a n g e in t h e shape of t h e
c u r v e s with j o i n t p o s i t i o n , I t is n o t p o s s i b l e t o c a l c u l a t e t h e
a c t u a l c o ~ p l i a n r e of t h e SEC b e c a u s e o f t h e error i n t r o d u c e d b y
t h e me thod u s e d t o d e t e r w i n e t h a t v a l u e , T h e s i m i l a r i t y of t h e
c u r v e s p r e s e n t e d h e r e w i t h t h o s e p r e s e n t e d e l s e u h e r e v e r i f y t h e
c h a r a c t e r i s t i c s as r e p o r t e d by W i l k i e (1950)-
4, #ilkie*s s i n g l e e q u i v a l e n t h o r i z o n t a l m o d e l is n o t
a p p l i c a b l e t o m u s c u l a r c o n t r a c t i o n over t h e f u l l r a n g e of j o i n t
excursion, T h e e f f ec t of t h e a n a t o m y of t h e j o i n t i ~ p l i e s t h e
i n c l u s i o n of a n o t h e r f a c t o r i n his model , This factor would
t a k e i n t o a c c o u n t the changes i n t h e a n g l e of p u l l of t h e
t e n d o n as t h e j o i n t a n g l e became more a c u t e ,
While n o t an o r i g i n a l q u e s t i o n t h e p r o b l e m s a s s o c i a t e d
s i t h t h e a p p l i c a t i o n of B a c P h e r s o n 3 s aethod t o i a t ac t m u s c l e s
p r e s e n t e d some curious i n f o r m a t i o n , T h e u s e of MacPherson8s
t e c h n i q u e i n t h e p r e s e n t s t u d y d i d n o t p r o d u c e r e s u l t s s i ln i l a r
t o t h a t reported elsewhere, T h i s i n a b i l i t y a p p e a f e d t o be t h e
c o n s e q u e n c e o f some f a c t c r h i t h e r t o u n r e v e a l e d , A number of
a t t e m p t s t o obtain r e s u l t s sirnilas t o o t h e r s t u d i e s were
c o m p l e t e d b u t t h e s e d i d n o t p r o d u c e results t h a t were a n y
d i f f e r e n t from those o h t a i n e d i n the first i n s t a n c e - ),\)
, ,
T h i s s t u d y b e q a n w i t h the aim of e x p l o r i n g a number of
p r o b l e ~ s a s s o c i a t e d w i t h human muscular c o n t r a c t i o n ,
H i s t o r i c a l l y t h e b a s i s of a n u n d e r s t a n d i n g of m u s c u l a r
c c n t r a c t i o n h a s cowe from e x p e r i m e n t s d e a l i n g with i s o l a t e d
m u s c l e s , T h e s e p r e p a r a t i o n s p e r m i t t e d c o n t r o l of v a r i a b l e s
that a f f e c t e d the o u t p u t of t h e m u s c f s s , T h e a i a of t h e
e x p e r i m e n t a t i o n was t o d e v e l o p a c o n c e p t u a l m o d e l t h a t
d e s c r i b e d the observed c h a r a c t e r i s t i c s oE s t r i a t e d musc2e* By
1938 the c o n c e p t u a l model c o m p r i s e d three c o m p o n e n t s that c o u l a
t o some d e g r e e be a s s o c i a t e d w i t h anatomical p a r t s of t h e
~ u s c l e , T h e s e c o ~ p o n e n t s were t h e coa t r ac t i l e c o a p o n e n t , a
series e l a s t i c c o ~ p o n e n t t h a t t r a n s n i t t e d t h e f o r c e t o its
a t t a c h m e n t s w i t h b o n e s , a n d a p a r a l l e l e l a s t i c c o ~ p o n e n t t h a t
p r v v i a e d some r e s i s t a n c e to s t r e t c h a t longer l e n g t h s , This
model a d e q u a t e l y d e s c r i b e s t h e o b s e r v e d c h a r a c t e r i s t i c s o f
i s o l a t e d m u s c l e s ,
T h e n e x t t a s k facing researchers was t h e adaptation of t h i s
~ u d e l t o i n t a c t human m u s c u l a r c o n t r a c t i o n , T h e r e is n o r e a s o n
t o s u s p e c t t h a t h u a a n s t r i a t ed ~ u s c l e h a s a n y d i f f e r e n t
c h a r a c t e r i s t i c s t h a n o t h e r m u s c l e s , However , t h e r e are a numbes
o f v a r i a b l j 6 t h a t a r e more d i f f i c u l t t o c o n t r o l i n i n t a c t w u s c l e s
t h a n i n i s o l a t e d m u s c l e s , Key e x a m p l e s are a c t i v a t i o n ,
relationship of the m u s c l e t o the joint a b o u t wh ich it is
acting, a n a t h e n a t u r e of v o l u n t a r y control, S i n c e t h e
i n v e s t i g a t o r h a s t o r e l y o n t h e subject m a i n t a i n i n g c o n s c i o u s
c o 2 t r o L t ~ c i n v c s t i g a t c r h a s to be aware of the ~ o o d s of t h e
subject and the possde effects of t h a t m o d on the o u t c o m e of
t h e experiment,
It was thought t h a t for the p r e s e n t study t h e s e f a c t o r s
c o u l d be s u f f i c i e n t f g c c a t r o l l e d to p e r ~ i t the c o l l e c t i o n of
t h e i n f o r m a t i o n des i r ea , A p p a r a t u s was designed and built to
p e r m i t the i n v e s t i g a t i o n o f the properties of the CC and the
SEC, These properties were t o be e x p l o r e d u n d e r conditions of
iso~etric c o n t r a c k i o n and d y n a m i c c o n t r a c t i o a , Two techniques
were d e v i s e d f o r t h e e x p e r i m e n t , The t e c h n i q u e d e v i s e d for
i s o m e t r i c c o n t r a c t i o n s was a modified version o f oae d e s c f i b e d
by MacPherson ( l 9 5 3 ) , To explore t b e n t u s c f e under d y n a m i c
c o n t r a c t i o n s a new technique was developed,
w i t h t h e s e t e c h n i q u e s the investigator proposed
exagioation of the characteristics of t h e CC and the SEC of
human intact human musc2es, Some of t h e data c ~ h i e c t e d provided
s t a r t l i n g information, Xt seemed apparent t h a t & h e ~ u s c l e c o u l d
react instantaneously t o subtle variations i n the resistance l o
contraction, studies d e a l i n g with i s o l a t e d muscles do n o t show
t h i s response p r i m r i l y because they are i s o f d t e d from the
whole s y s t e m , The phenomenon appears to o c c u r i n i n t a c t muscfes r only. I n spite of a t t e ~ p t s t c p r o d u c e d a t a that d i d not
exhibit these a n a o a a l i e s , T h e data r e m a i n e d the sa@e a s it was
u h e n init i a l f y cof lec ted ,
The use of u y n a m i c c o n t r a c t i o n s a l o n e in t h e d e t e r m i n a t i o n
of the c h a r a c t e r i s t i c s of intact human @ u s c L e s p r e s e n t s a
l i m i t e d view, I n s p i t e of the l i m i t a t i o n s t h e data was
i n + , - 3 r e s ? r i n g S There v 3 s an effect af - j c ink position on t h e
p r o d u c t i o n of force b y t h e C C , This effect was s e e n a s a
d e c r e a s e in t h e f a r c e p r o d u c e d a s t h e a n g l e o f t h e j o i n t became
smaller i,e, w i t h f u r t h e r e x t e n s i o n of t h e ~ u s c l a , T h e q u e s t i o n
of m a j c r c o n c e r n h e r e was w h e t h e r t h e decrement i n force uas
d u e t o c h a n q e s i n l e n g t h o f the CC or t o t h e i n t e r a c t i o n o f t h e
m u s c l e s w i t h t h e b o n e s of t h e j o i n t . It was c o n c l u d e d t h a t t h e
j o i n t a n a t o m y p l a y s a l a r g e ro l e i n d e t e r a i n i n g t h e o u t p u t of
t h e i a u s c l e , f t was d i f f i c u l t t o assess the e x t e a t o f change i n
l e n g t h of t h e CC b e c a u s e is not e a s y o r p a i n l e s s t o m e a s u r e
this l e n g t h . M e a s u r e m e n t s t a k e n from a skeleton s h o w e d that f o r
t h e range of j o i n t excursion i n t h i s s t u d y t h e r e was a c h a n g e
i n t h e d i s t a n c e between o r i g i n a n d i n s e r t i o n of the b i c e p s i n
exess o f 21%- The a c t u a l c h a n g e i n l e n g t h of t h e m u s c l e b u n d l e
as s e p a f a t e from the t e n d c n s w o u l d be s u b s t a n t i a l l y l a r g e r -
This r a n g e of l e n g t h i m p l i e s some c h a n g e s i n t h e length of t h e
CC but # & e t h e r t h e changes were sufficient to p r o v o k e a
decrease i n torque s i m i f a s : to t h a t repor ted by B a h l e r st a1-
(1968) rcxiains u n d e t e r m i n e d ,
T h e corupliance of t h e SEC was d e t e r m i n e d E r o n i s o m e t r i c
contractio@. The r e l a t i o n s h i p of c o m p l i a n c e , t o r q u e a n d elbow
posit iort i m p l y t h a t t h e cfiaracterisZrics o f t h e SEC are
u n n a f f e c t e d b y elbow position, Bo a b s o l u t e v a l u e s fo r
c a i t i p l i a n c e %ere d e t e r m i n e d because of t h e problems a s s o c i d t e d
w i t h t h e u s e of a d y n a m i c t o r q u e - a n g u l a r velocity c u r v e a n d an
i s o m e t r i c t o r q u e time curve, T h e e r r o r is one 0 5 m a g n i t u d e o n l y
i n t h e middle p o r t i o n s o f t h e c o m p l i a n c e - t o r q u e curve, This
p o r t i o n i n t h e prxsent d a t a was v e r y similar t 3 t h a t reporte2
by W i l k i e (1950),
T h i s s t u d y h a s shown t h a t t h e t h r e e c o ~ p o n e a t model can be
a p p l i e d t o i n t a c t human muscle o n l y when some m o d i f i c a t i o n s a rc
made, T h e r e i s a g e o m e t r i c a l f a c t o r which m u s t be t a k e n i n t o
a c c o u n t a s t h i s f a c t o r c a n a f f e c t t h e f o r c e t h a t is r e c o r d e d a t
t h e hand, Such a c o r r e c t i c n , o f c o u r s e , uouhd depend on the
m u s c l e g r o u p being examined , A c t i v a t i o n a p p e a r e d t o v a r y q u i t e
s u b s t a n t i a l l y froin c o n t r a c t i o n to con t r a c t i o n i n s p i t e of
a s s u r a n c e s b y t h e s u b j e c t t h a t h e was c o n t r a c t i n g c o n s i s t e n t l y .
T h e a r e a of a c t i v a t i o n r e q u i r e s much work, The d e v e l o p m e n t of a
t e c h n i q u e of a o n i t o r i n g and q u a n t i f y i n g a c t i v a t i o n would b e a
g r e a t boon i n a c h i e v i n q a c o m p l e t e u n d e r s t a n d i n g of n u s c u l a f
c o n t r a c t i o n , P e r h a p s further s t u d y on t h e EHG v i l f p r o v i d e a
s o l u t i o n , T h e p r o b l e m t h a t a rose u s i n g aacPherson's t e c h n i q u e
is, p e r h a p s , t h e ~ o s t i n t e r e s t i n g , T h e r e do n o t seem ti> b e a n y
a v a i l a b l e mechanisms t h a t d e s c r i b e why the a n o ~ a l y o c c u r r e d ,
T h e area oT s t u d y d e a l i n g ~ i t h i n t r a - a u s c u l a s receptors a n d
r e s p o n s e 02 muscle t o d i f f e r e n t l o a d s w i l l o b v i o u s l y h a v e t o h e
e x a m i n e d f u r t h e r , 3
A b b o t t , L C , and Lowy ,J. (19521, W e c h a n i c a l p r o p e r t i e s o f H y t i l u s muscle, J, ~ h y s i o l , 120, SOP,
Abbott,B, C, a n d W i l k i e , D, l?, { 1 9 5 3 ) - The r e l a t i o n be tween v e l o c i t y of s h o r t e n i n g and the L e n g t h - t e n s i o n c u r v e o f s k e l e t a l muscf e, J, P h y s i o l , 3 20, 214-223,
3 a h l e r , A, 3,. F a l e s , J , an6 zierler,K, 11 968) , T h e dynant ic p r o p e r t i e s of s k e l e t a l musc le , J, Gen. P h y s i o l . 5 3 , 368-384,
a l i x , a . ( 1 8 9 3 ) - Skand Arch, P h y s i o l , Q, 399 , c i t e d i n H i l l , 1938 , p, 181,
B o u k e a r t , P , CapelZan,L. and d e BTende,J. (1 %O) , The v i s c o - e l a s t i c properties of: frog m u s c l e , J w P h y s i o l , 69, 473-492-
Chapman,A, E, ( l 3 7 3 ) , T h e r e l a t i o n b e t w e e n l e n g t h and t h e f o r c e - v e l o c i t y c u r v e of a single e q u i v a l e n t linear m u s c t c a t the hand d u r i n g elbow flexion, P r o c , Q t h Ink. Seal, Biomech, i n p r e s s ,
Close,fi,I, 11972) - Dynalnic p r o p e r t i e s of inaznmafian s k e l e ' k a l m u s c l e , P h y s i o l , Rev. 5 2 , 129-397,
D e r l a , H-J, L e i l i n e , Js E, a n d f t f a i r ,H , A, (1967) . F o r c e s exerted a t different v e l o c i t i e s o f s h o r t e n i n g * Amer,. J, P h s i o l - 151, 415-437,
Pernn,B,O, a n d B a r s h , 3.5, { l 9 3 5 ) , f i u s c u l a r force a t d i f f e r e n t s p e e d s sf shortening, J, P h y s i o l , 85, 277-292-
F i c k , A, ( 1882) -iYiech. WrLei t u, W a r r a e e n t i ~ i c k e l u n g b, d, B u s k e l t h a t i g k e i t - L e i p a i g : B r o c k h a u s , cited i n H i l l , 1938, p, 181,
G a s s e r , c S . a n d H i l 1 , A . V . (1921)). T h e d y n a m i c s o f a u s c u l a r contraction, Proc, Roy, Soc, B96, 398-437,
Golfnick, !?,a,, P i e h f ,Kg a n d S u l t i n , B , (1971) - 3 e f e c t i v e g l y c o g e n d e p l e t i o n pattern i n human m u s c l e f i b r e s a f t e r e x e r c i s e of v a r y i n g intensity a n d at v a r y i n g p e d a l 1 i n g rates. J, P h y s i o l , 243, 45-57,
Gordon,A. 3, Huxley , A,P, a n d J u i i a a , F , J, ( 1 9 6 6 ) - The v a r i a t i o n i n ismetric t e n s i o n w i t h sarcomere l e n g t h i n v e r t e b r a t e m u s c l e f i b r e s , 3, P h y s i o l , 184, 176-182-
Guytsn,A,C, (1 971) . T e x t b o o k of Bed ica l P h y s i o l o g y , W - 3- S d u n d e f s Co, , T o r o n t o ,
i f , A , , [3922), T h e maximum work a n d m e c h a n i c a l e f f i c i e n c y of human muscles and t h e i r most economical s p e e d , J, ~ h y s i o f , 5 G , 19-41,
--------- (19381, T h e h e a t of s h o r t e n i n g a n d d y n a m i c c o n s t a n t s o f m u s c l e , Psoc , Roy, Soc , 3126 , 136-795,
--------- (1949) , The a b r u p t t r a n s i t i o n from rest t o f u l l a c t i v i t y i n rauscle, Proc, Roy* Soc , BY 3 6 , 399-426,
--------- (1950)- E l e c h a n i c s of t h e c o n t r a c t i l e elerneat of ~ u s c l e , N a t u r e 1 6 6 , 415-419,
---------- (1970) - first a n d L a s t E x p e r i m e n t s i n E u s c l e Y e c h a n i c s , U n i v e r s i t y P r i n t i n g H o u s e , London,
HouF,,J,C, [ 1 9 6 3 ) , A w a t h e ~ l t a t i c a l model o f t h e s t r e t c h r e f l e x i n t h e human muscle systea , c i t e d i n P l i l h o r n , 1966,
H u r s b , J O B , j 1 9 3 8 ) , T h e f o r c e exerted by dogfish p h a s c o l o s o m a a t d i f f e r e n t v e f o c i t i e s of s h o r t e n i n g l 3 , Cell, Camp P h y s i o f - 11, 333-
JeweZP,B.R, and K i f k i e , L H , (1958), An a n a l y s i s of t h e m e c h a n i k a l c o m p o n e n t s i n f rocj's s t r i a t e d m u s c l e - J, P h g s i o l , 1 4 3 , 515-540,
Ratz, 9, ( 1 9 3 9 ) . T h e r e l a t i o n between force and s p e e d i n m u s c u l a r c o n t r a c t i o n . 3, P h y s i o l , 96 , 45-64,
Lanczos, G, 1 3 956), Appf i e d A n a l y s i s , P r e n t i c e - H a l l , E n q f e v o o d C l i t f s , C a l i f o r n i a ,
L a u f a a i e , F, ( 1 905)- E l e m e n t d e Physiologic, P a r i s , cited i n H i l l , 1970, p, 23 ,
a n d Pyman, J, (1927) - T h e v i s c o - e l a s t i c o f inuscle, P r o c , Roc, SOC, 810 1, 238-243,
L u p t o n , Ei, ( 3 9 2 2 ) - An a n a l y s i s of t h e effects of s p e e d sn t h e ~ e c h a n i c a l e f f i c i e n c y of human m u s c u l a r movement. 3- P h y s i o l , 57, 337-353-
R a c P h e r s o n , L, [ 1 9 5 3 ) , A meehod o f d e t e r m i n i n g t h e force v e l o c i t y r e f a t i o u o f muscle fro^ t w o i s o m e t r i c c o n t r a c t i o a s . 3 , Physiol, 322, 172-177,
o r , f l%b) , T h e A p p l i c a l t i o n of C o n t r o l Theory to P h y s i o h o g i c a l S y s t e m s , E, 0, S a u n d e r s Co,, London,
Noble, B- ( 1 9 7 5 ) - P e r s o n a l c o m m u n i c a t i o n -
ParmLey,W,W, Yeatman,&, A, a n d S o n n e r n b l i c k , E,B, ( 3 970) , D i f f e r e n c e s be tween i s o t o n i c a n d i s o a e t r i c f o r c e - v e l o c i t y r e l a t i o n s i n cardiac a n d s k e l e t a l m u s c l e . Amer, 3, ' P h y s i o l , 219, 544-530-
PsLissar,b,~, f 1 9 5 2 ) - p h y s i c a l c h e m i s t r y o f t h e c o n t r a c t i l e process i n m u s c l e . Amer, J, P h y s i o l , 168, 766-1317,
P r i n g l e , J , tu', S , . f l 9 5 9 ) , E o d e l s o f m u s c l e , Sac, E x p e r , B i o l , 1 4 , 41-68,
R a l s t o n , i i , J , 1 I g t j l ) , fJses a n d l i m i t a t i o n s of E i e c t r o r a y o g r a p h y i n t h e q u a n k i t a t i v e s t u d y of s k e l e t a l musc l e f u n c t i o n , Amer, J, Q r t h o . 47, 524-530,
i i a l s t o n , H , J, fnnan ,V. S t r a i t , L , artd S h a f f r a t t r ,L [ lgi l .7) , B e c h a n i c s of h u ~ a r i isolated v o l u n t a r y m u s c l e , Amer, J, P h y s i o l , 1 5 1 , 632-620,
Ramsey,R, a u d S t r e e t , S , (1940) , The isometric l e n g t h t e n s i w d i a g r a m 0 2 i s o l a t e d s k e l e t a l m u s c l e f i b r e s of the f r o g , J, C e l l , Oomp, P h y s i o l , '15, 11-34,
Bitchi. ; ,J ,?l , (1954), The r e l a t i o n between force and v e l o c i t y i n r a t ~ u s c l e , 3, P h y s i o l , 123, 633-639,
Stolov,W, C, and WeiEepp,T,G, ( 1 9 6 6 ) - P a s s i v e 1 e n g t h - t e n v i o u kekation~hi~s oE i i i tact m u s c l e , ep in tys iu i a a n d t e n d o n i n n o r m a l a n d a e n e r v a t e d g a s t r o c n e m i u s of t h e ra t . i i rch , PAys, Hed, 47, 612-620,
Wilk ie ,D ,R , [ l 9 5 O ) , T h e r e l a t i o n between force a n d v e l o c i t y i n human ~ u s c l e , J, P h y s i o l , 110, 249-280,
------- -- ( 1 9 5 6 ) - B e a s u r e ~ e n t of the series e l a s t i c c o m p o n e n t a t v a r i o u s times d u r i n g a s i n g l e m u s c l e t w i t c h , J, P h y s i o l , 134 , 527-530,
-L (1 968)- B u s c l e , ------we---
Edward S r n o l d (Publishers) Ltd. , London.
Wyman,J, j 1 9 2 6 ) - S t u d i e s o n the r e l a t i o n of work a n d h e a t i n t o r t o i s e m u s c l e . 2, P h y s i o l . 6 1 , 337-352,
A P P E N D I X 1
Table 1: The ages, w e i g h t s and s t a tu res of t h e s u b j e c t s i n g r o u p s one a n d too.
SUBJECT AGE W E I G H T HEX GNT Y E A X S KG, Cu4,
79-5 177,5 YO. 9 178.0
APPEMDIX 2
The prograa ADFOCA-SV was u s e d to acquire the data into t h e cosputer nemory, T h e operator r e s p o ~ d e d to each q u e s t i o n with a response a p p r o p r i a t e t o the n e e d s of each particular a c q u i s i t i o n ,
DACAL . SV
G = l s 5 ; D % H F ( 1)=3.1416/(H(3)-kt(2))iS HF(2)=3.1416/(R(5)-H(4>) Mi( l ) = i I < 2 ) * H F ( 1 ); S H R < 2 ) = H ( 4 ) * H F ( 2 ) "TOHQ A P P L V[UI"TAj !;S T F ( 1 ) = T A / ( T < 5 ) - T ( 3 ) ) i S T F ( 2 ) = T A / < T C e ) - T ( 4 ) ) GLC 1 ) = ( 1 ' < 3 ) - T ( 1 ) ) ;s G L < 2 ) = T ( l ) - T ( 2 ) ; S MEIT( 1 ) D 1 . 4 1 7 1 S AFCl)n9.81/(A<2)-A(l))*DJS AF<2)~9.81/(A(l)-A(3))*D A G = ( A ( Z ) - A ( 3 ) ) / 2 i S MA*A( 1 ) X l 2 . 0 R r @ ' H F ( l ) " H F ( 1 ) s " R/U"r ! " H F ( ~ ) " H F < ~ ) J " H/U'*r I ! "hh( 1 )"riR( 1 ) r " R", I " R R ( 2 ) " H R ( 2 ) B " h " ~ ! ! " I ' F ( l ) " T F ( l ) r " V M / U " r ! " T F ( 2 ) " T F ( 2 ) r " Nd /U"r ! I " G L ( l ) " G L < l ) r " U " r ! " G L < 2 ) " G L ( 2 ) r " U " r ! ! * ' A F ( l ) " A F ( l ) * " H PER S t 2 1 " A F ( 2 ) " A F ( 2 ) r W H PEh S t 2"s ! !"AG'eAGJ" U"J !"iYA",UIAr" U". !"MT**NTr" Er+E( 1 ): T X 1 5 . 0 6 r " E R EMG REMA1WDER"EHr" U", ! J = 2 r SI D 4 E F = 0 ; F J = 2 ~ 5 ; S E F = E F + E F ( J) XI 5.d6r "NEAU E F EMG FACTOH**EF/4 r1 ' MVOLTS/U!b I
5 ~ 0 ; 8 H = 8 0 9 2 + l 0 0 ~ Q I S T = 9 0 9 2 + 100*G: S A = 8 5 9 2 + 1 0 0 t G J S E = 9 5 9 e * i @ 0 * Q I = l r 1 0 0 i D 3 H ( G ) * S / 1 0 0 I S S=0IS h = T J F I = l r l 0 0 f D 3 T ( G ) = b / l 0 0 I S S = 0 f S R = A l F I = l r l 0 0 ; D 3 A < G ) = S / l 0 0 I S S=B;S R n E l F I = l r l 0 0 ; D 3 E ( G ) = S / 1 0 0
S * S + F C O R < H + I - 1 )
"EMG M I L L I V O L T I V P U T I S " ; T X l r J J A E A < J ) E F ( J ) = E A ( J > / ( E < J)-EtZ1;T " E F ( " r X 1 r JB") " ~ X l S r 0 6 r E F ( J ) r " M V / U " f
3
NEWMIS. SV
GRAV . SV
PLOTDA. SV
25.50 S Cz03F I=lrNID 27 25.53 S L=Yl;S YlsY1+400iF IllrN3D 27 25.56 S P=3000/Cf T "MAX ABCISSAoer X8. 048 C0 ! 25.58 S Cm0IS YlsTliF I P L I N ~ D 27 25.60 T "MAX TORQUE'@C/40r ! i S C=2000/CJ S Y lrL 25.65 D 26 25.70 I ( 3 -1 )25*8r25*8~25 .85 25.80 T "RESET PLOTTER G 24. 55'@3S YlmYl-200iQ 25.05 T "RESET PLOTTER G 23.lne3Q
0 5 . k l 5 3 V=SIIW; A " I<Fw~F , "AF"AFI"TF"~'F,"D"DI 1 L15. I6 A '.I \I1*I;rJ, "i<tr"hH, "A(;"AG~"MA"MA~ l i F I = l r 8 I A "BI"i3( I ), I k+',.17 5 Yl=6143;5 E1=1859 l i5 E2=10791iS i i l=BSYliS H2=8191;5 A1=9391 05.19 .5 A2=8991;S TI=I01911b F 2 ~ 9 7 9 1 II5.2@ 5 X=0iF I= l .N lb X=FCOH(El+I)+X*.9512;5 Z=FCOH(El+I,X/5) 05.$?1 5 X=0;F I = l r N i 5 XaFCOH(E2+1 )+X*.YSl21S %=FCOH(E2+I,X/5) 05.22 5 B=El IF V=l rS iD 4 0 5 - 2 3 A "EP1M"H. I ; 5 B=EefF V=lr'VlD 4 0 5 - 2 5 T "EP2MM.liF I = l r N i D e l 85.3U b L.hli5 HliIc2iF I = l r V i D 21 05.35 5 K l=Li5 L = T l i 5 T l = l t l i F I=lsV-4;D 25 85.37 5 D=t t l iF V=l,NID 4 05.40 5 Tl=H2iF I=l ,V-4JD 2 5 9 5 - 4 2 S n=H2;F V=l,ViD 4 05.44 5 TlaLiT %H.04r"HPI"FCOH(H1+5)/1000 05.46 T " HP2"FCOH(R2+5)/l000r l i S Pa03 F 1.3rX-2;D 1 5 85.48 T "MItPl"P/l000ib L ~ i l l f S Rl=f<2;5 P = 0 i F I=3,V-2;D 1 5 05.50 S Hl=L;T " MHP2"P/l0001 ! I F I=3,V-2iD 22 85.53 52.=11;5 T l=Al ;F 1=3rV-6iD 2 5
B=Al;s Tl=L;T "D A1"JF V=l.N;D 4 05.58 L = A l i 5 L l = H l i 5 AlsA2iS Rl=H2iF 1 - 3 ~ V - 2 i D 22 k35*56 f 05.60 S Al=L;> HI-L1;S L i T l J S T l = A l i F I=3,V-61D 2 5 05.62 5 T l = L l S B = A 2 i T U D A2"rI fF V=lrViD 4 05.64 F I=5rV-4;D 2 3 05.66 F 1*5rN-BiD 2 5 85.68 5 B=TlIT "D T1";F VnlrYlD 4 05.70 5 LnTl lS T l=T2fS L l = A l l S AlfAZi5 L2tHl:S H b H 2 I F 1=5rM-4iD 2 3 05.72 S A l n L l i 5 HlnL2)F Ix5rN-BiD 2 5 0 5 - 7 4 S BnT2;S rlaL;T " D T2"r l i F V=lrY;D 4 05.75 S +O;F 1=8,N-81D 24 05.76 b UmA115 LaIIlIS L l = A l i T "D V1"iF V=lrNlD 4 05.77 S Hl=H2i5 Al=ADlF I=B,N-BSD 24 05.78 S BzA2IT " D V2"r!iF U=lrY;D 4 8 5 - 7 9 5 HlnLJS A l i L l 05.83 S SQ=0iD 20 05.84 T " P'dWPlr! fS P2.P1;5 Tl=LIT "6 5.87 FOk SECO'VD PASS", ! iQ 05.87 5 t i l=8791;5 1<2=83Yl:b A1=959IIS A2a91911S r l = l 0 3 9 1 j S T 2 ~ 9 3 9 1 05.86 S Y15694315 E l * l 0 9 9 1 I 5 E2511191iG 5.2
ADFOCA . SV 02.&+8 E k32. l a T " ANALOGUE ACQUI51 IOV PtlOGHAMWr ! ! ! 89-18 A "IYTEtlilUPT PEHIOD IN MSEC IS t "CPa I 1 02.14 A "COYTHOL 'FUitN O N DELAY IV MbEC IS 8 "DEJ !! 02-16 A "MIY O N LEVEL (VOLTS) 8 "LO, !;S LO~FITR(LO*l02*4) 02.17 A "MAX ON LEbE!, (VOLTS) : " H I I ! ~ S HI=FITH(iiI*102.4) 02-16 R "TOTAL ACQUIbTIOV TIME IV MbEC I S 8 "TMI! 1 02.20 A "NO OF CHANNELS ACTIVATED r "NCJ!! 02.22 A "NO OF PASSES FOR THIS INITIALISATIOY : "NGI ! 1 02.24 S Tlm3967iS T!i?=7934i S X=T2+3839 02.26 A "AilE TOTAL DATA AHHAYS* 3839 r "AVbr! 02.28 1 (AVS-OYES)2.3012.32,2.30 02.30 5 TE=T2+lib Mn0iS JFn23G 3.10 02.32 S TE=0;5 M=4;5 JF=0
03.18 F ~ ~ 1 3 7 ; ~ "COLLECTING FROM C H W J T X1,A ;A " 8 " Sk(A)r ! 03.11 1' I ! ! 03.12 F Ae1~7;D 4 03.14 T "THIS I S ALL THE DATA HEQUIHED TO IYITIALISE"r!! 03.16 F A t l ~ 7 1 D 5 03.18 F Anl17lD 6 03-19 b AA=AA*NG 03.20 1 (AA-X)3.2413.24,3.22 03- 82 T "TOO MUCH DATA 03.84 T "AMOUNT OF DATA1*IT X ~ I A A J ! ! 0 3 - 2 6 T "CHANNEL START ADDRESS FIELD ARhAY SIZE". ! 1 83.28 F A11~71D 8 03.30 S TE=DE/CP;S DE=FITR(TE)t I (DE-TE)3.3213.3413.32 03.32 T "TURIV OhJ DELAY PERIOD NOT COMPATIBLE WITH IhJTEHFilJPT PEkIOD"r! 03.34 S DE=-(DE+l) 03.36 F Aslr71D 9 03.37 A "IS THIS A GOOD IVITIALISATIOY t "AVSI !; I <ANS-OYES)2* lE1303812Q 03.38 S AA=AA/iUGI I (AA-4096)3.40~ 3 . 4 0 ~ 3 . 4 2 03.40 b LbnAAI G 3.48 03.42 I (AA-8192)3 .44~3 .44~ 3 -46 03.44 5 LbrAA-409635 Mb=lIG 3.48 03.46 S LSaAA-8192J5 MS=2iG 3.48 03.48 S Z=FCOfi( 122531-7); S Z=FCOR( l 2 2 5 4 ~ - 7 ) ; S Z=FCOh( 12267r-LS) 03.49 S Z=FCOH( 12268~-MS) 03-50 b L=FCOH( 12271,-HI )i S Z=FCOH( 122721-LO);S Z=FCOkC 12273rDE) @3.51 5 L=FCOki( 122741DE:)IS Z=FCOH( 12278s-YG) 03.52 F A = l j 7; b Z=FCOH( 12050+A1-T(A)/cP) 03.54 F A= 1 ~ 7 ; 5 Z=FCOR< 12085+A~-1'(A)/CP) 03.56 F A s 1 J 7;b Z=FCOH< 12057+A1G(A) ) 03.58 F A=l*7; S Z=FCOH( 12064+A~AD(A)) 03.60 F A ~ l r 7; b Z=FCOh( 12071+A1CF(A)) 03.62 F A s 1 ~ 7 ; S L=FCOH( 12078+A~bC(A)) fl3.64 !J <=FC013< 193219); 5 Z.rFCOR(212t319);S <=FC01((3~3968) 03.66 b Z=FADC< 1 )
04. 10 1 (Sk<A))4 .1214 .12~4 .14 84.12 it 04.14 T "GAIN FOH CHAYNEL"iT 211 A f A " % " G ( A ) J ! 04.16 1 "PEHIOD FOH CHAVNELM;T % ~ J A J A " :"T(A) J ! !
ADFOCA.SV (continued)
- - .--
DFV . SV
( % ', , . I , 1- I = ( . l r c l . r l r c ~ ) ; s I . = I . C C ~ I ( 1 , ~ ) 147 I : . 1 u=:'(!(>;b i j f i s i j 1,) 1 ; ~ A C = r ( S + l ; s l O = ~ k > 2 1 ; b b..q=).r+ I ; ! - r 8 = l r ~ J 3;5 P b = t . l 4 : i
1:' 5 I5=6543iS r , k . = 6 4 4 3 ; A "At l o ' c \ b ( l ) # " P h P " f i k ( T ) r m 1 b " ' 1 h ~ " t ke'k t r " bk R P?. 1 L, A W q I "MI *I Ij-L,, " fiAelMA, AZj"Atir I "k.Te'hT, " th"P . tqr I ; k I = 1 8 Y 3 f i " C l "C( 1 P:'. l l 5 < = C I : X [ ( - 5 / E T ) ; C I = l r ' J ; S L = b C ( ' k ( I A + I r ( C l ; C ~ F ( I > P + l ) * F C - > F ) * 1PC"V) @ P a 1 9 h I = l r V - 4 ; D P9 P 2 . P P b I = 3 r V - ? i l l PH C"?.T3 5 L = b A ; S h p = A C ; C I = 3 r a J - b i b 23 F?.PS S F P = L : E I = S r N - 4 ; D ? I p?.?7 S L = h P ; S F A = T O ; t I = S r h l - H ; l ~ 29 r?.?a s r - P = r ; b I = S , N - H ; L I ~3 (*:'.3C S f?fi.;L;b I , = t C C ' h ( b l 4 4 r D ) ; S Y = @ ; k I = ? r N ; L , P4 C P . 3 2 S Y = @ ; F I = S r 1 4 ; S X = X + E C W i ( A C + I ) @ P o 3 3 F 1 = 7 r N - 4 i D 23 02.34 5 L = f t P i S H A = f i S ; t 1 ~ 7 r d - Y ; D 29 O P . 3 5 S F A = V E ; b 1=7riV-~:%l 29 @?.BY T " P O I N T T O L O U L AIQG b O L A.'JULL"r ! f i P r 4 C S f1A=L;A " S P " S P r ! l fi V = S F r N - 1 2 : L, 8 f l P . 4 2 ( 3 i T " F O I NT E W C E V CL LLI'JU'IY G W ( 8 03.44 F V = S P r N - I P I D 9 PP.5F S X t 1 3 2 5 7 ; S Z = E C C I R ( X - ~ J A E ( I ) * ~ P ~ ~ ) ; S Z = t C O h ( X - l r ( A E ( 1 ) * 1 P t 6 ) - F C O R I 02.52 S Z = F C O ~ ( X - ~ J A F ( ~ ) * 1 P t 3 ) i S Z = C C O h ( X - 3 r ( A l . ( P ) * l @ t b ) - h C O h ( X - 4 ) * 1 i W O ) f i P . 5 3 S Z = F C O F i < X r H b * l @ t 6 ) 1 S Z = C C O I < ( X + l r ( h C * l P t / ) - l ' c O H ( X ) * l P ) W.55 S Z = F C O H ( X + P , R N * l 1 ? 1 3 ) i b Z = b C O h ( X + 3 r ( f i h * l P f 6 ) - t C D h ( X + ? ) * l P @ @ ) f i P . 5 1 F' I * ~ J H J D 36 D P . 5 9 S Z = F C O H ( X + 2 P , M P ) ; S P n ( M A - k C P h ( X + 2 P ) ) * 1 0 P i S Z ~ b C O F > ( X + 8 1 r l 3 ) f'+R*hl S Z = F C O R ( X + P ? . A t i ) i S B = ( A c i - b C O h ( X + ? ? ) ) + 1 @ t 3 ; S Z = h C O H < X + ? 3 , R ) e2.63 S X = k C O H < X + 2 4 r T F * LOCI); S H = ( 1 t * 1 0 1 5 ) - F C O H ( X + Z U ) * l P t 3 i S Z=kCnh(X+i?SE 0 P . 6 5 S ? = h c f l n ( X + ? 6 r [ q f * l P S 4 ) ; S Z = b C O H < X + 2 7 s D * l @ t 3 ) e 9 . 7 5 o
P R . 3 2 T XY .P5rV+lrFCOhlTO+V+1)/?8iS )!=A;1. J o V - I D V+R;S XmX+( C C C b h ( R S * J ) - 1 I I m.35 T " " X / l 6 * " " F C O H ( H A + V + I ) / l ~ 1 @ O r !
C"9*RI, T V + l r b C O H ( O + V + 1 ) / 5 1 S X = @ i F J=U-7,b+H;b X = X + ( E C P f i < V L + J ) - l P ) P ) P I / ? 1 3 P P9.35 T " " X / l h r " " F C O S < E C D H < H A + V + 1 ) / l C l n C I ) J I
? 3 * @ 5 S P = F C O E < E A + I - 1 ) / 1 C 4 0 @ 2 3 . 1 P 5 X=(PCOb(hA+I+I)-ECCR(hA+I-3) > * 1 f i i b I . * S C O h ( H b + I - l r X + 1C4P)EJ 23.891 S Z = k C C I H < V E + f - ~ J < X * ~ * F S I N ( P ) ) + ~ ~ ? P P )
