Post on 06-Sep-2018
AN ADJUSTABLE SIX-BAR MECHANISM WITH VARIABLE INPUT SPEED
FOR MECHANICAL FORMING PRESSES
Ren-Chung Soong
Department of Mechanical and Automation Engineering, Kao Yuan University
Kaohsiung, Taiwan, R.O.C.
Contact: soongrc@cc.kyu.edu.tw
Received April 2008, Accepted November 2008
No. 08-CSME-12, E.Le. Accession 3050
ABSTRACT
An adjustable six-bar mechanism mechanical press, in which one of its link length can be adjusted
and its driving crank also can be varied according to different forming processes, is proved to be feasible
in this paper. By properly designing the speed trajectory of the driving crank and the adjusting
magnitudes of the adjustable link in length, the desired kinamatic characteristics of the ram can be
obtained. The examples are given to verify its feasibility and effectiveness in practical applications.
Keywords: Adjustable mechanisms; Variable input speed; Mechanical Presses
UN MECANISME ASIX BARRES AJUSTABLE AVITESSE VARIABLE POUR
PRESSES MECANIQUES DE FORMAGE
RESUME
Cet article demontre la possibilite de concevoir un mecanisme asix barres ajustable, dont la longueur
d'un des maillons peut-etre ajustee et Ie bras de levier modifie pour s'adapter aux differents procedes de
formage. En evaluant convenablement la vitesse de trajectoire du bras de levier et l'amplitude de
l'ajustement de la longueur du maillon ajustable, on peut obtenir les caracteristiques cinematiques
souhaitees. Des exemples sont donnes pour verifier en pratique la faisabilite et l'efficacite de
I'application.
Mots-cles : mecanismes ajustables; vitesse variable; presses mecaniques
Transactions ofthe CSME Ide fa SCGM Vol. 32, No. 3-4,2008 453
1. INTRODUCTION
The metal forming press is one of the most commonly used manufacturing machineries today. In
general, there are two major types of press that have been developed for practical industrial applications,
the one is the mechanical presses the other one is hydraulic presses. The former is fast and energy
efficient, but lacks flexibility. The latter is flexible, but is expensive to build and to operate. There are four
types of metal forming process such as cutting, bending, deep drawing and forging. Among these
processes, the different kinematic requirements of ram have to be satisfied such as trajectories of position,
velocity and acceleration in a cycle. An existing mechanical press usually only is designed for the one of
the four processes mentioned above. Moreover, the kinematic characteristics of the ram are functions of
the link lengths and the kinematic characteristics of driving link of the presses. Therefore, if we can
design a press in which one of its link length and trajectories of position, velocity and acceleration of the
driving link can be adjusted according to different forming processes, the higher flexibility of applications
will be obtained. This is a reasonable choice instead of redesigning the new presses when an existing
press has to satisfy different types of forming processes.
Many researches have been conducted to study mechanical forming presses. Some works focus on
either Finite Element Analysis (FEA) or structure improvement of the presses. For example, computer
simulation and dynamic analysis are performed for a single-point-drive eccentric press [1]. A Lagrange
multiplier method is proposed to synthesize the dimension of a drag-link drive mechanical press for
drawing [2]. A design procedure, which combines the linkage synthesis and the trial and error method to
optimize the dimensions, is developed for the nine-bar linkage press [3]. Also a two phase optimization
technique is proposed to reduce the shaking force and shaking moment of the drag-link mechanical
presses [4]. Some researchers are devoted to improve the performance and to raise flexibility of practical
applications by varying speed trajectory of the input link for mechanical presses. Such as, Yossifon and
shivpuri [5-6] discussed the design, analysis and construction of a servo-motor controlled mechanical
press for precision forming. Doege and Hindersmann [7] designed the non-circular gears to drive
mechanical presses for optimizing kinematics. Van and Chen [8-9] proposed a novel approach by varying
the input speed of the crank to make the ram's motion suitable for both deep-drawing and
precision-cutting processes. Recently, the concept of the hybrid mechanism, also call controllable
mechanism or hybrid machine, is applied to design the mechanical presses. Du and Gue [10] designed a
2-degree-of -freedom seven-bar linkage mechanism whose performances are programmable, including
the trajectory and velocity of the ram driven by a large constant speed motor and a small servomotor. A
Genetic Algorithm to optimize the design parameters of the linkage is also included. Meng et al. [11] used
the inverse kinematic analysis and optimal synthesis method to design a hybrid driven a seven-bar linkage
mechanical press. Mundo et al. [12] presented a design method to optimize kinematics of mechanical
Transactions ofthe CSME Ide la SCGM Vol. 32, No. 3-4,2008 454
presses by optimal synthesis of cam-integrated linkages.
This paper proposes a new design concept for mechanical forming presses that the driving link is
driven by a servomotor and the one of its link length can be adjusted. The adjustable link is a screw-nut
link also driven by servomotor corresponding to the driving link. By properly designing the kinematic
trajectories of driving crank such as position, velocity and acceleration and determining the magnitude of
the link length of the adjustable link, the desired forming performance of an existing press can be
obtained for satisfying different type forming processes.
2. THE ADJUSTABLE MECHANICAL FORMING PRESS
An adjustable mechanical forming press defined in this paper is a six-bar mechanism in which there is
a screw-nut link its link length can be adjusted and its speed of driving link also can be varied and driven
by servomotors as shown in Fig. 1.
Fig. 1 An adjustable mechanical forming press
3. SPEED TRAJECTORY OF THE INPUT CRANK
We assume the input link of the adjustable mechanical forming press is a crank. In this paper, theposition trajectory ofthe crank is defined by an nth order Bezier curve [9] ¢J (t) with parameter t as
follows:II
¢J(t) = Le; .R;,II (t);;0
Where
Transactions ofthe CSME Ide la SCGM Vol. 32, No. 3-4, 2008
(1)
455
n'· .B. (t) = . . t' . (1- t)n-II,n ., ( ')'Z.· n -Z .
t E [0,1] (2)
in which¢ (t) is a Bezier curve that represents the angular displacement of the input link defined by
control points e;. Parameter t is regarded as the normalized time from 0 to 1. Since the Bezier
curve is nth order differentiable, this guarantees smoothness of the entire motion. Hence, the angularvelocity wet) and acceleration aCt) of the input link can be derived by continuously differentiating
Eqs. (1) and (2) with respect to the time as follows:
Where
w(t) = d¢(t) = Ie; .dBi,n (t)dt i=O dt
d 2¢(t) n d 2B. ((t)aCt) = ="e . I,n
dt 2 f::t I dt 2
dB. (t) n' . 1 .',n = . . t'- . (1- t)n-Idt (i -1)!-(n - O!
n' . .---'--. t' . (1- ty-'-Ii!-(n - i-I)!
(3)
(4)
(5)
n! .ti-2 .(I-t)n-i _ n! .ti-I.(I_t)n-i-l(i-2)!-(n-i)! (i-l)!-(n-i-l)!
n' n'- . . t i-1• (1- tr-i-l + . .t i .(1- tr-i-2
(i -1)!'(n - i-I)! i!-(n - i - 2)!
(6)
After doing the kinematic analysis of the adjustable mechanical forming press by vector loop approach,
all the kinematic magnitude (positions, velocities and accelerations) of each movable link can be obtained
as function of the driving crank motion.
4. THE ADJUSTING MAGNITUDE OF LINK LENGTH
In order to be corresponding with the angular position of driving link, the adjusting magnitude of the
adjustable link in length is also designed with Bezier curve. The adjusting magnitude of the adjustable
link in length !1r is also defined by an nth order Bezier curve !1r(t) with parameter t the same with
equation (1) as follow:
n
!1r (t) = I A; . B;,n (t);=0
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456
Where !:!r(t) is a Bezier curve that represents the adjusting magnitude of link length of the adjustable
link defined by control points A.i .
5. DESIGN OF OPTIMIZATION
The optimization procedure is applied to determine the design variables to obtain the desired forming
performance for an existing adjustable six-bar mechanical forming press. For the purpose to fmd the
proper speed trajectory of the driving crank and the adjusting magnitude of the adjustable link in length
the general optimization equations can be defined as follows:
n/
Minimizing f(eoe, ..,en_l,en,A.o,A.l,. ..,A·n_I,A.n) = Lobi;;=1
Subject to
i=l, ... ,nc
i = 1,. oo,ng
(8)
(9)
(10)
Where obi; is the desired performance objective function, n; denotes the number of the desired
performance objective function, nc and ng denote the number of equality and inequality constrained
equations. Note that the equality and inequality constraints are defined to obtain the desired
performance.
Up to here, all information for optimization is derived. Any optimization methods can be used to
determine the design variables. A sequential quadratic programming subroutine [13] is applied to solve
design variables in this approach.
6. EXAMPLES AND DISCUSSIONSHere examples will be demonstrated to prove the feasibility of this proposed approach. A 10lb order
Bezier curve (with 11 control points) is used to represent the trajectory of the input crank and the
adjusting magnitude of the adjustable link in length. It is clear that eo, ,.1.0' en and A.n are the
boundary conditions for speed trajectory of the crank and the adjusting magnitude of the adjustable link in
length in a consecutive cycle. Therefore, eo = eudc ' ,.1.0 = 0, en = eudc + 27r and A.n = 0 must be
Transactions ofthe CSME Ide fa SCGM Vol. 32, No. 3-4, 2008 457
specified, and elide is the corresponding crank angle when the ram is at upper dead center. And the
average speed of input crank is set to be 60 rpm in all examples. An existing press in which the link
length of link 4 is adjustable and its link lengths are shown in Fig. 2 and Table 1, respectively. In these
two examples, the goal is to design the proper input speed trajectory of an existing six-bar mechanism
forming press shown in Fig. 2 to have the desired ram performance: smooth pressing to avoid large
transient force and vibration, long dwelling time with lower forming speed during its work stroke over a
relatively large rotational angle of the driving link to ensure uniform metal deformation and to minimize
spring back and driving torque.
Table I Dimensions of an existing press
fl (mm) f2 (mm) f3 (mm) f4 (mm) rs (mm)
80 42.16 82.35 46.39 59.8 251.84 150 148 20
d
Fig. 2 An existing adjustable mechanical forming press
Example 1
In this example, in order to prolong the life of dies, to raise the quality of products, to lower the
vibrations and noises of the presses and to decrease the loading of the brake of the presses in the return
stroke, the work is designing the speed trajectory of the driving link and the adjusting magnitudes of
adjustable link in length for an existing six-bar mechanism mechanical press to keep approximately
constant speed of ram over the specific period before and after forming and to minimize the peak of
acceleration of the ram.
The objective function can be defined as follows:
Transactions ofthe CSME Ide fa SCGM Vol. 32, No. 3-4,2008 458
Minimize f(B» ... ,B9 A, ,....,~) = peak of aram
Subject to
cZ (BI'".,B9 ) = az(O)-az(l) = 0
C3(el' ... ,e9,~,.... ,A9) =s(ta) =Samax =Semax
(11)
(12)
(13)
(14)
(15)
Where a ram is the linear acceleration of the ram, S denotes the displacement of the ram for the
adjustable press, samax and semax are the maximum linear displacement of the ram for the adjustable
press and the existing press, respectively, ta represents the normalize time corresponding to Sa max and
Semax' la is the link length of the adjustable link, lu and II are, respectively, the maximum and the
minimum link length of the adjustable link to satisfy the Grashof low for keeping the driving link to be a
crank, v denotes the linear velocity of the ram of the adjustable press, tds and tde represent the time
of the beginning and the end in two specific periods, e v and ea are small numbers and set to be 0.5 in
two examples. The first two constrained equations of equality are for having continuous angular velocity
and acceleration of the input crank in two consecutive cycles. The third constrained equation of equality
guarantees to have the same stroke of the adjustable press with the existing press. The first two
constrained equations of inequality keep the adjustable press to be a crank rocker six-bar press. The last
two constrained equations of inequality are in order to force the velocity of the ram to be an approximate
constant speed during periods from tds1 to tdel and from tdsz to tdeZ
The optimal control points of the speed trajectory of the driving crank and the adjusting magnitude of
link length of adjustable link are, respectively, shown in Table 2 and Table 3 in this example. The
magnitude and fluctuations of the angular displacement, velocity and acceleration of the driving crank are
shown in Fig. 3, respectively. The magnitude and fluctuations of the linear displacement, velocity and
acceleration of the ram are shown in Fig. 4, respectively. The adjusting magnitude of link length of
adjustable link is shown in Fig. 5.
Transactions ofthe CSME Ide fa SCGM Vol. 32, No. 3-4,2008 459
Table 2 The control points of the speed trajectory of the driving crank for Example 1
76.2 129.5 237.5 o 185.5 360 162.5 184.4 283.7
Table 3 The control points of the adjusting magnitude of the adjustable link for Example 1
65.23 0 0 0 0 0 0 0 o
·200r--~-~--,---,---,----r---,-----.------.---,
2 ------;
-_._---_.,,-----
, . .."'------'.----_._----· . .· . ., . .· . ., . .
, . ., . .· . .
-...... ' .:,. .....-->'\-_:_-----_!_-----~------~-- ---,------~----)<~~: -----
, , ' I '
'\ : ----- existing press : /' :
'\ : -- adjustable press :,' :------:- \,:--:------r-----1- -----~- -----y-----:---, \' , , , I' I
..:_----~-:------~-----_.:__ ._--~----};------;, \' , I I " ,, \ , , I I'
'\ • , 'I'
··\:,·1·····:/·····" , ,I" , .,~~';~--T-----y---
------0._---- .._--
, . ,------'- 0. -_._-----300
-320 '--_-'--_-'--_...L.._--'--_-'-_--'__'---_-'--_-'-_-'
o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Nonnalized lime
'0 -260
~E
~ -280g-o
E.s -240
~":;
I • , I. __ . ., ----- .. ----.-.--._-, I • ,
, I • ,I I , ,
I I , I
, ""------~-----,--" -- -~!'<. -.:-. --_..:- -_. --~- ----- ~------~---- _.; -----i l,,~,"~ ~ : ~ ~ ~ 1
--- +-/~:-------:----- :------i------i------i-----',' " .."
,'/1 ': ~] ~ ~"--_-'--_-'--_-'-_-1__-'--_-'-_--'-__'---_-'--_-'
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Normalized lime
5 -- ----~------:- -- ----:- - -.: ----- existing press ,
~ : -- adjuslable press :4 ------~------, - ----,-- -- - --,-- - - - - -:--- --
~u :::'0 ~ __ . __ .~_. .~._. _..... _.
~E
~g.iJ
'":;g>«
(a) (a)
i
,',• I • : , :: \ , , :• ----','-' ----,-------,-------,--- ----,--- ----,-, {A,. , ., _
, , 'I \' , ,
: ----- existing press :: \: : :
-- adjuslable press: :: \ ' :-._._-~. - ----~ -- --- -~------~."----~ - ... -~-- .. _.;~\-----
: :: 1 '\: .' \, I'
.. ----~. - -- - -~ -- --- -~ - -----~. --- --~ _. -_. :~_ .. -_.:, , I , , J' ,
': :::, ,I
--- ---~- --_. -~ - -- - - -~ - -- - - -~ - - - -- -~ :-~ - - ----~ - - - -- -~ - - - - -.:--- - - ~"'''', : " : : : '
' ..: /~ ~ : : :
... L,·~,_._T>/:···-·····~-···-····
800
600
~
~ 400
.sEl!! 200":;'0.2:-gQj>
----- existing press
-- adjuslable press
· , ,_____ L. '. ,__
· , ,· , ,
14,--,..--.,.---r---,----,---,--,---.,.---,---=",",
12 -- ---~------~------~ -r-'--.=..--'-'O".=..--",-.=..--",''''"-"'--==-=;
.>f.Cl!!o'0
~ 6 -·-:::-·-·t':':'"·-:· ~-_"':::--":~:-.:-.-::~.-:::-:-.-:~:-.-:-::~_-:::-----:!':':":::::'~.~ " , ,
ffii 4 ····_-t------:--- ------.'.-- ... , ------:------«
0'~ 10 ..
l
0 -4000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized lime Normalized lime
(b) (b)
Transactions ofthe CSME Ide fa SCGM Vol. 32, No. 3-4, 2008 460
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Normalized time
20000 r-........,.--,---,--..,---r--r----,----r--,-,--,
15000 ----- ----- ----- ----- ------;-----:l------~----- -----,------~ : :~ :~ ----- existing press I 1'1 '
E -- adJ'ustable press : : :1 :E ' ,'I '
E 10000 - ----:------~·_----~------~-·-·--~----1-~:-----~----- ------,------
~ ~'~ j j i ! \ ;
'0 :,:::: : ~ :.9. 5000 --- _..:- -- _. - .:- -- - - - -:- --- --.; - - - --- +. ---l-r -} --- -:. ---_. ----- ---- ---... :::::: : ~ :~ ."" I' I I
~ ,:://(---~\ i : ~ ~ , _o ~~~-:_-~~~~~;;;;!- -rOOM_Or ~I--r--\! ,i~ __--~----
: : : : ' : \ : ,,: :
: : : \ :,/: I
, I I \" I
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Normalized time
(c)
Fig 3 The angular displacement, velocity and
acceleration of the driving crank for Example 1
(c)
Fig 4 The displacement, velocity and acceleration of
the ram for Example 1
E 30 ,---,---,---,-----,----,----,.----,.----,.----,.---,.§.
0.90.80.70.4 0.5 0.6Normalized time
0.30.20.1
, ,
~Vl- 5 ----.-~-------:-. ----~-- ---~-------:-------~------~-------~.----.~---- .., , , : : ; , , ,
"'6'IIIQ).<:: 0 ~--'-_...J-. _~_.i_.._ _=::::...oio.__....._ ......_ .....__J
f- a
, .! 25 -- - : - - - -- - ~- - --- --~~~~~- ~;i~~;~~-~;~~~-~--- __ oj ------
i ,." --adjustable press :
.E 20 - - - - -! ---- --:-- -----t-- --- -:-------:-- -----:-- ----t- ----~--- --- (- ---f; : :::::::C) , ""'"c: .".".,.Q.) ., I , , , • • •
:;;; 15 - ----~------~- -----~------~-------~------~------~-------~------~------
:§ :':::::':'0 : : : :: ::G : : : :: :'0 10 -----:------,----- -~------~-------~------~------,-------~------~------.2 :: :
'"'"E
Fig 5 The adjusting magnitude oflink length of the adjustable link for Example 1
Example 2
ill this example, in order to ensure uniform metal deformation and to minimize spring back and driving
torque, the work is designing the speed trajectory of the driving link and the adjusting magnitudes of the
adjustable link in length for an existing six-bar mechanism mechanical press to keep approximately zero
speed of the ram over a specific period before and after forming and to minimize the peak of acceleration
of the ram.
The objective function is the same with Example 1. The constrained equations are also the same with
Example 1 from Equation 10 to Equation 13 except Equation 15 as follow:
Transactions ofthe CSME Ide La SCGM VoL. 32, No. 3-4, 2008 461
(16)
where a denotes the linear acceleration of the ram for the adjustable press, Sv and sa are small
numbers and set to be the same value with the example 1. The purposes of the three constrained equations
of equality and the first two constrained equations of inequality are the same with example 1. The last
constrained equations of inequality are in order to force the ram to have an approximate dwelling forming
period from tds to tde .
The optimal control points of the speed trajectory of the driving crank and the adjusting magnitude of
link length of adjustable link are, respectively, shown in Table 4 and Table 5 for this example. The
magnitude and fluctuations of the angular displacement, velocity and acceleration of the driving crank is
shown in Fig. 6, respectively. The magnitude and fluctuations of the linear displacement, velocity and
acceleration of the ram is shown in Fig. 7, respectively. The magnitude and fluctuation of link length for
adjustable link is shown in Fig. 8.
Table 4 The control points of the speed trajectory of the driving crank for Example 2
68.2 55.6 260.3 230.6 74.4 242.6 261.9 142.8
Table 5 The control points of the adjusting magnitude of the adjustable link for Example 2
70 5.32 0 0 0 0 0 0
291.8
24.87
From the design results as shown in Fig. 4, the ram of the adjustable press keeping an approximate
constant speed before and after forming can be verified in Example 1. Therefore, the goal of Example 1,
prolonging the life of dies, raising the quality of products, lowering the vibrations and noises of the
presses and decreasing the loading of the brake of the presses in the return stroke, can be certainly
obtained. According to the design results as shown in Fig. 7, the ram of the adjustable press having an
approximate specific dwelling period including before and after forming is proved in Example 2. The
purpose of Example 2, to ensure uniform metal deformation and to minimize spring back and driving
torque, can be surely reached in Example 2.
Moreover, the peak of acceleration of the ram of the adjustable press is substantially minimized in two
examples as results shown in Fig. 4 and Fig. 7. The trajectories of angular velocity and acceleration of
driving crank are continuous in two consecutive cycles coincide with our design constraints as shown in
Fig. 3 and Fig. 6.
Transactions ofthe CSME Ide la SCGM Vol. 32, No. 3-4, 2008 462
From the results, apparently, it is not necessary to redesign the link dimensions when the design
requirements have been changed. We just have to find out a new set of control points of speed trajectory
of the driving crank and the adjusting magnitude of link length of the adjustable link by optimization
procedure for an existing adjustable press.
7. CONCLUSION
An adjustable six-bar mechanism press, in which one of its link length can be adjusted and its
driving crank also can be varied according to different forming processes, is proved to be feasible in this
paper. It can be a new choice for metal forming processes. By properly designing the speed trajectory of
the driving crank and the adjusting magnitude of link length of the adjustable link with Bezier curve can
satisfy the kinematic requirements of the ram for different forming processes. That makes the adjustable
six-bar mechanism presses programmable and adjustable and increases the flexibility of practical
applications. Moreover, the linear acceleration peak of the ram can substantially minimized, it is excellent
for dynamic forming performance to the adjustable forming presses. But the cost has to pay is to
overcome the problem of the control technology for the driving crank and the adjustable link
simultaneously.
, , ,, , ,
5 --- - -- ~ -- -- - - ~ - -- - - .: -- -- - _: -- - - - _: - -- - - - ~-- - - - - ~ - - - -- -; - - -- - -; --/: : ----- existing press : : : ,,~"
j :: -- adjustable press: : : / :i 4 .. _- .-~-._---~.-----:--_. --;------; - -- .. _~-_ ... ·r-·~;;,F~---<-----~ :::::: ,~/ : :~ 3 ------[------[------~------r------:--~),~:-'--f--- r----r-----~ "".,' "
~ 2 --. - -- ~ - -- -. - ~ _. - -- - ~ -- --: --;;,~~_. - . - - ~ - - -- - - ~ -- - . - - ~ - . - - -- t-----% : ;*,',:::'
i:J>__<CJi I ' I',,," , , , . , , ,
,,/! ~ : ' : ~ : l ~_1l<-----'-_-'--_-'------'_--'-__-'-_-'-----'-_-'----'
o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Nonnalized time
(a)
-200,-~-~-~---,---,---~-.-----,-~-------,...........~
",+\+-----+···--~------~------~------f---)<-- ~-----
, \: : ----- existing press : ,': :E ,\,: -- adjustable press : ,': :i -240 c_ ----c\;\~,-f------r------r------r-----y----:- ----:------ "\""'0 •
i:••••••I••••••i••••J\\'\<.i•••••V.'·•••••I••••••I•••••. , , , .. , , . ,• , I • ,
-320 '----'---'----'------'---'---'---'------'----'---'o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Nonnalized time
(a)
Transactions ofthe CSME Ide fa SCGM Vol. 32, No. 3-4, 2008 463
-4oo0'---:"'-:----''?::--:'0.-=-3--:0:'-.4,...--=0':.S:--0:'.-=-6--:0':.7::----:'0.'::e--:0~.g=--:
Nonnalized time
----- existing press
-- adjustable press, , ,, , , ,... ----_._ ..... '_ .. - ...._----, , , ,
: : : '
----~-----~----~-----:-----7
°0'---0"-.1---0L.2--0-'-.3--0-'-.4--0--'-.S----'0.-6-~0.'-7--oL.e---:o-'-.g--'
Nonnalized time
600 ._--_.'.----_. __ . __ .
: ----- existing press
, __.~ a~~~::~~le_~~~s.
(b) (b)
20000,.--,---,--....-,---,-.,.-....-...,---,-,
, , ,_...--_._ .. ------,.-----.
, , , ,_···-·,-··--·r------,·--·--l-·, , , ,
: ----- existing press
: -- adjustable press
, , . , ,-._~ _.. _.~. _.... ~ .. _ .. -:... _ .. ~ ...
, 1,1 , , ,, ,,1
"I,"':1I ,I ,- -. - -... • t ~ .. - .
1'1 '
: ::" I" ,
.-j.. -.~ J.\I' ,
: : ~, ' I, ' II' ,
0'-"';".lo-+'--r~.. -L. -~,,' \:, '
\ ~ /'. '-50000'----,0-'-.1--0--'-.2---..,.0."-3---:0-'-.4--0,....-=-5-.,.0"-.6--"0"'=.7,---0,....-=-e-"'O."-g---'
Nonnalized time
15000
".c155 5000
~§«
1:~.sE ooסס1 ..~
, , ,_'•• J ~, , ,
, , ,_._'•• __ ._J l
, , ,, ., ., ., ,, ,, ,, ., ", , , , ,.,-- .. ' ,-"---' ····-r-·----,---, , ,
, , ,, , ,, , ,, , ,
----- existing press
-- adjustable press
-150 '--_'--_-'-_-J'__,__...L...._---'---_-L_--'__'----..J
o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 o.e O.gNormalized time
(c) (c)
Fig 6 The angular displacement, velocity and
acceleration of the driving crank for Example 2
Fig 7 The displacement, velocity and acceleration
of the ram for Example 2
Transactions ofthe CSME Ide la SCGM Vol. 32, No. 3-4, 2008464
-----:------: -_ .. ;-- --:··_-":'-·--1'", , , , , ,, , " ,: :' :, ,
I , , ,. _.. -,.. .. ~ .. - .. - - - -.. - _. - -.- - - - - .- -_., ,
~~ 15
15
" ,, .,.,.,~ 25 •. _.-;•••.• - "-- -- _w_: w J __ ••• '._. _ .'--._ •• -:_ •• - ~-
.2!: : ----- existing press : •~ : - adjustable press :
~ 20 • _.~. __ •• " •.• - -:"":'- :". --:- .• _-~---_.~-_.
, : : : :, , ,
, ,, , , , I , , , •
.~ 5 .. ---:- •• -~ .-- ~--- -;... ---;---_.:-_. -~_. _.:-._ .• ~_.-
~ j ~ ! ' i ' : ~ ~nl " I • , ,
~ O-~-_:_i ; ; ~~.... 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Normalized time
Fig 8 The adjusting magnitude oflink length for adjustable link for Example 2
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