Ryan Muller - Optimization of a non-Grashof compound four bar linkage mechanism for cutting surgical...
-
Upload
ryan-muller -
Category
Documents
-
view
207 -
download
3
Transcript of Ryan Muller - Optimization of a non-Grashof compound four bar linkage mechanism for cutting surgical...
STAFFORDSHIRE UNIVERSITY
Final Year Project (BEng) Optimization of a non-Grashof compound four bar
linkage mechanism for cutting surgical wires
Ryan Muller
Award: Mechanical Engineering
Student number: 08003271
Supervisor: Professor Peter Ogrodnik
4/7/2012
Final Year Project (BEng) 2012
a
Abstract
The following paper investigates the improvement of a non-Grashof conforming compound
four bar linkage mechanism by modification of the input link fixed pivot of the external
mechanism. The mechanism in question is an integral sub assembly found in a pair of wire
cutting pliers from the company GEOMED, a manufacturer of orthopaedic equipment, which
is used in order to magnify the input force by a factor of 9.5 in order to shear 2-3mm 316L
surgical wire.
Theoretical calculation is made of the original configuration in order to obtain a benchmark
value for the mechanisms mechanical advantage, which is then compared to a software model
using Working ModelTM
. The software model is then modified using a matrix of input link
fixed pivot coordinates in order to obtain an optimum position.
Finally, through a practical investigation, a Wheatstone bridge is created in order to measure
tensile strain and therefore the force output of the system indirectly, through use of a rapid
prototyped planar model. The results show that the revised input link fixed pivot position
yields a 37% increase in output force when compared to the original position used by
GEOMED and allows the product to be scaled by a factor of 0.73; allowing the manufacturer
to save on material and production costs.
Final Year Project (BEng) 2012
b
Acknowledgements
First and foremost, I would like to thank Professor Peter Ogrodnik in giving me the
opportunity to carry out this project. Along with its challenges and points of triumph, the
project has allowed me to better myself in terms design, problem solving, research methods
and testing, which has allowed me apply all of the skills gained from modules taught at
University.
A special thanks also to the lab technicians in F12 at Staffordshire University, for providing
support and guidance during experimentation and demonstrating procedures for various
aspects of testing the physical prototype.
Finally, I would also like to thank my parents and friends for proof reading and suggesting
areas of improvement in order for ideas and statements to be conveyed as intended for any
reader.
Final Year Project (BEng) 2012
I
Contents
List of figures ..................................................................................................................... V
List of tables ..................................................................................................................... IX
Nomenclature ................................................................................................................... IX
1 Introduction .......................................................................................................... 1
1.1 Development of cutting instruments with respect to cutting force ............................. 1
1.2 A brief history of kinematics ....................................................................................... 5
1.3 Linkage Mechanisms................................................................................................... 5
1.4 The four bar linkage .................................................................................................... 8
1.5 Practical investigations regarding four bar linkage mechanical advantage .............. 10
1.6 Degrees of freedom of planar mechanisms ............................................................... 13
1.6.1 Grashof’s criterion ........................................................................................................ 14
1.7 Dual or compound linkage mechanisms ................................................................... 15
1.8 Classical and current methods of linkage synthesis and analysis ............................. 15
1.8.1 Computer aided linkage synthesis and analysis ............................................................ 16
1.9 Existing Patents review ............................................................................................. 17
1.9.1 Non-Surgical cutting instruments ................................................................................. 17
1.9.2 Surgical cutting instruments ......................................................................................... 24
1.10 Current state of the art ............................................................................................... 29
1.11 Ergonomic analysis of hand tools ............................................................................. 31
1.12 British standards for surgical cutting instruments and maximum loading ................ 33
1.12.1 Stainless steels for surgical cutting instruments ........................................................ 33
1.12.2 Guideline cutting forces for lever assisted cutting pliers .......................................... 34
1.13 Conclusions from background literature and market research .................................. 36
2 Project aims and objectives based on background literature.............................. 37
2.1 Generalized method layout to fulfil project objectives ............................................. 38
Final Year Project (BEng) 2012
II
3 Hypothesis .......................................................................................................... 39
4 Instantaneous transmission ratio based on the kinematic constraint equation ... 40
5 Linkage configuration analysis of Geomed-Gold Cut wire cutting Pliers ......... 43
5.1 Apparatus/Software required for obtaining linkage point coordinates ..................... 44
5.2 Method of obtaining linkage point coordinates / internal angles .............................. 45
5.2.1 Preliminary initial measurement with ruler: ................................................................. 46
5.3 Hercules Gold-cut join coordinates ........................................................................... 47
6 Reverse Engineering of Geomed wire cutting pliers ......................................... 48
6.1 Product design specification...................................................................................... 48
6.2 CAD development ..................................................................................................... 51
6.3 3-Dimensional computer model summary specification ........................................... 57
7 Theoretical kinematical and torque transmission analysis ................................. 57
7.1 Geomed internal four bar linkage transmission ratio (relaxed position) ................... 58
7.2 Geomed internal four bar linkage transmission ratio (3mm offset) .......................... 59
7.3 Combined mechanical advantage of Geomed wire cutting pliers ............................. 60
7.4 Mechanical advantage using lever ratio equation from BS 3087-7:1996 ................. 61
8 Excel analysis of internal linkage mechanism ................................................... 62
9 Working model analysis of standard configuration ........................................... 66
9.1 The test model and initial conditions ........................................................................ 66
10 Input link fixed pivot modification .................................................................... 67
11 Modification of Working Model analysis setup ................................................. 68
12 Working model results using input link matrix .................................................. 70
12.1 Output force using rigid member configuration ........................................................ 70
12.2 Output force using spring configuration ................................................................... 72
12.3 Theoretical results discussion.................................................................................... 72
Final Year Project (BEng) 2012
III
13 Initial rapid prototype in order to compare theory with practise........................ 73
13.1 Creation of planar mechanism model in Pro EngineerTM
......................................... 73
13.2 Kinematic analysis in CAD of revised input link fixed pivot location and initial
problems encountered .......................................................................................................... 75
13.3 DXF drawing creation and CNC laser setup for initial prototype............................. 79
13.4 The finished planar acrylic model for analysis ......................................................... 80
14 Finite Element Analysis of planar mechanism ................................................... 81
14.1 FEA Analysis using COSMOSTM
............................................................................. 81
14.2 FEA analysis comparison using MSC NASTRANTM
............................................... 83
14.3 Comparison of Finite Element Analysis results ........................................................ 84
15 Method of testing the physical prototype ........................................................... 85
15.1 Preliminary equipment setup and calibration ............................................................ 86
15.1.1 Creating the Wheatstone bridge for strain measurement .......................................... 86
15.1.2 Calibration of the strain gauge .................................................................................. 89
15.1.3 The final physical test setup ...................................................................................... 90
16 Results of testing the physical model ................................................................. 92
16.1 Discussion ................................................................................................................. 96
16.2 Comparing results with theory .................................................................................. 96
16.3 Fair test factors .......................................................................................................... 98
16.4 Anomalous results and limitations of the experimental procedure ........................... 98
17 Conclusions ........................................................................................................ 99
17.1 Recommendations ................................................................................................... 100
18 References ........................................................................................................ 101
19 Appendix .......................................................................................................... 107
Appendix 1- BS EN ISO7153-1:2001 (Metallic materials for surgical instruments) ........ 107
Appendix 2 – Full derivation of the four bar kinematic constraint equation ..................... 108
Final Year Project (BEng) 2012
IV
Appendix 3 – Four bar linkage force transmission ratio table data ................................... 109
Appendix 4 – Raw data for stress vs. strain when loading physical model ....................... 111
Appendix 5 - COSMOS Finite Element Analysis Report .................................................. 112
Final Year Project (BEng) 2012
V
List of figures
Fig. 1-1: Surgical scissors from the Huntington and Marsh manuscripts (Spink and Lewis,
1973) followed by a non-surgical example in a similar time period (Ward-Perkins, 1940) ..... 2
Fig. 1-2: Modification of blade design with introduction of bevel (Brunschwig, 1497)
followed by a decreased blade to handle length ratio by Woodall (1639). ................................ 2
Fig. 1-3: Curved and compound surgical scissors with adjustable angle (Savigny, 1800) ....... 3
Fig. 1-4: Bone cutting pliers with curved handles and assisting opening spring (Kirkup, 1998)
.................................................................................................................................................... 3
Fig. 1-5: Nickel plated bone cutting pliers followed by compound Stainless Steel gouge
cutters ......................................................................................................................................... 4
Fig. 1-6: A cutting mechanism based on the four bar linkage (Eckhardt, 1998) ....................... 6
Fig. 1-7: The standard four bar linkage model (Phelan, 1988) .................................................. 8
Fig. 1-8: Free body diagram of the four bar linkage (Phelan, 1988) ......................................... 9
Fig. 1-9: Maximum and minimum allowable transmission angle in a four bar linkage (Patel,
2011) ........................................................................................................................................ 10
Fig. 1-10: Example of an Elastrator (Midha et al, 1984) ......................................................... 11
Fig. 1-11: Variation of mechanical output of the system based on input force (Midha et al,
1984) ........................................................................................................................................ 12
Fig. 1-12: Early cutting pliers / pinchers followed by variant products (right) utilizing a four
link mechanism (Lindsay, 1874).............................................................................................. 18
Fig. 1-13: Ergonomic design patent as opposed to complex linkage mechanisms or an
increase in overall size (Smith, 1876) ...................................................................................... 19
Fig. 1-14: A compound mechanism design with adjustable internal spring-back mechanism
(Porter, 1880) ........................................................................................................................... 19
Fig. 1-15: Compound mechanism with interchangeable single fixing blades (Broadbooks,
1902) ........................................................................................................................................ 20
Fig. 1-16: A portable hand held compound linkage mechanism with patented inverted "J"
cutting head (Geddes, 1940) .................................................................................................... 21
Fig. 1-17: Hand held compound rod cutters for use in the building trade, Shurtleff (1975) ... 22
Fig. 1-18: Multi-functional transportable cutting pliers, Rowe (1981) ................................... 23
Fig. 1-19: Cutting/gripping pliers with adjustable rack configuration, Caravello (2008) ....... 24
Fig. 1-20: Surgical combination tool with interchangeable cutting heads (Koeth, 1905) ....... 25
Fig. 1-21: Small surgical pliers for use in Endodontic applications, Rosen (1960) ................ 26
Final Year Project (BEng) 2012
VI
Fig. 1-22: Surgical cutting pliers for use in jaw surgery and orthodontic procedures, Tippy
(1975) ....................................................................................................................................... 27
Fig. 1-23: The wire retention device proposed by Mooney (1999) for the cutting of softer
wires ......................................................................................................................................... 28
Fig. 1-24: A design patent for compound surgical wire cutters from GEOMED, 2003 .......... 29
Fig. 1-25: Grip force vs. handle size (Edgren et al, 2004) ....................................................... 31
Fig. 4-1: Generalized four bar linkage model for constraint equation derivation (Rothenhofer,
2010) ........................................................................................................................................ 40
Fig. 4-2: Modification of figure 4-1 to illustrate derivation of trigonometric terms ............... 41
Fig. 5-1: Geomed Hercules Gold-Cut wire cutting pliers (Geomed, 2011)............................. 43
Fig. 5-2: Geomed compound linkage break-down (Geomed, 2011) ....................................... 44
Fig. 5-3: Shadowgraph from Midland Metrology Ltd ............................................................. 45
Fig. 5-4: Physical Geomed wire cutting plier image ............................................................... 46
Fig. 5-5: Hercules Gold-Cut joint coordinates taken with shadowgraph ................................. 47
Fig. 6-1: The modelled LHS handle ........................................................................................ 51
Fig. 6-2: The modelled linkages .............................................................................................. 51
Fig. 6-3: CAD model representation of linkage constraints to set correct angles ................... 52
Fig. 6-4: CAD model of RHS cutter ........................................................................................ 52
Fig. 6-5: The modelled right hand side handle ........................................................................ 53
Fig. 6-6: The modelled Tungsten-Carbide blades .................................................................... 53
Fig. 6-7: The finished computer generated model ................................................................... 54
Fig. 6-8: Rendered images of the Geomed wire cutter computer generated model using the
standard linkage configuration ................................................................................................. 55
Fig. 6-9: Summary technical drawing to illustrate critical dimensions ................................... 56
Fig. 6-10: Model mass properties ............................................................................................ 57
Fig. 7-1: Internal four bar linkage analysis of Geomed wire cutting pliers ............................. 58
Fig. 7-2: Internal linkage angles for 3mm cutter offset ........................................................... 59
Fig. 7-3: Transmission quality compared to claimed value by Geomed (Geomed.de, 2011) . 60
Fig. 7-4: Cutting end gap between blades based on BS 3087-7:1996 ..................................... 62
Fig. 8-1: Torque transmission of Geomed wire cutting pliers with respect to input link angle
.................................................................................................................................................. 63
Fig. 8-2: Working model representation of internal mechanism in starting position .............. 64
Final Year Project (BEng) 2012
VII
Fig. 8-3: Working model representation of internal mechanism in maximum force
transmission position ............................................................................................................... 64
Fig. 8-4: Working model representation of internal mechanism in negative torque region .... 65
Fig. 8-5: Illustration of non-Grashof conformance .................................................................. 65
Fig. 9-1: Working model analysis of original Geomed linkage configuration ........................ 67
Fig. 10-1: Modification of input link fixed pivot in order to create matrix grid for data
collection .................................................................................................................................. 68
Fig. 11-1: Measurement anomalies using the spring setup in Working model ....................... 69
Fig. 11-2: Rigid member setup in Working model for increased repeatability between tests . 69
Figure 12-1: Values on design model giving rise to highest output force when using rigid
member at cutting end .............................................................................................................. 71
Fig. 13-1: The planar model with relocated input fixed pivot ................................................. 74
Fig. 13-2: Bolt-on blade tips to eliminate shear condition of planar mechanism at the cutting
end ............................................................................................................................................ 74
Fig. 13-3: Insufficient cutter head travel relative to handle displacement ............................... 75
Fig. 13-4: adjustment position using data from table 6 to obtain input link fixed pivot location
yielding a significant increase in mechanical advantage of the mechanism ............................ 76
Figure 13-5: The finalized model to be laser cut to begin practical analysis followed by the
updated 3-dimensional model .................................................................................................. 77
Fig. 13-6: The final rendered model with modified input link fixed pivot positioning ........... 78
Fig. 13-7: DXF drawing template to be laser cut followed by the laser cut parts after
component placement revision to minimize waste .................................................................. 79
Fig. 13-8: The physical test model ........................................................................................... 80
Figure 14-1: Stress flow analysis of the original configuration and revised configuration ..... 81
Fig. 14-2: Stress analysis results at cutting head for each input link configuration ................ 82
Figure 14-3: FEA analysis of planar mechanism in NASTRAN with input link in original
position ..................................................................................................................................... 83
Figure 14-4: FEA analysis of planar mechanism in NASTRAN with input link in modified
position ..................................................................................................................................... 84
Figure 15-1: The Wheatstone bridge (U.A. Bakshi; A.V. Bakshi, 2003) ................................ 87
Fig. 15-2: The finished strain gauge with top-side and underside ........................................... 89
Fig. 15-3: Test setup for strain gauge calibration .................................................................... 89
Fig. 15-4: The final test setup in order to test the physical model ........................................... 91
Final Year Project (BEng) 2012
VIII
Fig. 15-5: The cutter head wire loop in order to measure strain .............................................. 91
Fig. 16-1: Strain vs. load for original configuration ................................................................ 93
Fig. 16-2: Strain vs. load for modified configuration .............................................................. 94
Fig. 16-3: Comparison of strain vs. load between original and modified configuration ......... 95
Final Year Project (BEng) 2012
IX
List of tables
Table 1: Common linkage designs employed by various manufacturers of surgical cutting
instruments ............................................................................................................................... 30
Table 2: Surgical steels suitable for wire cutting pliers (BSOL, 2011) ................................... 34
Table 3: Maximum permissible cutting force for lever assisted side cutting pliers (British
standards online, 2011) ............................................................................................................ 35
Table 4: Design requirements for 3-Dimensional model ......................................................... 50
Table 5: Output force in working model using rigid member (SPAR) .................................... 70
Table 6: Output force in working model using a spring .......................................................... 72
Table 7: Strain calibration ........................................................................................................ 90
Final Year Project (BEng) 2012
X
Nomenclature
Notation Definition Units (SI)
Force
Compliance equivalent load
Load to main pivot length
Main pivot to load length
Normal force
Coefficient of friction
Torque (Tension)
Linkage angle
Input rubber band stretch
Output rubber band stretch
Mobility of a mechanism
No. of links
No. of joints
Longest link in system
Shortest link in system
Length of remaining links
Handle span open
Handle span closed
Relaxed cutting jaw distance
-
-
-
-
Final Year Project (BEng) 2012
XI
Transmission angle
Stress
Transmission ratio
Resistor (circuit)
Current
Voltage
Galvanometer
Emf (Young’s Modulus)
Standard uncertainty
Standard deviation
Variance
-
-
-
-
-
-
Abbreviations
Mechanical advantage
Factor of safety
Tungsten mono-carbide
Final Year Project (BEng) 2012
1
1 Introduction
Wire cutting pliers are commonly used in industry in order to trim lengths of cable or wire
to a specific length. The design of the pliers will depend on the type of application and will
therefore need to meet specific specifications set by the manufacturer or the customer; this
will ultimately determine what size the pliers depending on the thickness or gauge of the
wire (or cable) to be cut.
An important design consideration associated with cutting pliers is that of the input force
required to shear a specific gauge wire. From simple lever theory, an increased handle
length relative to the distance between the cutting end and the main fixed pivot or joint will
provide a greater moment of rotation and therefore allow for lesser load to be applied to the
handles. However, in applications where space is limited, an increase in handle length
becomes an inefficient method of increasing the mechanical advantage of the mechanism;
therefore another approach is needed in order to maintain a high mechanical advantage or
force transmission ratio with no appreciable increase in size of the mechanism.
1.1 Development of cutting instruments with respect to cutting force
Surgical instruments form an array of tools from which the surgeon can carry out a variety
of complex tasks and procedures. Some of the most common instruments available to the
surgeon include Retractors, Forceps, Scissors and Rongeurs with the roles of retracting
bone or flesh, grasping and cutting respectively. Scissors in a surgical environment for
example are estimated to have been used as early as AD 1000 for the use of eye surgery
and C-shaped blades for tonsillectomy, as illustrated by Spink and Lewis (1973) based on
drawings taken from the Marsh [1271-1272] and Huntington manuscript [1465-1466];
early non-surgical scissors are illustrated by Ward-Perkins (1940) whereby a domestic
example was found at Tuna, Sweden at a burial site and dated between AD 800-850 based
on association of coins found within the area.
The instruments uncovered from the Marsh and Huntington manuscripts alongside the find
in Tuna, Sweden are illustrated in figure 1-1.
Final Year Project (BEng) 2012
2
According to Kirkup (1998), advancements of surgical wire cutters in order for increased
cutting capacity and efficiency were made by modification of the blade bevel and by
alteration of the cutter length relative to the handles; this allowed for more complex tasks
to be carried out and for an increased control of power over variations of tissue section
length. The highest ratio of 0.55 was most common for use during post-mortems where a
relatively low output force is required in order to shear through extended lengths of bowel
tissue followed by a ratio of 0.44 for use of cutting bandages. Lower ratios such as 0.3
were used for applications where a higher output force was needed at the cutting end and
include instruments used for bone cutting; these modifications are evident from the work
published by Brunschwig (1497) and Woodall (1639), shown in figure 1-2.
Fig. 1-1: (Left) Surgical scissors from the Huntington and Marsh manuscripts (Spink and Lewis, 1973)
followed by a non-surgical example (right) in a similar time period (Ward-Perkins, 1940)
Fig. 1-2: (Left) Modification of blade design with introduction of bevel (Brunschwig, 1497) followed
by a decreased blade to handle length ratio by Woodall (1639), right.
Final Year Project (BEng) 2012
3
Kirkup also goes to describe the importance of adjustable compound joints which were
used in conjunction with blade ratios of less than 0.2 for use in scissor action cutters and
for linear cutters in order for increased efficiency and customizability of transferring power
from the input load; an example of the implementation of compound joints is illustrated in
figure 1-3 from the work of Savigny (1800).
Since the 19th
century, the development of scissors and other cutting instruments based on
their linkage configurations did not change significantly. However, subtle changes to the
handle shape meant that a more comfortable grip could be achieved and thus a more
controlled power input; the mechanism was also assisted by an opening spring in order to
retract properly when cutting through dense tissues such as bone. An example is illustrated
in figure 1-4.
Fig. 1-3: Curved and compound surgical scissors with adjustable angle (Savigny, 1800)
Fig. 1-4: Bone cutting pliers with curved handles and assisting opening spring (Kirkup, 1998)
Final Year Project (BEng) 2012
4
Finally, an example of straight or linear (including compound) cutters, illustrated from the
work of Kirkup (from the manufacturers Arnold [1910] and Stille [1965]) are illustrated in
figure 1-5; these particular examples are Nickel plated and made from Stainless Steel
respectively.
The comprehensive study carried out by Kirkup illustrates the evolution of surgical cutting
instruments with minimal changes of the cutting tool design over a considerable time
period. The most noticeable changes arise from changes to the handle design (with respect
to the ergonomic properties of the product), modification of the number of joints (and more
importantly the customizability of the linkages) used and subtle changes to the design of
the blades.
In his other work on the evolution of materials used in surgical instruments, Kirkup (1993)
states that the first tools were most likely to have been made from Bronze with Steel
cutting blades, based on findings in Pompeii which date to AD 97. However, development
of the materials used in cutting instruments was needed due to ferrous metals corroding
and compromising the antiseptic qualities needed for surgery. More expensive tools would
have handles made from ivory, pearl or ebony during the 18th
and 19th
centuries with the
introduction of Nickel or Chrome plated blades which were introduced in 1883 and 1893,
with these materials being resistant to corrosion. Further sterilization was achieved by pre-
heating the instruments before use.
Fig. 1-5: (Above) Nickel plated bone cutting pliers followed by compound
Stainless Steel gouge cutters (below)
Final Year Project (BEng) 2012
5
1.2 A brief history of kinematics
The design of the surgical cutting instruments illustrated in figures 1-3 and 1-4 (with the
exception of the compound cutting pliers in figure 1-5) is based a type of linkage
configuration known as the 2-bar linkage and can be easily identified due to two handles
(or bars) with one fixed revolute joint. This design is essentially based on simple lever
theory and can be dated back to the time of Archimedes [ca. 287–212 BC] in which the
theory of mechanical advantage was based on that of the principles of equilibrium (such as
a simple seesaw with a fixed pivot); this theory was used in order to raise water from wells
and in order to lift various other types of loads not manageable by man himself (Chondros,
2010).
Since this time period, there have been numerous attempts in the history of Engineering to
categorize machine linkages according to their application or type of motion they produce.
Some consider a particular mechanism as a whole while others examine the mechanism as
basic elements. It is agreed by many, including that of Ceccarelli and Moon (2007) that
Leonardo da Vinci attempted to describe the first collection of machine elements in the
Codex Madrid, 1493. Over three centuries after publication of the Codex Madrid, Franz
Reuleaux [1829-1905], often considered “the father of kinematics” (Hanfried and
Mauersberger, 2009) went to describe the mechanism elements as a kinematic chain; this
concept was defined as a system where the motion of a particular element or part is
constrained by all the other adjacent elements.
Engineers and mathematicians have carried out analyses on various configurations of
mechanisms for particular uses with the aim of converting one type of motion into another,
primarily for the function to transmit a force in order to do work (as used during the
industrial revolution) and can be traced back to the time of James Watt [1736-1819], who
utilized linkage mechanisms (from the work of Newcomen) based on the application of
thermodynamics in order to convert pressure energy into mechanical energy. This
mechanism could then translate rotary motion into straight line motion which would
eventually be used on modern steam engines and beguile the minds of other scholars in the
development of machinery and tools, as illustrated by Ferguson (1962).
1.3 Linkage Mechanisms
A linkage mechanism can be described as a closed chain consisting of links (or bars) and
joints with the role of transmission of a particular input force and to provide a means of
Final Year Project (BEng) 2012
6
rotation respectively. In terms of scissors for example, the moving handles are described as
resistant bodies in which enough resistance to the input load is provided in order to allow
the mechanism to move (Eckhardt, 1998). Additionally, in order for a linkage system to be
defined as a mechanism, it is required that one of these resistant bodies remains rigidly
fixed and is known as a ground link, which constrains the other remaining links to follow a
predetermined motion path. In terms of scissors one handle is the ground and the other is
the remaining link.
With mechanisms consisting of more than 2 bars, the same rules still apply. Let us consider
the four bar linkage mechanism in figure 1-6 in the form of cutters where B does not move
relative to the ground and therefore is considered to be part of the ground. The 4 links or
bars are connected by 4 revolute joints and therefore form a 4-bar linkage; additionally, the
mechanism can clearly be seen to be a closed chain and is constrained by only one input
motion.
Suh and Radcliffe (1978) state that three common types of mechanical devices exist which
can be used as part of a mechanism, namely:
1. Gear systems where circular toothed elements in contact transmit a particular
motion between rotating shafts with the aim of maintaining a constant angular
Fig. 1-6: A cutting mechanism based on the four bar linkage (Eckhardt, 1998)
𝐹
𝐶
𝐿
𝐵
𝑃
𝐺𝑟𝑜𝑢𝑛𝑑
Final Year Project (BEng) 2012
7
velocity. However non circular toothed elements are also used for non-uniform
motion transmission.
2. Cam systems whereby a uniform input motion is transformed into a non-uniform
motion at the output. The input motion can be converted into shaft rotation, slider
translations or other specific follower motions by creating a contact between the
particular input cam shape and the follower.
3. Plane and spatial linkages for creating mechanical motions for a point or a rigid
body which can be used for three different types of task
a. Rigid body guidance whereby a body is guided through a series of
predestined positions in space.
b. Path generation. A specific mechanism in which a point on a rigid body
is guided through a series of points on a pre-specified path in space
c. Function generation. A type of mechanism whereby a specific output
motion is generated relative to a particular input motion
In the context of cutting instruments, these particular mechanisms consist of planar and
spatial linkages and can be described as function generators due to the output motion
relying on the type of input motion which is constrained by the configuration of the joints
in the system.
Final Year Project (BEng) 2012
8
1.4 The four bar linkage
According to Phelan (1988) the most common type of linkage used for planar movement
and function generation is the 4-bar linkage where the individual links can be classified as
a:
1. Rocker – A link which can only oscillate
2. Crank – For any link that rotates
3. Coupler – A link which connects a crank to a rocker or a rocker to a rocker
Figure 1-7 illustrates the standard four bar linkage model with an input crank A-D, a
rocker C-B and a coupler A-B.
It is usually the case that power must be transmitted through the linkage from the driver
(A-D) to the output or follower. Phelan also illustrates that if an assumption is made that
the parts within the linkage are frictionless and rotation is slow, that the effects of
acceleration and inertia can be considered as negligible. With reference to figure 1-7, link 3
is a “two-force” member which can only transfer a particular force to B via A and is either
in tension or compression.
Let us consider the output link which is rotating in a clockwise direction against a
counteracting torque from the output link. In order for the system to remain in
equilibrium, the sum of the torques about the output link fixed pivot must equal zero;
therefore the force on the follower as a result of a compressive or tensile force due to the
coupler link can be described by:
Fig. 1-7: The standard four bar linkage model (Phelan, 1988)
𝐴
𝐵
𝐶
𝐺𝑟𝑜𝑢𝑛𝑑
𝐷
Final Year Project (BEng) 2012
9
(1.0)
A free body diagram is illustrated in figure 1-8.
By inspection of equation (1.0), the component of the force acting long the coupler link
will have a minimum value when is equal to 90 and will increase as becomes smaller,
eventually becoming infinite as A-B approaches a parallel condition with respect to B-C,
however a maximum moment on the output angle is applied when is equal to 90 . The
coupler or Transmission angle is of particular interest to the engineer as a mechanism with
a small coupler angle will to lock or jam due to not being able to overcome friction; hence
angles of less than 45-50 are to be avoided (Ambekar, 2007). The positions where the
torque transmission has a maximum value are called Toggle positions and allow for high
degrees of mechanical advantage of the output relative to the input link and are favoured
in applications such as bolt cutters where a high output force is required from a relatively
low input force.
The concept of a useful transmission angle is clearly illustrated by Patel (2011) in figure 1-
9, whereby the maximum and minimum angles are illustrated in order to do useful work.
The input crank link rotates in a clockwise fashion and transmits a force along A-B
whereby the maximum moment is placed on B-Bo when is 90 . However, once the link
Fig. 1-8: Free body diagram of the four bar linkage (Phelan, 1988)
𝐹 𝐷
𝐷
2
𝑇
𝐴 𝐹
𝐹 𝐴
3 𝐵
𝐹
𝐵
4
𝐹 𝐹 𝐶
𝐶
𝐹
𝛾
𝑇
𝐹
Final Year Project (BEng) 2012
10
A-Ao has performed a revolution of 180 , no appreciable transmission of force is applied to
the output link (B-Bo) when becomes a minimum value.
According to Alt (1932), the consideration of the transmission angle of a particular
mechanical system is critical in order for optimum synthesis of a particular linkage
configuration; this relates directly to compound linkage configurations used in cutting tools
in which the transmission angle will determine the output path of the coupler alongside the
corresponding output force.
1.5 Practical investigations regarding four bar linkage mechanical advantage
An experiment carried out by Midha et al (1984) analysed the mechanical advantage of a
four bar double crank and slider mechanism with single-input and multiple-output ports
based on the instantaneous transmission angle over the global range of movement. The aim
of the study was to investigate the mechanical advantage of the system by use of an
opposing external force on the system with a simple spring. The rubber band tension and
the input handle force were obtained as functions of the rubber band displacement; this
meant that the input force could be directly correlated to the tension of the spring.
Assuming the conservation of incremental energy between the input and the rubber band
extension, the mechanical advantage could be given as:
(2.0)
Where is the rubber band tension, is the input force and and are the input and
output displacements (handle displacement and cutter displacement respectively); this
means that the mechanical advantage of mechanisms such as shears, bolt cutters and wire
Fig. 1-9: Maximum and minimum allowable transmission angle in a four bar linkage (Patel, 2011)
𝐴0 𝐴
𝐵
𝐵0 𝐴0
𝐴
𝐵
𝐵0
𝛾𝑚𝑎𝑥 𝛾𝑚𝑖𝑛
Final Year Project (BEng) 2012
11
cutting pliers for example can be simply calculated from the ratio of the displacement of
the handles relative to the displacement of the cutting end.
The double crank and slider mechanism or Elastrator used in the investigation is shown in
figure 1-10 and illustrates the positioning of the input force relative to the main fixed pivot;
figure 1-11 illustrates the correlation between the input force and mechanical advantage of
the system as a function of the rubber band stretch.
𝑆𝑙𝑖𝑑𝑒𝑟
𝐹 𝑑𝑠𝑖
𝐹 𝑑𝑠𝑖
𝐿𝑖
𝐻𝑎𝑛𝑑𝑙𝑒
𝐹𝑖𝑥𝑒𝑑 𝑃𝑖𝑣𝑜𝑡 𝑅𝑖𝑔𝑖𝑑 𝐸𝑙𝑒𝑚𝑒𝑛𝑡
𝑇
𝑇
𝑇
𝑇
𝑑𝑠𝑜
𝐹𝑙𝑒𝑥𝑖𝑏𝑙𝑒 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
Fig. 1-10: Example of an Elastrator, utilizing the double crank and slider mechanism (Midha
et al, 1984)
Final Year Project (BEng) 2012
12
An investigation carried out by Balli and Chand (2002) concluded that the optimum
transmission angle of the coupler within a four bar linkage mechanism is dependent on a
particular link or element having a minimum transmission angle which is greater than the
minimum transmission angles of all the remaining links. It was also found, with reference
to Hall (1961), that the optimum transmission angle of 90 leads to less vibration in the
system and allows the mechanism to be used in high speed applications.
It is the case however, that when more than four bars are used in a particular linkage
configuration, that the transmission angle and therefore the mechanical advantage of the
system cannot be identified easily using standard linkage theory. It was concluded by Wu
(1990) that more than one transmission angle is needed to describe the quality of force and
motion transmission of a particular mechanism, this was suggested from work carried out
where the derivations of the dead centre configurations could be used in order to find the
modified transmission angles for any linkage configuration.
Fig. 1-11: Variation of mechanical advantage of the system based on input force (Midha et al, 1984)
𝑅𝑢𝑏𝑏𝑒𝑟 𝑏𝑎𝑛𝑑 𝑠𝑡𝑟𝑒𝑡𝑐 𝑠𝑜
𝐹𝑜𝑟𝑐𝑒 𝑀𝑒𝑐 𝑎𝑛𝑖𝑐𝑎𝑙 𝐴𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒
. 916
0
0 0
~35𝑁
𝑀𝑒𝑐 𝑎𝑛𝑖𝑐𝑎𝑙 𝑎𝑑𝑣𝑎𝑛𝑡𝑎𝑔𝑒
𝐹𝑜𝑟𝑐𝑒
𝑇𝑜𝑟𝑞𝑢𝑒
Final Year Project (BEng) 2012
13
According to Cheung and Zhou (2004), the four bar linkage configuration can generate
multi-phase motion from the adjustment of the driven link fixed pivot which would allow
the system to generate a variety of non-linear motion paths; it was also found that the force
transmission (or mechanical advantage) of the linkage configuration remained at a
maximum with motion paths of high non-linearity. Other authors including Norton (2004)
state that more complex motion paths can be achieved with five and six bar mechanisms
with the introduction of additional position vectors; however the solution to the kinematic
motion of these linkage systems is more difficult to solve due more complex mathematics
which require an iterative solution.
1.6 Degrees of freedom of planar mechanisms
An important design consideration to the Engineer is to determine the number of degrees
of freedom of a particular mechanism and is determined by how the system is constrained
to carry out a particular motion path. For planar linkages, the mechanism is subject to
three degrees of freedom; namely one being rotational and two being translational.
According to Rothenhofer (2010) the number of discrete coordinates needed to describe
the motion of the system are reduced when links are joined together (for example by a
fixed revolute joint). The mobility or number of degrees of freedom of a mechanism can be
calculated using the Kutzbach-Gruebler equation:
3 1 2 (3.0)
Where the number of links is denotes the number of joints in the system.
For a mechanism with 4 links and 4 joints:
3 4 1 2 4 1 (3.1)
Therefore the four bar linkage has only one degree of freedom, or in other words, only the
movement of one particular link (be it the input, coupler or output) will cause the entire
system to move; it is however only the input or output which are usually defined.
Final Year Project (BEng) 2012
14
1.6.1 Grashof’s criterion
In order to further understand the motion of four-bar linkages based on their mobility or
degrees of freedom, Grashof’s criterion allows the engineer to define a four-link kinematic
chain with respect to each link or elements length (Chang et al, 2005).
Where s is the shortest element in a mechanism and l is the longest link, p and q are the
lengths of the two remaining elements.
This can also be written as:
(4.0)
According to Grashof’s theorem, at least one a crank (or fully rotational element) is present
with respect to the remaining links if:
(4.1)
Grashof linkages can be defined in three groups of mechanism based on the position of the
shortest link, namely:
1. Crank-rocker– a mechanism where if the shortest link is adjacent to the ground,
that it is allowed to fully rotate where the remaining adjacent link to the ground is
left to rock or oscillate
2. Double-crank – a mechanism where if the ground link is the shortest link, that
both remaining ground adjacent links are allowed to fully rotate
3. Double-rocker – a mechanism where the coupler is the shortest and is allowed to
fully rotate. The remaining input and output links are only able to oscillate or rock
Therefore from the Grashof definitions, it can be determined that the Grashof’s theorem is
fulfilled if the shortest link can fully rotate with respect to the remaining links. Conversely,
a non-Grashof mechanism has three moveable links which are always in an oscillating
condition.
Final Year Project (BEng) 2012
15
1.7 Dual or compound linkage mechanisms
Compound mechanisms are a means of increasing the total mechanical advantage of a
particular system relative to a mechanism which employs only one simple linkage. The
theory behind compound linkages is that two separate linkage configurations work in
unison in order to scale the total mechanical advantage as a product of each sub-system’s
individual mechanical advantage in order to create appreciable gains of output force, as
stated by Keenan (2006:442) “The total, or overall, mechanical advantage of a compound
machine is equal to the product of the mechanical advantages of the several machines that
make it up”.
1.8 Classical and current methods of linkage synthesis and analysis
The graphical method of determining the motion path of linkage mechanisms has been the
most common means of synthesis of a particular machine in order to carry out a particular
task. It is usually the objective to ascertain the optimal linkage lengths alongside the
transmission angle (also known as coupler geometry) in order for the machine to carry out
the desired motion (Anoop, 2009). In terms of a function generating mechanism, the
objective is to ensure that the constructed machine is designed such that the generated
motion path matches that of graphical methods based on known geometry. An example of
classic basic four bar linkage synthesis is based on the four bar kinematic constraint
equation which is based on the four natural coordinates and is characteristic of a four bar
linkage (Slocum, 2010) allowing the engineer to be able to predict the behaviour of the
mechanism based on the angles of the constituent links and their relative lengths;
Grashof’s theorem also aids the design process by determining how the system will behave
based purely on the linkage lengths; all information needed to kinematically model the
system is then known to the Engineer.
The main limitation of using graphical methods of characterizing the motion of a four bar
linkage is that of only being able to visualize an instantaneous position of all constituent
links; in order to analyse the system dynamically, the use of software integration is a key
tool in accelerating the design process before manufacture of a working model.
Final Year Project (BEng) 2012
16
1.8.1 Computer aided linkage synthesis and analysis
Wang (1996) carried out an analysis of planar four bar linkages using the programmes
MATLAB and Working model. Synthesis of the models was accomplished by design of
one and two dimensional bodies acting as links which were connected by revolute joints
and allowed for analysis of the mechanisms instantaneous position, velocity and
acceleration and also allowed for the model to be analysed in real time; the models created
included the standard four bar linkage, a slider-crank and inverted slider-crank variations.
Wang states that MATLAB is able to solve a variety of numerical problems in much
shorter time periods instead of a bespoke programme written in FORTRAN or C.
MATLAB for example can also be used to analyse singularities of specific linkage
configurations according to when the mechanism reaches its toggle position; this is also an
indicator of the linkage configuration not satisfying the Grashof criterion. Additionally, the
software package is also able to determine when the torque required is too large for a
particular action and illustrates the problem by halting the simulation at discrete positions.
Finally, Working ModelTM
is a mechanism simulation package with the addition of being
able to analyse inertia. Additionally, the particular program is designed such that 2-
dimensional models of the mechanism can be created and analysed in real time and create
graphs of positional vectors, acceleration velocity and other dynamic properties such as the
mechanical advantage of the system.
Shirazi (2007) used 3-dimensional computer modelling techniques in order to construct a
Burmester curve based on Burmester theory for synthesis of spherical mechanisms. The
analysis was carried in order to determine the motion curves with reference to function
generation compared to spatial mechanisms for the role of carrying out complex tasks. The
author states that a variety of CAD (Computer Aided Design) packages can be used for 3-
dimensional motion analysis such as NASTRAN, COSMOS MOTION and ADAMS
VIEW in order to determine whether a designed linkage performs to the intended
specification.
The use of computer programmes also allows for complex calculation to be carried out
quickly and accurately with minimal human error. Other complex arithmetic can also be
carried out by various computer aided programs including that of Finite Element Analysis.
According to Ajuria et al (2010), Finite Element software allow for modelling of linkages
on methods based on energy concepts with the ability to calculate error functions of the
Final Year Project (BEng) 2012
17
inherent design; the user is also able to solve linear and non-linear velocity, position and
acceleration problems with any number of degrees of freedom. In addition of the FEM
method using a global stiffness matrix for a particular set of elements as opposed to the
more complex Jacobian matrix method, no derivation of the inherent constraint equations
or closed loops are required in order for synthesis of a working model.
1.9 Existing Patents review
The following chapter reviews the development of non-surgical and surgical cutting tools
between 1874-2008 and 1903-2005 respectively in order to understand the evolution of
compound mechanisms for various uses.
1.9.1 Non-Surgical cutting instruments
An invention consisting of a compound four-bar linkage design which could be used for
cutting and gripping was suggested by Lindsay (1874) and is illustrated in figure 1-12. The
inventor claims that the design of the linkage allows the user to operate the cutting jaw
with a much greater force than previous designs and that a greater mechanical advantage of
the lever mechanism is achieved during the global travel of the handles.
The design works such that when the handles are in the relaxed position or open, the
pivoted ends of the cutting arms ( ) are brought inwards by the toggling action of the
inner handle pivots ( ), thus opening the shanks of the cutting end. When a load is
applied to the handles, the pivoted arrangement works such that the inner handle pivot
linkage applies a compressive force to the outer cutting shank which ultimately rotates the
blade arrangement around the centre fixed pivot.
Final Year Project (BEng) 2012
18
Smith (1876) suggested the design of a small pair of wire cutting nippers which are
designed such that the curvature of the handles would aid the user apply a greater force
(and hence stress) to the wire. The Ergonomic feature of this design would be to ensure
that a maximum area of the hand is in contact with the handle as well as ensuring a
comfortable grip; this lead to a more convenient method of cutting small wires and allowed
for greater ease of transportation.
This particular design is illustrated in figure 1-13
Fig. 1-12: (Left) Early cutting pliers / pinchers followed by variant products (right) utilizing a
four link mechanism (Lindsay, 1874)
Final Year Project (BEng) 2012
19
An invention by Porter (1880), illustrated in figure 1-14, utilized the theory of compound
mechanisms for the use in heavy duty wire/bolt cutters. This particular design claims that
the introduction of the arms and which are connected to and at one end and to and
on the other provide substantial adjustability when their positioning is modified by bolt
. The author states that this adjustment allows for less wear to be applied to the cutters by
variation of the force transmission for particular tasks.
Fig. 1-13: Ergonomic design patent as opposed to complex linkage
mechanisms or an increase in overall size (Smith, 1876)
Fig. 1-14: A compound mechanism design with adjustable internal spring-
back mechanism (Porter, 1880)
Final Year Project (BEng) 2012
20
A similar but portable variation of this design can be seen from the invention by
Broadbooks (1902) in figure 1-15 in which a similar compound mechanism to figure 1-14
is utilized for smaller gauge wires.
The author states that the design is a “useful improvement” and provides compound
leverage of the cutting head in order for powerful but yet simple operation. The invention
also gives rise to a secondary design feature for a hand held wire cutting device in which
the blades are interchangeable with different cutting heads and are simply removed via two
bolts.
A hand held compound lever device designed for the military for the use of cutting heavy
duty barbed wire is presented by Geddes (1940), figure 1-16. This particular design
comprises of a cutting head lever in the form of an inverted “J” and is operated by a
compressive load being formed at “18” rotating about point “20”. The main revolute joint
at “14” allows for rotation of the cutting head and hence for the input load to be transferred
to the desired object to be cut. The author also states that the invention is based on a
previous patent by Francis T, Lind with patent number 2,239,852 and is designed such that
manufacturing costs are reduced alongside an increased cutting force due to the compound
nature of the linkages.
Fig. 1-15: Compound mechanism with interchangeable single fixing blades
(Broadbooks, 1902)
Final Year Project (BEng) 2012
21
It is argued by Shurtleff (1975), that no compound mechanisms had existed which could
shear through mild steel rod by using only one hand due to inadequate power generation
without long handles or that a specific design utilized a ratchet mechanism. The invention
is intended for the building trade, in which brick-layers are substantially slowed down
when cutting steel rod which is used to reinforce bricks. The author claims that the
patented design can be used on site whilst holding mild steel rod in one hand, and being
able to cut with the other. Two moderately sized handles are shaped such that the input
force is applied in a perpendicular fashion which is then transferred to the cutting head due
to a revolute joint at point “57”. The addition of the compound mechanism where two links
are present either side of the cutting head allow for balanced force transmission and aid to
increase the mechanical advantage of the system. The second handle is mounted such that
maximum force multiplication is transferred to the second cutting jaw in order to provide a
maximum stress on the object to be cut.
The invention by Shurtleff is illustrated in figure 1-17.
Fig. 1-16: A portable hand held compound linkage mechanism with patented inverted
"J" cutting head (Geddes, 1940)
Final Year Project (BEng) 2012
22
A patent applied for by Rowe (1981), suggested the use of multifunctional pliers for the
electrical trade in which various bladed through-holes performed the role of stripping
various sized cables (mainly for coaxial). The tool, illustrated in figure 1-18, is intended to
combine the roles of various tools which crimp, cut, strip, remove and tighten connectors.
One side of the handle is designed to loosen and remove fittings followed by a handle for
connecting and removing cable by virtue of an external thread on the lower boundary of
the handle with accompanying centre thread.
The main centre revolute joint or pivot allows for handle rotation; the length of the handles
relative to the distance of the blades from the fixed pivot allows for a fair mechanical
advantage to be placed on the wires to be cut or stripped. The arrangement of the locating
holes between the bladed segment allows for a greater force to be applied to thicker gauge
Fig. 1-17: Hand held compound rod cutters for use in the building trade,
Shurtleff (1975)
Final Year Project (BEng) 2012
23
cabling followed by a lesser required force to be applied to smaller cables and hence is
positioned further away from the fixed pivot centre.
A final patent worth nothing which illustrates appreciable differences to other common
pliers and cutting tools is the invention by Caravello (2008), illustrated in figure 1-19.
Caravello states that previous products which have been manufactured and incorporate
linkage mechanisms such as levers, cams and gears to act as a compound mechanism for
force amplification have limitations in the sense that the usable gripping or cutting opening
size compared to the opening size of the handles is minimal. Whereas ratchet mechanisms
have been utilized to minimise this particular problem, they are not always the easiest tool
to use with a single hand and do not always release when wanted. Another consideration
which is stated by the author is that of adjustable rack systems in which the force
amplification ratio changes with modification of the rack positioning; this problem is also
evident on sliding fulcrum mechanisms where the distance of the main fixed pivot is
altered with respect to the cutting end and the length of the handles.
The particular invention stated by the author uses a rack system which is adjustable, but
where the pivot point locations are not modified and therefore changes in the mechanical
advantage are negligible.
Fig. 1-18: Multi-functional transportable cutting pliers, Rowe (1981)
Final Year Project (BEng) 2012
24
1.9.2 Surgical cutting instruments
An invention by Koeth (1905) enabled for the user to have a spring assisted pair of multi-
functional pliers with interchangeable cutting heads. The Patent is based on the area of
being able to disassemble the handle configuration and replace the cutting heads with a
punch or wire cutting head for surgical applications; the pivot plate at “18” is allowed to
rotate about “20” and therefore allows for simple removal of the cutting head. This
invention is shown in figure 1-20.
Fig. 1-19: Cutting/gripping pliers with adjustable rack configuration, Caravello (2008)
Final Year Project (BEng) 2012
25
An Endodontic device for securing silver points in root canals is proposed by Rosen
(1960), figure 1-21, in which a novel method cutter has been devised such that minimal
disturbance is caused to the surrounding pulp tissue followed by being able to retrieve cut
wire from the area by use of a special bevelled blade design. Although the pliers are not
particularly large, it is intended for the design to cut a sufficiently soft metal and to finally
produce a flush finish of the point without disturbance and without the possibility of
causing voids around the root canal.
The mechanism is a simple two bar linkage with a single fixed pivot and does not require
for a high mechanical advantage to be produced due to the application. Furthermore, the
smallness of the device is wanted in order to prevent disturbance to surrounding tissue of
the root canal.
Fig. 1-20: Surgical combination tool with interchangeable cutting heads (Koeth, 1905)
Final Year Project (BEng) 2012
26
Tippy (1975) proposed a wire cutting design in which the wire cut-offs would be retained
by a “resilient member” against one of the cutting faces of the tool. The idea is such that
when carrying out orthodontic procedures or jaw surgery, that the user (i.e. surgeon) could
cut the wires shortly enough in order to eliminate interference to internal skin tissue from
excessive lengths of wire; the design encompasses a novel design in order to cut wires
cleanly with no left sharp edges. The design of the blades allows for a shearing action to
occur followed by being retained by the cutting blades in order for efficient and safe
removal without wire elements being left inside the patient’s mouth.
The wire cut-off holder concept can be clearly seen in figure 1-22.
Fig. 1-21: Small surgical pliers for use in Endodontic applications,
Rosen (1960)
Final Year Project (BEng) 2012
27
A variation of the surgical cutting pliers suggested by Tippy is illustrated by Mooney
(1999), figure 1-23, in which several cavities are utilized near the cutting edge in order to
remove wire during certain applications where the excess is not simply allowed to fall after
being disposed from the shearing action. The cutting pliers which are designed for surgical
applications for wire cutting employs a simple 2-bar linkage configuration with a single
fixed pivot design and is characteristic of the size of wire to be cut for the intended
application; the author states that the intended device is best suited for the cutting of softer
metals such as copper, nickel and silver and also explains that harder metals are cut with
greater difficulty and are also less likely to be retained by the cutting head device for
removal.
Fig. 1-22: Surgical cutting pliers for use in jaw surgery and orthodontic procedures, Tippy
(1975)
Final Year Project (BEng) 2012
28
Finally, a patent applied for by illustrates a novel design for a pair of wire
cutting pliers which are specified to be able to cut through 2mm wire with one hand and is
to be used for surgical applications (figure 1-24). The intended application for the product
is for the cutting of wire during operations on bone and joint fractures followed by the
cutting of seams; it is stated by the author that conventional wire cutters cut strands of
specific material individual rather than cutting across evenly and can cause issues for the
patient.
The point of interest for the project lies in the analysis of wire cutting mechanisms and
more specifically the linkage mechanisms employed. The Patent applied for by GEOMED
also encompasses a special linkage configuration which, from figure 1-24, is illustrated by
the intermediate linkage “21” which is allowed to rotate about “22” and transmit the force
from the handles to point “24”. It is to be noted that this particular type of mechanism
satisfies the condition for a “Compound mechanism” due to the fact of intermediate
mechanisms being used to further amplify the mechanical advantage of the system;
furthermore the compound mechanism can be seen to consist of two 4-bar linkages where
the linkage “21” is used to couple the torque to the output link “24”. Finally, to ensure that
the mechanical advantage remains sufficiently high to cut 2mm wire, the distance from the
cutting blades to the main fixed pivot “16” is far less in magnitude when compared to the
Fig. 1-23: The wire retention device proposed by Mooney (1999) for the cutting of
softer wires
Final Year Project (BEng) 2012
29
length of the handle tips to the pivot; therefore it can be seen that this design utilizes all
features from previous surgical and non-surgical mechanisms in order to maximise the
force transmission to the cutting end.
1.10 Current state of the art
Despite the age of the design of scissors and other cutting instruments, the basic concept
has remained more or less the same despite some changes to the linkage design for variable
torque output depending on the application (as illustrated in figure 1-3). In order to gain an
appreciation into the “state of art” of surgical and non-surgical instruments, research is
needed into current products and how these differ to designs pre-dating the 21st century.
Market research on current surgical instruments available which employ various linkage
designs are illustrated in table 1 in order to determine commonly used linkages and if any
linkage configurations differ to the common four-bar link mechanism employed on other
hand cutting tools.
Fig. 1-24: A design patent for compound surgical wire cutters from GEOMED, 2003
Final Year Project (BEng) 2012
30
Surgical wire cutters (other products other than wire cutters excluded, i.e. scissors)
Geomed Accrington Surgical Key surgical Sirag surgical Simplex medical
Hercules double action
wire cutters for 1-2mm
wires. Compound four
bar configuration
Accrington TC wire
cutters for 1.5mm wire.
Simple 2-bar
mechanism with one
fixed revolute joint
Basic wire cutters with
single fixed revolute
joint. No performance
figures are given on
website.
“Small” wire cutters
from Sirag surgical;
basic fixed pivot design
.
Single fixed pivot
design. Maximum
capable cutting
capacity, 1.1mm.
Hercules Gold cut wire
cutters consisting of a
compound four bar
mechanisms
Accrington TC wire
cutters for 2.5mm
wires. Compound four
bar linkage design
Basic wire cutters from
key surgical, no
performance figures
given. Compound Four
bar linkage
configuration
“Medium” wire cutters
from Sirag surgical;
same basic design with
increased handle
lengths
Medium sized wire
cutters with four bar
linkage. Maximum
cutting capacity,
2.4mm
Hercules Gold cut XS
wire cutters: same 2-four
bar configuration as
normal Hercules wire
cutters, however with
greater handle lengths
Accrington TC wire
cutters for 1.6mm hard
wire or 2.0mm soft
wire. Here the four bar
linkage seems to
increase mechanical
advantage.
Heavy duty wire cutters
from key surgical.
Greater mechanical
advantage is given by
longer handle lengths.
However, only one four
bar linkage is used; no
size constraints for this
application
“Heavy” wire cutters
from Sirag surgical.
Same basic single fixed
pivot design although
with longer handle (or
lever) length for
increased input
moment
Maximum sized wire
cutters from simplex
medical incorporating a
four bar link
mechanism and
550mm handles
Table 1: Common linkage designs employed by various manufacturers of surgical cutting instruments
Final Year Project (BEng) 2012
31
1.11 Ergonomic analysis of hand tools
Edgren et al (2004) carried out an experiment to measure the magnitude of grip force on
different sized cylindrical handles where the aim of the investigation was to compare this
compressive force between 61 males and females of different age groups for an increased
knowledge for designers into the optimum size of handles for operators of varying hand
sizes. The particular apparatus consisted of a cylindrical strain gauge measuring forces in a
single direction across the cylinder length at 50 Hz, using an analogue to digital converter
and amplifier. This made it possible to record the grip force overtime and also allowed for
analysis of particular tendons in the forearm being used when gripping at different
orientations relative to the wrist positioning with different areas of the hand (a pinch-grip
for example, which subjects tendons in the forearms to a higher stress). The author states
that larger diameter handles are favoured to minimize contact stress between the hands but
could consequently lower the applied grip force when exceeding the optimum diameter; if
a handle is to be pulled, that the force should be normal to the surface of the palm in order
to further minimize tendon stress and the chance of injury. From the 61 subjects tested, the
maximum average grip force for males and females was at a span (or radius) of 3.81cm
with a force of 306N and 169N respectively and illustrates the importance of a comfortable
grip for the user for an increased efficiency of force transmission.
The results of the investigation can be viewed in figure 1-25.
0
50
100
150
200
250
300
350
0 2 4 6 8
Fo
rce
(N)
Handle size diameter (cm)
Grip force Vs. handle size
Males
Females
Fig. 1-25: Grip force vs. handle size (Edgren et al, 2004)
Final Year Project (BEng) 2012
32
According to Mcgorry (2004), the main factors to consider when designing hand tools
include the frequency of use, the posture of the user when using the equipment, rest
periods between use and the magnitude of the force which is applied, where these design
considerations are crucial to avoid musculoskeletal injuries and disorders and of which
were a key factor of 9% of work related injuries during 1984 in industry.
Another important design criterion is that of the safety factor applied to hand tools relative
to grip stress. Theoretically, the minimum grip force required is that to provide equilibrium
by balancing the forces to prevent the object slipping. The force which essentially keeps
the device in the hand is based on grip and friction at the interface and depends on various
factors including the use of gloves or if vibration is present. The work force ratio can be
expressed as the working gripping force divided by the minimum force needed to keep the
device in the hand and is a useful quantitative measure of minimizing hand strain and/or
injury by excessive force for a particular application.
(5.0)
Working force ratio (which is also a form of a factor of safety) can then be expressed as:
(5.1)
Where the “FOS” will always be greater than one, however smaller numbers indicate a
lower working force ratio and therefore a lesser likelihood of hand strain due to repetitive
tasks with high grip forces.
Other factors also need to be considered for optimum ergonomic hand tool design and
depend on the application of the particular device; these include the specific shape of the
handles for varying degrees of force distribution along the handle and how the hand works
in conjunction with the mechanism in order to provide sensitive movement or a “power-
grip” which essentially maximises the generation of force along the handle major axis. For
screwdrivers for example, one of the design considerations is that of the shear force at the
interface between the hand and the handle and is a function of the handle radius.
A kinematic model of the human hand was proposed by Buchholz and Armstrong (1992)
for ergonomic and potentially orthopaedic uses, whereby the grip force was predicted for
varying hand postures using an algorithm to compute surfaces of contact between
Final Year Project (BEng) 2012
33
simplified elliptical polygons in order to estimate the contact area of skin with cylinders
based on ideal joints. The algorithm was synthesized such that the degree of flexion could
be assessed for individual digits based on an increase in cylinder size (and therefore span
of the hand) alongside a measure of the joint angle of each digit in order to assess a
potential grip strength, which was estimated by a hypothetical model of the assumed soft-
tissue deformation. It was found that an increase in cylinder size for which to apply a
gripping force allowing for less flexion of the major joints. As expected, an increase in
hand length illustrated increased flexion of the hand for all four digits (where the thumb
was neglected due to negligible mobility).
1.12 British standards for surgical cutting instruments and maximum loading
British standards are a method of ensuring a particular process is carried out in a pre-
specified manner and is a means of providing an agreed document between buyers,
manufacturers, regulators and users in order to increase the reliability of particular
products and services (BSI group, 2011). In order to ensure the safe and intended use of
cutting instruments in an orthopaedic environment for example, regulations and guidelines
are given to ensure the product is chemically safe; for non-surgical applications, guidelines
are available in order to produce mechanically sound plier designs based on guideline
geometry.
1.12.1 Stainless steels for surgical cutting instruments
The British standard BS EN ISO7153-1:2001/BS 5194-1:1991 “Steels for surgical
instruments” lists the material compositions which are suitable for use in a surgical
environment (all of which are stainless steels); of the materials listed, only three are stated
as being preferable for use in surgical wire cutting pliers.
The stainless steel compositions allowed for wire cutting pliers in a surgical environment
are illustrated in table 2; the complete list of surgical steels suitable for varying instrument
use is illustrated in appendix “1”.
Final Year Project (BEng) 2012
34
Steel grade Chemical compositions (%)
Ref Grade No.
According tob
C Si
(max)
Mn
(max)
P
(max)
S Cr Mo Ni Other
Elements
ISO
4957
ISO
683-13
Martensitic Steels
D
H
I
—
—
—
—
—
—
0,42 to 0,50
0,35 to 0,4
0,42 to 0,55
1
1
1
1
1
1
0,04
0,045
0,045
0,03 max.
0,03 max.
0,03 max.
12,5 to 14,5
14 to 15
12 to 15
—
0,4 to 0,6
0,45 to 0,9
1 max.
—
—
—
V: 0,1 to 0,15
V: 0,1 to 0,15
Table 2: Surgical steels suitable for wire cutting pliers (BSOL, 2011)
Realistically, all of the material compositions stated in BS EN ISO7153-1:2001/BS 5194-
1:1991 could potentially be used for wire cutting pliers so long the material properties meet
the intended specification of the manufacturer. It is stated by Baratz (1999) that common
Stainless Steel alloys used for biomedical applications include the types AISI 316 and
316L, where L denotes the reduced carbon content of 0.03% maximum 0.08% compared to
standard 316. The author also states that the Engineer is not limited to only using Stainless
Steel’s but has an extended choice covering other materials such as Titanium and certain
Ceramics; commonly used for biomedical implants.
The British Stainless Steel Association (BSSA, 2010), with reference to BS EN ISO7153-
1:2001/BS 5194-1:1991, states that the grades A, B and C are broadly classified as AISI
410 and 420 Steels and used comprehensively in the field of surgery and dentistry due to
good corrosion and wear resistance; additionally, these properties can be improved by
means of heat treatment. The BSSA also states that Martensitic Steels provide long service
lives for surgical equipment through proper maintenance and that some instruments can
have service lives of up to 30 years; although wear is to be expected from instruments with
the function of cutting for example, it is critical for the tool to be resistant to corrosion.
1.12.2 Guideline cutting forces for lever assisted cutting pliers
Additionally, wire cutters (surgical and non-surgical) should conform to BS 3087-7:1996,
ISO 5747:1995, a specification for dimensions of lever assisted side cutting pliers, end and
diagonal cutting nippers, which illustrates the geometry of a particular design with its
corresponding maximum guideline application of force. Table 3 illustrates the variable
input forces with respect to a maximum cutting force relative to a specific gauge wire and
mechanical advantage of the mechanism.
Final Year Project (BEng) 2012
35
L L1
Lever ratio
(mechanical
advantage)
Cutting test Load test
Diameter
of hard test
wire
Db
Maximum
cutting
force
F1 (max)
Load
Maximum
permanent
set
smaxc
mm mm mm N N mm
125
140
160
200
60
75
90
125
15
15
15
15
1,25
1,4
1,6
2
260
310
370
530
360
450
540
750
1
1
2
3
Table 3: Maximum permissible cutting force for lever assisted side cutting pliers (British
standards online, 2011)
The equation relating to the maximum cutting force with the basic plier geometry is given
as:
(6.0)
Where:
is the measured distance from the applied load to the main fixed pivot
is the distance from the main fixed pivot to the applied load from that given in
table 3
F is the load given in table 3
is a compliance equivalent load.
For lever assisted side cutting pliers with specifications that do not match those details
given in table 3, the following equation can be used.
2
(6.1)
Where:
2 is a correction factor for hard wire
is the measured span of the handles when open
is the measured span of the handles in the closed position
is the relaxed distance of the cutting jaws
Final Year Project (BEng) 2012
36
Additionally, the lever ratio (LR or MA) of the system can be expressed as:
(6.2)
However it is stated that the equations illustrated are for the purposes of verifying a
particular linkage design and does not affect the design of a particular product.
1.13 Conclusions from background literature and market research
An appreciation has been gained toward the historical development of surgical and non-
surgical cutting tools in the form of blade and linkage design in order for the instrument to
be used for a particular application; aside from increasing the efficiency and cutting
capacity of cutting instruments from an increase in overall size, the methods employed
include the re-design of the cutting heads with respect to their length ratio to the main fixed
pivot relative to the handles alongside wire removal features - which allow for variable
design to meet an intended specification.
Furthermore, limitations have been determined from using graphical methods of
interpreting the commonly used 4-bar linkage kinematic behaviour due to analysing the
mechanism at one instantaneous point in time. For this reason other methods are employed
in order to analyse the motion paths of mechanism by use of computer aided software such
as “Working Model”, “Nastran”, “Adams View” or “Cosmos Motion”; Finite Element
Software is also available for analysis of the distributions of stress within the system. It
has been established that the design of the individual linkage lengths alongside their
respective angles relative to the ground are crucial to determine the correct motion path
and for synthesis of the force transmission characteristics over the global range of travel
and ultimately determines the amplification of the force used in compound 4-bar link
mechanisms.
From the market research undertaken alongside a review of surgical and non-surgical
patents, the most commonly used type of mechanism is indeed the 4-bar linkage – most
notably used in compound configurations for increased output forces for use in cutting
instruments.
It has also been made clear to consider the shaping of cutting tool handles as well as the
form of loading (as illustrated by Mcgorry, 2004) to ensure that strain injury is minimized
from continuous high loading and/or repetitive use. From the work of Edgren et al (2004),
the importance of handle span of a particular hand tool has a substantial influence on the
Final Year Project (BEng) 2012
37
gripping force with a maximum of 306N and minimum of 180N with a handle diameter of
3.81cm for males.
From research into British Standards regarding surgical and non-surgical wire cutting
pliers, it is understood that strict criteria need to be met in order to ensure that the material
used is non-reactive, non-corrosive and not susceptible to external influences
(heat/humidity changes); for this reason only a limited amount of Stainless Steels can be
used for surgical/orthopaedic applications. The Engineer does still however have
reasonable selections of materials and is not limited to one specific Steel alloy
composition; this is confirmed by the BSSA and authors such as Baratz (1999) who state
that other types can be used such as AISI 410 and 420 although 316 and 316L are the most
commonly used. Additionally, the guidelines on the maximum input and cutting forces
have been established with respect to the wire cutting plier’s geometry and are useful for
determining the performance of a particular linkage design.
2 Project aims and objectives based on background literature
The aim of this paper is to review the design of a particular pair of Hercules gold cut wire
cutting pliers from GEOMED, a manufacturer and supplier of premium surgical
equipment, due to possible improvement being made to the product’s linkage configuration
in order to increase the mechanical advantage of the system, allowing the user to apply a
reduced load to the handles whilst maintaining an equivalent output force. The scope of
the paper is to review both the theoretical model associated with the linkage configuration
on the GEOMED wire cutting pliers and to compare this model with experimentation in
order to determine an optimized solution for the mechanism.
The investigation to be carried out will continue from the work of Cheung and Zhou
(2004) by analysing the systems mechanical advantage (by inspection of the transmission
angle of the design) from adjustment of the driven link fixed pivot. The work will also be
taken further by considering the four bar linkage as part of a primary single fixed pivot
system rather than an individual mechanism (as utilized by GEOMED in their existing
products); this will require a more in-depth analysis of the flow of the force from the
predetermined input at the handles, through to the internal four bar linkage configuration
and will be analysed by using program’s such as “Working Model” to determine how the
linkage configuration affects the overall output of the system . Working model has been
Final Year Project (BEng) 2012
38
chosen over other kinematic modelling software packages due to the programs simplicity
and versatility for analysing linkages.
From a practical investigation carried out by Midha et al (1984), the basis of determining
the mechanical advantage of the system can be related to using a force balance at the
output in order to analyse the mechanical advantage through the overall range of
movement of the handles; this also forms a basis for the project to carry out a practical
investigation for a proposed working model of the GEOMED Hercules Gold-Cut wire
cutters with variable input linkage positioning in order to verify the results obtained from
computer aided analysis.
2.1 Generalized method layout to fulfil project objectives
Based on the background literature the generalized project layout and methods of
accomplishing the project aims and objectives will be to:
1) Perform an initial analysis on the Geomed Hercules wire cutting pliers kinematically,
whereby measurement data is needed of the product’s joint coordinates in order to
determine the corresponding linkage lengths and internal angles; this is to be carried
out using a DS401SM/JT12A-B shadowgraph machine from Midland Metrology Ltd
and measured from the specified datum. The particular machine is capable of
measuring X,Y and Z coordinates with a sensitivity of 0.001mm in order to ensure
that measurements are taken as accurately as possible with minimal error;
additionally, the magnification of 20 used on the projecting screen, alongside a static
target display, ensures that any movement of the wire cutters is reduced and that
repeatable measurements can be taken to ensure the measurements are taken
correctly.
2) Obtain a transmission ratio index for the internal linkage mechanism which can be
multiplied with the mechanical advantage of the “scissor” or external linkage
mechanism associated with the handles and will give an estimated value for the total
mechanical advantage of the mechanism
3) Create a 3-dimensional model of the Hercules Gold-Cut wire cutting pliers based on
results taken from measurement data from step 1; the program of choice for this
process will be Pro EngineerTM
Wildfire 5 due to a robust interface for creating part
bodies / solids. Upon obtaining a finished model, an assembly of the model is to be
imported into a drawing sheet from which a particular view can be exported into
Final Year Project (BEng) 2012
39
Working Model in DXF format; this is then to be constrained using pin joints in
order for the model follow an identical motion path to that seen on the Geomed wire
cutting pliers.
4) Compare initial kinematic analysis with that of the computer generated model to
validate the theoretical principle of mechanical advantage; the program of choice to
measure the overall output force of the system will be Working ModelTM
due to
effective results obtained by Wang (1996) and being able to visualize the
instantaneous mechanical advantage based on input displacement and spring
tension.
5) To modify the 3-Dimensional model with a series of adjustments to the driven link
fixed by variation of the joint in X and Y; using geometry, the input link will have
to be altered accordingly in order to prevent an increase or decrease in handle span.
This model modification can then be exported as a DXF back into working model
in order to verify an increase or decrease in the systems mechanical advantage
6) Obtain an appreciation of the stress distribution within the Geomed wire cutting
pliers by exporting the model into SolidworksTM
as individual components and
constrained in an assembly for subsequent analysis; this will allow to visually
(indirectly) gauge the flow of the force from the handle to the cutting end and allow
to visualize which areas are under high stress
3 Hypothesis
Based on the statement made by Phelan (1988) where the torque transmission of the
internal compound linkage should have a maximum value when the input link angle is
oriented such that the transmission angle is 90 degrees, in this position, the cutting pliers
should have be in a position of maximum force transmission through the coupler link; the
maximum force transmission will occur in the toggle position, or when the coupler link is
parallel with the output link.
From preliminary inspection of the Geomed Hercules wire cutters, the input link of the
internal patented mechanism is such that a maximum transmission angle is present at the
start of travel and approaches a perpendicular condition to the coupler link over the global
range of movement; for this reason it is expected that the mechanical advantage of the
system will be maximum at the end of travel and minimum at the start of travel.
Final Year Project (BEng) 2012
40
Finally, it is predicted that the internal linkage mechanism should behave as a crank-
rocker, a double crank or a double rocker depending on the corresponding internal linkage
lengths. However if Grashof’s theorem is not satisfied where the longest link plus the
shortest link is less than the sum of the remaining link lengths; then the system is not a
Grashof linkage and can therefore not rotate fully. It is expected that the system will not
conform to Grashof’s criterion due to the application in which the mechanism is used (over
small distances/arcs); additionally, the torque would reverse if the input angle is greater
than that needed to create a toggle position and would therefore not be practical for use in
wire cutter design.
4 Instantaneous transmission ratio based on the kinematic constraint
equation
In order to truly understand how the transmission ratio changes with respect to the input
and output link angles (relative to the ground), let us again consider the generalized four
bar linkage (figure 4-1). Rothenhofer (2010) discusses that any angle can be found in the
four bar linkage mechanism based on all instantaneous values of the remaining angles
(with reference to the Kutzbach-Gruebler equation) by use of the kinematic constraint
equation and can be derived by use of simple trigonometry
Fig. 4-1: Generalized four bar linkage model for constraint equation derivation (Rothenhofer, 2010)
𝑏
𝑏
𝑎
𝑎
𝑐
𝑐
𝑑
𝑑
𝜃 𝜃
𝜃
𝜃
𝛾
𝜇
Final Year Project (BEng) 2012
41
With reference to figure 4-1, it can be clearly seen that application of the cosine rule with
respect to links d and c must yield the same answer of applying the same method to b and
a. Using this relationship, the derivation of the constraint equation can be carried out.
Modifying figure 4-1 for ease of illustration to create figure 4-2:
Using the cosine rule:
2 1 0 2 1 0 (7.0)
Also:
(7.1)
And:
(7.2)
By using basic rules of trigonometry, the constraint equation can be described as:
2 2 2 0 (7.3)
𝜃 𝜃
𝜃
𝜃
𝛾
𝜇
𝑎
𝑎
𝑏
𝑏
𝑐
𝑐
𝑑
𝑑
𝑅
𝑅
Fig. 4-2: Modification of figure 4-1 to illustrate derivation of trigonometric terms
𝑐𝑠𝑖𝑛 𝜃
𝑐𝑐𝑜𝑠 𝜃
𝑎𝑠𝑖𝑛 𝜃1
𝑎𝑐𝑜𝑠 𝜃1
𝑆𝑡𝑎𝑡𝑖𝑐 𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑒 𝑗𝑜𝑖𝑛𝑡
Final Year Project (BEng) 2012
42
In order to obtain an instantaneous torque transmission value, equation (7.3) needs to be
differentiated with respect to time.
2 2 2 0 (7.4)
Where:
(7.5)
From simple gear theory where the ratio of the angular velocities of each element gives
rise to a constant, namely the ratio of torques, the ratio of
can also be used for four bar
mechanisms due to the movement being a particular motion about an arc.
Then dividing by yields:
(7.6)
Hence an expression has been developed which relates the transmission ratio to the
instantaneous angular position of all the links within the system.
A full derivation of equation (7.6) is illustrated in appendix 2.
Final Year Project (BEng) 2012
43
5 Linkage configuration analysis of Geomed-Gold Cut wire cutting
Pliers
It has been determined that the most common types of linkage configuration used in
cutting pliers is that of the four bar linkage, usually in compounded form in order to
increase the mechanical advantage of the mechanism further; by inspection, the Hercules
Gold-Cut wire cutting pliers also employ a compounded four bar linkage configuration in
order for boring wires up to 3.0 mm in diameter.
The Hercules Gold-Cut wire cutting pliers are illustrated in figure 5-1.
Figure 5-2, a modification of figure 5-1, illustrates each simple mechanism configuration
in order to create the patented GEOMED design; the orange and green links denoting the
simple lever and internal compounding mechanisms respectively. The green line represents
the shared link between the two mechanisms and is responsible for transferring the force
from the handles to the cutting end. Additionally, this is ultimately the input link to the
second mechanism and can be treated as link “a” – as denoted in previous examples.
Fig. 5-1: Geomed Hercules Gold-Cut wire cutting pliers (Geomed, 2011)
Final Year Project (BEng) 2012
44
As the shared link (green) is the input link and the ground being the fixed link associated
with the right hand side handle (with respect to figure 5-2), it is straight forward to
determine the coupler and output links and therefore a force transmission ratio. However,
in order for accurate analysis to be carried out on the Hercules Gold-Cut wire cutters,
accurate measurement data is required alongside the corresponding linkage angles in order
to obtain sensible and reliable results
5.1 Apparatus/Software required for obtaining linkage point coordinates
DS401SM/JT12A-B shadowgraph from Midland Metrology Ltd
Protractor to take initial angle data
GEOMEDTM
Hercules Gold-Cut wire cutting pliers
Pro-Engineer Wildfire 5TM
(Also known as Creo)
Ruler for initial measurement of basic plier dimensions
The shadowgraph is illustrated in figure 5-3.
Fixed joint
Moving joint
Main fixed pivot (Datum)
Fig. 5-2: Geomed compound linkage break-down (Geomed, 2011)
Final Year Project (BEng) 2012
45
5.2 Method of obtaining linkage point coordinates / internal angles
The method of obtaining the linkage point coordinates, in sequential order, was to:
1) Position the wire cutting pliers on the glass table of the shadowgraph, ensuring the
entire model sits on the projected face with no overlap
2) Use the main datum of the model as a reference for all other dimensions to avoid
anomalies caused by moving the model
3) Move the table in X and Y to measure the centre points of the remaining links with
respect to the main datum; the projected image on the screen of the shadowgraph
(magnification of 20X) would allow for precise measurement with minimal error in
the deviation of results from the centre line
4) To plot these points in Pro Engineer in order to obtain the internal angles of the
linkages which would be used for subsequent analysis to calculate the systems
mechanical advantage
Critical dimensions needed are illustrated in figure 5-4.
Fig. 5-3: Shadowgraph from Midland Metrology Ltd
Final Year Project (BEng) 2012
46
Fig. 5-4: Physical Geomed wire cutting plier image
5.2.1 Preliminary initial measurement with ruler:
Relaxed cutting end gap width - 5mm
Relaxed handle span – 105mm
Closed handle span – 70mm
Wire cutter weight – 4.134N (421.3 grams)
Tip of handle to datum – 185mm
Distance of cutting end to fixed pivot – 25mm
These measurements would be verified with joint positions of the relaxed wire cutting
pliers and would therefore be used in the creation of a 3-dimensional computer aided
design model in order to replicate the product as closely as possible. Variations in handle
breadth and cutter head shape should not have affected final results with the positioning of
joint rotation and spacing between static joints being most critical.
Relaxed
cutting end
width
Relaxed
handle
span
Handle tip to datum Distance of cutting end to
fixed pivot
Final Year Project (BEng) 2012
47
5.3 Hercules Gold-cut join coordinates
Measurement data taken with the shadowgraph is illustrated in figure 5-5. The dimensions
have been plotted on a drawing sheet in order to log the joint positions visually where all
measurements are in mm. The reason for measuring all joint positions with respect to the
main static joint was to prevent movement of the cutting pliers between each reading; this
would allow for the product to remain in a static position whilst measuring each data point
and minimize the chance of induced errors.
Fig. 5-5: Hercules Gold-Cut joint coordinates taken with shadowgraph
Final Year Project (BEng) 2012
48
6 Reverse Engineering of Geomed wire cutting pliers
In order to analyse the Geomed wire cutters dynamically with eventual modification of the
driven link fixed pivot, a Computer Aided design model needed to be created using Pro
Engineer. This would form the basis for subsequent Finite Element Analysis and for the
ability to import the 3-dimensional geometry as a drawing (2-Dimensional DXF) into
Working Model in order to validate theory with against practical results.
The computer generated model would allow for kinematic analysis of the internal and
external linkage mechanisms combined and how the movement varies upon modification
of the input link fixed pivot. The dimensioning of the model could then be checked through
the use of measurement tools within the CAD package to ensure that the specific tolerances
were met in order to obtain a good product benchmark.
6.1 Product design specification
In order to ensure the correct targets were met and that accurate analysis could be carried
out on the computer generated model, a product design specification would act as a means
to ensure all the relevant criteria had been met in order to obtain reliable results (based on
background literature). For example, the most commonly used Stainless Steel is that of
316L (Baratz, 1999), therefore the specification for the model material would be 316L in
order to utilize coherent mechanical properties for a specific material alloy.
The cutting blades were however made of Tungsten Carbide (Geomed, 2011) and therefore
have a significant difference in mechanical properties relative to the 316L used for the wire
cutter handles and linkages. According to Matweb (2011), a material library consisting of
over 86,000 metals, ceramics and polymers, Tungsten Carbide
(WC) has a Young’s modulus of 682.5Gpa (average), density of 15.7g/cc and ultimate
tensile strength of 344Mpa. For 316L (with negligible differences between annealed
bar, sheet plate and strip) the mechanical properties are 193Gpa for Young’s modulus,
a tensile strength of 560Mpa and a density of 8g/cc.
This data could then be used for subsequent Finite Element Analysis to ensure the model
behaved as closely as possible to that of the Geomed wire cutting pliers. Finally, the
product design specification (see table 4) is generated to ensure that the design dimensions
are as close to the existing product as possible, despite only having taken measurements of
the key joint positions. An estimation of how closely the model represents the ideal
Final Year Project (BEng) 2012
49
(Existing product) would be to take a final mass measure once the relevant materials had
been applied to the 3-Dimensional design model.
# Need Metric Importance
(out of 10,
10 being
highest)
Units Marginal
value
Ideal value
1 Wire cutters
have
increased
mechanical
advantage
over
standard
product
Output force 10 N 1.75-2.25 1.9
2 For product
to remain
comfortable
for use
without
significant
alteration to
handle span
Handle span
from centre
line
8 mm 100-110 105(measured)
3 For mass to
remain at
current
value of
original
product
Product mass 5 g 400-500 420 (weighed)
4 Cutter
geometry to
match
original
product
Cutter-head
span
7 mm 4.5-5.5 5
5 Wire cutters
to have
same input
torque from
handles
Handle length 9 mm 185-190 185
Final Year Project (BEng) 2012
50
Table 4: Design requirements for 3-Dimensional model
6 Output
torque to
match
existing
product
Distance of
cutter head to
main fixed
datum
9 mm 30-40 35
7 Closed
handle span
to match
existing
product to
determine
correct
benchmark
value of
total
mechanical
advantage
Closed handle
span
9 mm 70-75 70
8 Ensuring
body of
pliers
behaves
identical to
existing
product
Handle and
body to be
created as
316LStainless-
Steel
8 UTS
560Mpa
0 560
E
193Gpa
0 193
Density
8g/cc
0 8.0
9 Identical
deformation
of wire
Cutters to be
constructed
from Tungsten
Carbide (WC)
9 UTS
344Mpa
0 344
E
682.5Gpa
0 682.5
Density
15.7g/cc
0 15.7
Final Year Project (BEng) 2012
51
6.2 CAD development
The first step of designing a 3-Dimensional model of the Geomed wire cutters in order to
obtain benchmark values of force transmission before modification of the input link
positioning would be to model the left side handle, due to this component incorporating the
main fixed datum from which all other measurements are taken relative to; figure 6-1
illustrates the initial design component.
This would be followed by designing all constituent linkages to gauge the positioning of
the remaining components due to knowing the lengths of the linkages from preliminary
measurement; illustrated in figure 6-2.
Fig. 6-1: The modelled LHS handle
Fig. 6-2: The modelled linkages
Final Year Project (BEng) 2012
52
Figure 6-3 illustrates the linkages in the constrained condition using the preliminary
measurement data. Data points could be set at the coordinates obtained, followed by
measuring the angles between these coordinates.
As the main datum had already been implemented into the left side handle, the right cutter
could be designed with respect to this datum. The right blade was created using a mirror of
the left handle and split with a plane normal to the datum axis; this would create a direction
for the joint to be connected to the coupler link. The right cutter model is illustrated in
figure 6-4.
Fig. 6-3: CAD model representation of linkage constraints to set correct angles
Fig. 6-4: CAD model of RHS cutter
Final Year Project (BEng) 2012
53
The Right hand side handle shown in figure 6-5 could now be created with respect to the
span of the internal linkage configuration due to constraints applied in earlier stages; this
would also allow for correct joint placement on the right handle in order to obtain an exact
replica position of the original Geomed wire cutters.
The final critical components before component assembly would be to model the
Tungsten-Carbide blades (figure 6-6). This was achieved by using the left hand side handle
as a reference and sketching on a plane normal to the under-side of the cutter-head. The
blade was then mirrored to create a right hand part and finessed in order to ensure either
side would create a parallel touch condition.
Fig. 6-5: The modelled right hand side handle
Fig. 6-6: The modelled Tungsten-Carbide blades
Final Year Project (BEng) 2012
54
Using the constrained linkages from preliminary measurement, all constituent components
could then be constrained together using pin joints order to create a model which could be
analysed kinematically and exported into working model.
Figure 6-7 illustrates the finished model with added fixings and foam wire grips in order to
replicate the model weight as closely as possible.
A rendered image using Autodesk ALIASTM
is shown in figure 6-8 in order to view a
higher detailed model; figure 6-9 illustrates the dimensions which are needed to meet the
intended specification.
Fig. 6-7: The finished computer generated model
Final Year Project (BEng) 2012
55
Fig. 6-8: Rendered images of the Geomed wire cutter computer generated model using the standard linkage configuration
Final Year Project (BEng) 2012
56
Fig. 6-9: Summary technical drawing to illustrate critical dimensions
Final Year Project (BEng) 2012
57
6.3 3-Dimensional computer model summary specification
Using Tungsten as the material for the cutting blades and Stainless Steel for the cutter body
from Pro Engineer’s material library, the overall mass of the wire cutters was in the region of
405g (as seen in figure 6-10).
From table 4 and figure 6-9, the computer generated model met the intended specification,
lying in the specified ranges for each design criteria as generated from preliminary
measurement data.
As the computer generated model met the intended specification which therefore matched the
original wire cutters from Geomed, front views of the major components (handles, cutting
blades and linkages) could be exported into a drawing sheet and subsequently saved as a
DXF file, this would then be imported into working model to obtain a benchmark value for
the mechanical advantage.
7 Theoretical kinematical and torque transmission analysis
The following chapter will analyse the mechanical advantage of the Geomed wire cutting
pliers with respect to the external and internal linkages in order to create the compounded
four bar configuration. With reference to Rothenhofer (2010), the constraint equation will be
used to analyse the internal four bar linkage transmission ratio based on instantaneous
internal angles, followed by multiplying this value by the external linkage mechanism with
respect to the input. Finally, this value is then to be compared with the lever ratio stated by
the British standard BS 3087-7:1996 to check each method’s validity.
Fig. 6-10: Model mass properties
Final Year Project (BEng) 2012
58
7.1 Geomed internal four bar linkage transmission ratio (relaxed position)
Using the coordinates from figure 5-5 and joining the points to create lines and hence
measurable angles allows for creation of figure 7-1 where the mechanism is in the relaxed
state:
Fig. 7-1: Internal four bar linkage analysis of Geomed wire cutting pliers
Where 64. , 140.1 , and 133.3 .
Using the kinematic constraint equation (equation 7.6):
Then:
( 20.311 66.641 64. 20.311 34.443 64. 140.1
34.443 66.641 140.1 20.311 34.443 64. 140.1 ) (8.0)
1223. 2 6 6.9
14 2.33 6 6.9 0.69 (8.1)
The transmission ratio of the internal linkage in the open position is then:
1
0.69 1.45 (8.2)
𝐴 20.311𝑚𝑚
𝐵 = 31. 0𝑚𝑚
𝐶 34.443𝑚𝑚
𝐺𝑟𝑜𝑢𝑛𝑑 𝑅𝐻𝑆 𝐻𝑎𝑛𝑑𝑙𝑒
𝛾
𝜃
𝜃
𝐷 66.641𝑚𝑚
Final Year Project (BEng) 2012
59
7.2 Geomed internal four bar linkage transmission ratio (3mm offset)
From having created the three dimensional Pro EngineerTM
model and constraining the
assembly in order to obtain a fully functioning kinematic mechanism, the handles could be
closed in CAD based on measurement data in the relaxed position; this gave the angles 63.2
and 139.0 degrees for and respectively; as illustrated in figure 7-2.
`
Then:
( 20.311 66.641 63.2 20.311 34.443 63.2 139.0
34.443 66.641 139.0 20.311 34.443 63.2 139.0 ) (9.0)
120 .16 6 .20
1505. 6 6 .50 0.64 (9.1)
The transmission ratio of the internal linkage in the 3mm offset position is then:
1
0.64 1.56
(9.2)
The answer obtained from equation (9.2) may seem low initially, but this value is not too
dissimilar from that claimed by Geomed themselves (figure 7-3). With a transmission ratio of
1.56 compared to a value of 1 with no internal compound linkage, only 64% of the input
force is required to create an equal output force; thus allowing the user to apply a load 36%
less.
Fig. 7-2: Internal linkage angles for 3mm cutter offset
Final Year Project (BEng) 2012
60
As the value for mechanical advantage of the patented compound mechanism illustrated a
close correlation to the calculated theoretical value in the cutting position, kinematic analysis
using the kinematic constraint equation of a four bar linkage proves to be a valid method of
determining the instantaneous force transmission index (mechanical advantage) for any given
input angle – furthermore, the results also confirmed that the 3-dimensional Pro-Engineer
model had been created with a minimal deviation in geometry to the GEOMED wire cutting
pliers.
7.3 Combined mechanical advantage of Geomed wire cutting pliers
From Keenan (2006), the total mechanical advantage of a machine is the sum of the
individual simple mechanisms. Therefore the total mechanical advantage of the Geomed
cutting pliers would be the product of the internal and external linkage mechanisms.
From simple lever theory:
Fig. 7-3: Transmission quality compared to claimed value by Geomed (Geomed.de, 2011)
Final Year Project (BEng) 2012
61
(10.0)
Where the torque is exerted on the handles due to a perpendicular force acting to the
input linkage of the external mechanism (the handles) and is the output torque at the
cutting end. The output force relative to an input at the handles is simply then a ratio between
the length of the handle relative to its point of rotation and the distance between the cutting
end and the main fixed pivot or:
(10.1)
Then the lever ratio for the external mechanism (for maximum leverage) and using figure 6-9
is:
1 6.2 1 .0
24.0 .0 (10.2)
From Keenan (2006), the total mechanical advantage in the 3mm offset position is then:
.0 1.56 10.92 (10.3)
7.4 Mechanical advantage using lever ratio equation from BS 3087-7:1996
From BS 3087-7:1996, where the overall lever ratio is based on the displacement of the
handles relative to the cutting end (using equation (6.2)):
The total mechanical advantage or lever ratio based on angular displacement is then:
104. 1.9
3.0 10.93 (10.4)
Figure 7-4 illustrates the process of choosing 3mm as the offset gap for the cutting position.
Final Year Project (BEng) 2012
62
Fig. 7-4: Cutting end gap between blades based on BS 3087-7:1996
From a preliminary theoretical analysis, equation’s (10.3) and (10.4) gave extremely similar
results with negligible differences in mechanical advantage (less than 0.1%), illustrating the
validity of each method of calculation; hence proving the notion that the overall mechanical
advantage for a complex system is the product of the mechanical advantage of each
constituent simple mechanism.
Most importantly, the results showed that either method of calculation could be used in order
to determine the systems mechanical advantage for any instantaneous position of either the
handles (using the method from BSI) or the product of the mechanical advantage of the
internal compounded mechanism at the corresponding instantaneous linkage angles and that
of the external mechanism, i.e. the ratio of distances between the cutting end to specified
product datum (cutting end pivot) and the point of loading to the handle pivot.
8 Excel analysis of internal linkage mechanism
Inspection of figure 8-1 illustrated that the maximum force transmission quality is present
when the coupler link is parallel to the input link and supports the hypothesis based on the
work of Phelan (1988). From equation (1.0), it could be seen that when this condition was
approached, that the sin of the transmission angle approached zero causing the coupler force
to tend to infinity and therefore reaching its toggle position; these same results were
encountered by Chang and Lin (2002) who plotted the FTI (force transmission index) as a
Final Year Project (BEng) 2012
63
function of input link rotation and witnessed this index tending to infinity at the mechanisms
toggle position.
The data table for figure 8-1 can be viewed in appendix 3.
However, as the blades were oriented such that to cut the wire in question, this toggle
position was not reached due to having a value of 63.2 degrees and not the ideal 31 degrees
where the coupler and input link are in a parallel condition. It could therefore be the case that
a more suitable modification would be to use a shorter input link in the internal mechanism or
to use blades with a lower breadth in order to allow the internal input link to reach this toggle
position rather than adjusting the input link of the external mechanism.
Fig. 8-1: Torque transmission of Geomed wire cutting pliers with respect to input link
angle
-200
-100
0
100
200
300
400
500
0 10 20 30 40 50 60 70 80
Mec
ha
nic
al
ad
va
nta
ge
Theta 1 (degrees)
Torque transmission of internal four bar linkage Vs input link angle
Theta 1
Final Year Project (BEng) 2012
64
A simple 2-Dimensional drawing (created in Working Model) of the internal four bar linkage
utilized in the Geomed wire cutting pliers illustrated the process of the transmission angle
approaching the ideal 90 degrees as approaches 31degrees
1. By analysing figure 8-2, it was clear that at the starting position (when the pliers are
in the relaxed position) the output force had a minimum value due to the transmission
angle having a value near to 180 degrees and a coupler angle of a near 90 degrees.
2. From figure 8-3, as the transmission angle approached 90 degrees (or approached
31 degrees) the coupler force and torque transmission value had a combined
maximum value.
Fig. 8-2: Working model representation of internal mechanism in starting position
Fig. 8-3: Working model representation of internal mechanism in maximum force transmission
position
Final Year Project (BEng) 2012
65
3. As the input link passed 31 degrees a negative torque as applied to the output link
through the coupler and is illustrated in figure 8-4.
Additionally, it could be shown the internal linkage did not satisfy Grashof’s criterion due to
the linkage locking under complete rotation of the input link and can be seen in figure 8-5
where the mechanism could not crank completely when being rotated clockwise or counter-
clockwise.
Fig. 8-4: Working model representation of internal mechanism in negative torque region
Fig. 8-5: Illustration of non-Grashof conformance
Final Year Project (BEng) 2012
66
9 Working model analysis of standard configuration
The next step of the investigation would be to analyse the original configuration in working
model in order to obtain a value of the torque transmission (mechanical advantage) which
could be compared the theoretical values in chapter 7.
From the work carried out by Wang (1996), the method of obtaining a value for the
mechanical advantage of the mechanism would be to incorporate a spring balance into the
system (i.e. a counter-acting spring at the cutting end) which would measure the output force
as a function of the spring displacement and therefore tension. The simulation would be run
to neglect effects of mass/inertia with the left hand side handle being anchored to provide a
rigid support for all the remaining components.
9.1 The test model and initial conditions
Various configurations of spring tension were tested in order to obtain a maximum value for
the mechanical advantage; the values chosen for the spring in order to meet this requirement
whilst maintaining a non-touch condition between the two blades was achieved using a spring
stiffness (k) of 0.38N/mm at a length of 4.684mm (as measured from preliminary data).
A force vector of -100N was applied in the X direction on the right hand side handle whilst
anchoring the left hand side handle, yielding a maximum output force of -975N (the negative
sign denotes a compressive force) or a mechanical advantage of 9.75. This value correlates
closely to the theoretical value of 10.925 with a percentage difference of only 10.8% and
demonstrates the validity of the theoretical calculations.
The graph of output force versus spring displacement is illustrated in figure 9-1 alongside the
initial applied conditions and model representation.
Final Year Project (BEng) 2012
67
As a benchmark value had been obtained with a mechanical advantage which closely
represents the theoretical data, the modification of the driven link fixed pivot could be carried
out; this would be achieved by adjusting the pivot in X and Y using a matrix positioning
system in order to correlate data between rows and columns. Modification of the input link
would have the effect of modifying the force transmission index to the internal linkage
mechanism due to a different input moment from different input link lengths and varying
components of the input force along the coupler link.
10 Input link fixed pivot modification
In order to obtain a suitable test sample size, the fixed input link joint was patterned in 0.8
degree increments about the corresponding axis created for the right hand side handle to
allow for correct spacing of the 5mm diameter fixing rivets; seven joint locations were
created above the standard location (in Y) with 2 being below. In order to obtain results in X,
ten holes were patterned in X relative to each input link joint on the right hand side handle;
this would allow for analysis of the force transmission as the input angle approaches a
perpendicular condition to the second link within the system and beyond (relative to the
input). Figure 10-1 illustrates the modified handle to allow for a suitable number of data
Fig. 9-1: Working model analysis of original Geomed linkage configuration
Final Year Project (BEng) 2012
68
points in order to determine a fixed input joint location for an improved overall system
mechanical advantage.
11 Modification of Working Model analysis setup
It was found that using a spring to measure the tension between the cutting blades proved
unreliable due to the compound mechanism locking and in fact causing a state of tension
rather than compression when using the coordinate points furthest away from the handle in X;
for this reason the analysis was modified by using a rigid member to measure the tension with
the cutting blades offset by 3mm (due to the most commonly cut cable with the device being
2-3mm) which to provide greater repeatability between tests without the appearance of
sudden anomalies. Additionally, a single value would be obtained for the mechanical
advantage compared to a sinusoidal curve obtained in the initial Working model analysis; this
would aid to take readings rather than predicting the maximum from the graph plot
illustrating the tension versus time.
Fig. 10-1: Modification of input link fixed pivot in order to create matrix grid for data collection
Final Year Project (BEng) 2012
69
An example of an anomaly obtained using a spring configuration with the modified handle is
illustrated in figure 11-1 alongside the revised model setup for more accurate measurement;
illustrated in figure 11-2.
Fig. 11-1: Measurement anomalies using the spring setup in Working model
Fig. 11-2: Rigid member setup in Working model for increased repeatability between tests
Final Year Project (BEng) 2012
70
When re-constraining the right hand side handle and running the analysis using the standard
positioning (as used by Geomed), a slight discrepancy between output forces was seen
compared with the initial analysis (possibly due to errors during the constraint procedure by
not using pin joints exactly concentric to the linkage ends). An output force of -986N was
achieved compared with the initial model analysis of -975N; for this reason the latter value
would be used to maintain fair and accurate data for use of comparison to the standard
position.
12 Working model results using input link matrix
The following chapter illustrates the results obtained using the modified handle in order to
obtain a suitable number of data points from which to identify the optimum external input
link position at the fixed pivot.
12.1 Output force using rigid member configuration
Table 5 illustrates the results obtained using the matrix where each row and column directly
correlates to the row and column from the matrix of the right hand side modified handle; this
means that column 1 row 1 would be the uppermost data point on the right hand side handle
in the top left corner.
Table 5: Output force in working model using rigid member (SPAR)
Top 10 (values with highest mechanical advantage)
Legend
Greater magnitude of output force than control
Control value
1 2 3 4 5 6 7 8 9 10
1 -3.23E+02 -5.56E+02 1.07E+03 -3.56E+03 -4.80E+03 -1.68E+03 -1.10E+03 -8.60E+02 -7.26E+02 -6.40E+02
2 560.569 999.19 2128.629 3.40E+04 -3135.87 -1616.63 -1157.73 -925.233 -791.93 -703.141
3 943.908 1686.284 4816.12 -8910.47 -2550.91 -1587.64 -1105 -981.477 -847.356 -755.293
4 1432.11 2869.578 1.98E+04 -4.81E+03 -2302.16 -1576.9 -1230.42 -1028.86 -899.1 -804.122
5 2133.687 5316.551 -1.81E+04 -3.69E+03 -2158.99 -1572.58 -1262.9 -1071.47 -942.855 -847.296
6 3292.632 1.34E+04 -7.65E+03 -3.17E+03 -2.07E+03 -1.58E+03 -1.29E+03 -1.11E+03 -9.82E+02 -8.88E+02
7 5354.072 -1.13E+05 -5.37E+03 -2.87E+03 -2.02E+03 -1.58E+03 -1.32E+03 -1.14E+03 -1.02E+03 -9.25E+02
8 1.01E+04 -1.39E+04 -4.38E+03 -2.68E+03 -1.98E+03 -1.59E+03 -1.35E+03 -1.18E+03 -1.05E+03 -986.322
9 3.30E+04 -8.27E+03 -3.83E+03 -2.56E+03 -1.96E+03 -1.60E+03 -1.37E+03 -1.21E+03 -1.09E+03 -1.00E+03
10 -4.24E+04 -6.27E+03 -3.50E+03 -2.47E+03 -1.94E+03 -1.62E+03 -1.40E+03 -1.24E+03 -1.12E+03 -1.03E+03
Max 3.30E+04 1.34E+04 1.98E+04 3.40E+04 -1.94E+03 -1.57E+03 -1.10E+03 -8.60E+02 -7.26E+02 -6.40E+02
Min -4.24E+04 -1.13E+05 -1.81E+04 -8.91E+03 -4.80E+03 -1.68E+03 -1.40E+03 -1.24E+03 -1.12E+03 -1.03E+03
Matrix positioning (force in Newtons, negative sign denotes compression)
Final Year Project (BEng) 2012
71
The data from table 5 illustrated surprising results due to previous working model analyses
locking when using a spring arrangement rather than a rigid member between the cutting end.
The yellow cells in the matrix illustrated the locations which appear to give rise to the highest
mechanical advantage despite the fact that realistically at least, these positions would not
allow for the transmission of torque from the external mechanism to the cutting end via the
internal compound mechanism. This was due to the component of the force not being able to
provide a reaction from the input link of the internal mechanism. An explanation for these
anomalous results could be due to the external and internal input links reaching a parallel
condition and causing peak values as discussed in chapter 8 whereby a toggle position is
reached in terms of force output but no moment to transmit the force.
Figure 12-1 illustrates the top ten values for output force on the design model.
Figure 12-1: Values on design model giving rise to highest output force when using
rigid member at cutting end
Final Year Project (BEng) 2012
72
12.2 Output force using spring configuration
In order to validate the data using a rigid member at the cutting end, the test was re-run using
a spring configuration in order to analyse the output force over the global range of
movement; this would confirm whether the data cells from table 5 could be used to transmit a
suitable torque from the handles to the cutting end and would also allow to confirm the
results from any preliminary analysis in case of errors induced when re-constraining parts
between tests.
Table 6 illustrates the results from the second experiment using the modified handle by
measuring spring tension versus displacement.
12.3 Theoretical results discussion
From the secondary test carried out using the spring arrangement, the matrix position which
gave rise to the highest compressive output force was located in row 10, column 6 with a
value of -2030N or a mechanical advantage of 20.3 – a value almost twice the control value
of -1188N (a higher value compared to using the 3mm offset due to the cutting end closing
completely) and would allow the user to only need apply an input force which is 30% the
value of when in the original position due to a 70% increase in mechanical advantage. In this
Table 6: Output force in working model using a spring
1 2 3 4 5 6 7 8 9 10
1 FAIL FAIL FAIL FAIL FAIL -1.47E+03 -1.16E+03 -9.61E+02 -8.02E+02 -7.69E+02
2 FAIL FAIL FAIL FAIL FAIL -1620 -1301 -1090 -967 -864
3 FAIL FAIL FAIL FAIL FAIL -1670 -1346 -1169 -1021 -898
4 FAIL FAIL FAIL FAIL FAIL -1731 -1373 -1250 -1111 -935
5 FAIL FAIL FAIL FAIL -1180 -1767 -1454 -1307 -1120 -969
6 FAIL FAIL FAIL FAIL -1.21E+03 -1.80E+03 -1.51E+03 -1.34E+03 -1.13E+03 -1.03E+03
7 FAIL FAIL FAIL FAIL -1.26E+03 -1.91E+03 -1.52E+03 -1.37E+03 -1.19E+03 -1.11E+03
8 FAIL FAIL FAIL FAIL -1.29E+03 -1.94E+03 -1.53E+03 -1.38E+03 -1.24E+03 -1188
9 FAIL FAIL FAIL FAIL -1.30E+03 -1.98E+03 -1.54E+03 -1.40E+03 -1.31E+03 -1.22E+03
10 FAIL FAIL FAIL FAIL -1.32E+03 -2.03E+03 -1.60E+03 -1.41E+03 -1.38E+03 -1.26E+03
Max 0.00E+00 0.00E+00 0.00E+00 0.00E+00 -1.18E+03 -1.47E+03 -1.16E+03 -9.61E+02 -8.02E+02 -7.69E+02
Min 0.00E+00 0.00E+00 0.00E+00 0.00E+00 -1.32E+03 -2.03E+03 -1.60E+03 -1.41E+03 -1.38E+03 -1.26E+03
Matrix positioning (force in Newtons, negative sign denotes compression using spring)
Top 10 (values with highest mechanical advantage)
Legend
Greater magnitude of output force than control
Control value
Values which are not greater in magnitude than control
Final Year Project (BEng) 2012
73
particular location using the Geomed patented internal compounded linkage configuration,
the total increase in mechanical advantage over a mechanism which is simple class 1 lever (a
simple lever with an MA of 5.28 giving an output of 528N with an input of 100N) was now
284%
It is also worth mentioning that the locations which gave rise to the highest mechanical
advantage were to the right of the input link of the internal mechanism and furthest away
from the point of rotation – as would be expected due to torque being dependent on the
distance from the pivot multiplied by a force normal to the direction of travel.
13 Initial rapid prototype in order to compare theory with practise
Due to having found the input link fixed position which yields the highest mechanical
advantage of the system, the next step of the investigation would be to compare the
theoretical values obtained for mechanical advantage with that of a prototype model.
Rather than creating a full 3-dimensional FDM rapid prototype for the initial practical testing
phase, an initial planar acrylic model would need to be created using the University on-site
acrylic sheet laser cutter in order minimize costs in case of the mechanism not behaving as
intended and therefore also allowing for ease of modification – simple 2.5 mm screws could
also be used on an acrylic sheet model for ease of assembly.
13.1 Creation of planar mechanism model in Pro EngineerTM
In order to create the intended model, a similar method of creating the initial Working
ModelTM
components was carried out whereby top views were taken of the model followed
by extracting the edges of the each component and projecting them on a plane parallel to the
top view; this would then give a planar outline from which a simple extrude function could be
used to create a 3mm thick stamped sheet.
Figure 13-1 illustrates the planar (or sheet) version of the existing Geomed wire cutters with
the revised input link fixed pivot location.
Final Year Project (BEng) 2012
74
Due to the left and right cutting blades being stacked on-top one another, any object being
placed in-between these blades would be subject to a shear condition; to eliminate this, two
separate bolt-on blade tips were created which could be fixed on the front and rear of the left
and right hand side respectively in order to be able to place a spring or strain gauge in
between the cutting end.
This modification is illustrated in figure 13-2.
Fig. 13-1: The planar model with relocated input fixed pivot
Fig. 13-2: Bolt-on blade tips to eliminate shear condition of planar
mechanism at the cutting end
Final Year Project (BEng) 2012
75
13.2 Kinematic analysis in CAD of revised input link fixed pivot location and
initial problems encountered
Despite the theoretical value for mechanical advantage being highest in the revised location,
it was now the case that the cutting pliers could not close completely due to the right hand
side handle approaching a condition of rotation where the input link fixed pivot would not
transmit a component of force along the coupler link of the internal mechanism.
Figure 13-3 illustrates the problem encountered:
Having obtained a higher mechanical advantage at a 3mm offset where the cutters would
theoretically begin to the cut the wire had come at the expense of decreased cutter head travel
based on the displacement at the input; this particular finding also illustrated the balance
needed between the maximum mechanical advantage of the mechanism and allowable handle
travel without causing mechanism lock-out.
Fig. 13-3: Insufficient cutter head travel relative to handle displacement
Final Year Project (BEng) 2012
76
The second highest reading obtained for mechanical advantage from table 6 was located in
row 10 column 7 with an output force of -1600N (a reduction of 21.2% in mechanical
advantage from the reading from row 10 column 6). This location for the input link fixed
pivot of the external mechanism could then be tested to analyse whether a similar condition
would be obtained as seen in figure 13-3; this would be carried out by copying the coordinate
for the row 10 column 7 from the 3-dimensional model over into the planar mechanism in Pro
Engineer.
Figure 13-4 illustrates the remaining input coordinates of the external mechanism in row 10
from which the highest values of mechanical advantage had been obtained when using a
resisting spring arrangement. Using the second highest value of mechanical advantage from
row 10 column 7 would allow for the mechanism to fully close whilst not creating a clash
condition between the left and right hand side handles.
Fig. 13-4: adjustment position using data from table 6 to obtain input link fixed pivot
location yielding a significant increase in mechanical advantage of the mechanism
Final Year Project (BEng) 2012
77
To finalize the modification, all other input link fixed pivot locations were deleted where the
model was left only with the modified position which would provide the highest mechanical
advantage. Figure 13-5 illustrates the final test setup which would be compared with a
practical experiment after being laser cut from 3mm thick acrylic sheet; the updated 3-
dimensional model is also shown.
The original location had been included in order to have a control value during the practical
analysis and would also provide a data point from which the theoretical values from linkage
theory and working model could be compared.
A final render of the finished 3-dimensional model with the modified input link fixed pivot is
illustrated in figure 13-6.
Figure 13-5: (Left) The finalized model to be laser cut to begin
practical analysis followed by the updated 3-dimensional model
(right)
Final Year Project (BEng) 2012
78
Fig. 13-6: The final rendered model with modified input link fixed pivot positioning
Final Year Project (BEng) 2012
79
13.3 DXF drawing creation and CNC laser setup for initial prototype
The final process before creating a practical planar model would be to create a drawing of the
top views of each component to be able to create a DXF (or Drawing Exchange Format)
which could be recognised by the AutocadTM
software linked to the CNC laser cutting
machinery. All top views of each component were projected onto a drawing sheet and
subsequently saved in DXF format – upon importing these views into Autocad, each view
could be “closed” in order to be seen as a filled surface and rearranged for minimal waste of
the available acrylic sheet. 2 sets of acrylic sheet would be cut to create a “doubled up”
version (a total of 6mm in depth) in order to increase stiffness and minimize erroneous
results due to insufficient rigidity when using a single sheet acrylic model, and therefore
resulting component deformation.
The top view component DXF drawing sheet and laser cut parts are shown in figure 13-7.
Fig. 13-7: Above: DXF drawing template to be laser cut followed by the
laser cut parts after component placement revision to minimize waste
(below)
Final Year Project (BEng) 2012
80
13.4 The finished planar acrylic model for analysis
In order to fix each component together, M2.5 nuts and screws were used in order to
minimize friction and for ease of component disassembly in case of modification and for
when interchanging the input link of the external mechanism.
The finished physical model is illustrated in figure 13-8.
Fig. 13-8: The physical test model
Final Year Project (BEng) 2012
81
14 Finite Element Analysis of planar mechanism
As stated in the project proposal for this paper, a Finite Element Analysis was to be carried
out on the design model in order to gain an appreciation into the flow of the force across the
entire assembly for the original and revised input link fixed pivot positioning. In order for an
investigation such as this to be carried out, the model had to be constrained such that
sufficient contact surfaces, points of rotation and interaction types (penetrable / non
penetrable) were set up correctly in order to fully represent the system – Appendix “5”
illustrates the model setup with corresponding initial conditions and model configuration.
An applied clockwise torque of 13.384Nm would represent the input load as was applied to
the Working Model analysis (of 100N) due to the fixed pivot location on the original
configuration being 133.84mm from the point of rotation; this would also provide more
accurate results when analysing the revised input link fixed pivot location as no interpolation
of where to position the point load would need to be carried out.
14.1 FEA Analysis using COSMOSTM
The initial stress analyses of the original and revised configurations are illustrated in figure
14-1:
Figure 14-1: Stress flow analysis of the original configuration (left) and revised configuration (right)
Final Year Project (BEng) 2012
82
From initial inspection, the revised input link fixed pivot position evidently showed a greater
number of stress lines across the handle, cutter head and cutting wire; however in order to
quantify the stress accurately at the cutting head and wire, all assembly components other
than the cutting heads and wire were made rigid in order to eliminate displacement along
components perpendicular to the cutting plane which could cause possible anomalies.
The results after re-running the simulation for each configuration is shown in figure 14-2.
Fig. 14-2: Stress analysis results at cutting head for each input link
configuration
Final Year Project (BEng) 2012
83
14.2 FEA analysis comparison using MSC NASTRANTM
In order to validate the data obtained from Solidworks COSMOSTM
and in order to check for
any inconsistencies in model constraints, mesh and initial conditions, another analysis was
run using MSC NASTRANTM
whereby the Von Mises stress distribution was analysed
throughout the model.
The same initial conditions were used by fixing the left hand side handle, using frictionless
pin constraints and rigid bodies and using a torque of -13.384Nm on the right handle main
pivot.
The results are illustrated in figures 14-3 and 14-4.
Figure 14-3: FEA analysis of planar mechanism in NASTRAN with input link in original
position
Final Year Project (BEng) 2012
84
Figure 14-4: FEA analysis of planar mechanism in NASTRAN with input link in modified
position
14.3 Comparison of Finite Element Analysis results
The results from the two FEA analyses illustrated extremely similar results – as would be
expected using the same initial conditions and mesh size (see appendix 5). The maximum
stress (Von Mises) at the cutting end using COSMOSTM
for the original and modified input
link positions were observed as being 74.7Mpa and 94.3MPa respectively; this closely
matched the NastranTM
analysis results with 75.0Mpa and 93.8Mpa. The differences in stress
values were due to the alignment of the wire within the jaws when specifying tangency
Final Year Project (BEng) 2012
85
between the wire and cutter head faces; a slight deviation from the ideal 24mm from the main
datum would alter the amount of force applied to the cutting wire due to a change in the ratio
of lengths between the handle and cutting head.
A further observation aside from obtaining an increase value of stress applied to the cutting
wire with the input link in the modified position is that the handle was now subjected to
higher peak stresses (an increase of around 120%). This was due to the input link of the
internal mechanism (link 2) providing link 1 with a normal reaction force at the point of
cutting; link 1 (the input link of the external mechanism) was also then in a perpendicular
condition relative to the cutting head, thus causing the highest bending moment on the
handle.
15 Method of testing the physical prototype
In order to obtain an equivalent output force of the physical model at the cutting end, a force
balance system would be set up by loading the handle with a series of weights (0g-100g) and
measuring the corresponding output force at the cutter head using a force balance, as carried
out by Midha et al (1984). The setup would be slightly modified due to the low loads (as a
consequence of the models low stiffness) by incorporating strain gauges into the system to
measure minute changes in displacement of the cutter head; the procedure would be carried
out as follows:
1) To correctly create a Wheatstone bridge for two strain gauges measuring in tension
2) To calibrate the strain gauges using a series of weights (0-1000g) to measure strain
versus load
3) To test the setup by hanging weights on the loading arm (right hand side, using
weights 0-100g in order to create predicted 1000g output force with 100gram load on
input) and measuring the corresponding strain at the cutter head
4) To repeat each experiment three times (original input and modified input link
position) in order to obtain reliable data
The equipment needed to carry out these tasks would be:
2 Tokyo Sokki Kenkyujo linear strain gauges Type FLA-5-11 (2.11+/-1 gauge factor,
120+/-0.3 ohm gauge resistance)
An TQ-SM1010 Digital Strain Display using a gauge factor of 2.1
Final Year Project (BEng) 2012
86
An Aluminium strip in order to mount two strain gauges measuring in tension
o Acetone to remove grease from Aluminium surface
o Super Glue to stick strain gauge onto Aluminium surface
o Sellotape to provide insulation between strain gauge terminal and aluminium
strip
o Scoring tool
o Set square for scoring perpendicular lines for strain gauge alignment
o Digital vernier callipers in order to measure aluminium cross-sectional area
(sensitive to 0.01 )
4 wire telephone cable
Soldering Iron / Solder
Wire to attach cutter head to strain gauge
2 G-Clamps
Chemistry clamp
2 “dummy” strain gauges to complete Wheatstone bridge
Multimeter to ensure circuit has been soldered correctly
15.1 Preliminary equipment setup and calibration
The following chapter illustrates the processes which were carried out in order to create a test
setup for subsequent data analysis.
15.1.1 Creating the Wheatstone bridge for strain measurement
In order to obtain quantitative data for the deflection of the cutter head under tension with an
applied load, a Wheatstone bridge needed to be created using two strain gauges attached to a
13.86mm x 0.96mm cross-section aluminium strip on either side measuring tension.
U.A. Bakshi; A.V. Bakshi (2003) state that bridge circuits, consisting of four resistor arms in
order to form a closed circuit, operate on a null-indication principle whereby the bridge
compares an known electrical current with that of a known standard component. In a standard
bridge circuit the bridge is said to be balanced when no current flows through the null
detector (generally a galvanometer, a device for measuring small electric currents); this leads
to a relationship between the four resistors (or strain gauges in the context of the project)
whereby a balancing condition/equation can be synthesized in order to measure the current
through an unknown value when the bridge becomes unbalanced.
Final Year Project (BEng) 2012
87
U.A. Bakshi; A.V. Bakshi (2003) continue to illustrate the principle of a Wheatstone bridge
by means of demonstrating the derivation of the balance condition. The authors state that for
zero current to flow through the galvanometer, that points C and D must be in a state of equal
potential, thus arms AD and AC also being subject to the same potential.
Figure 15-1 illustrates the Wheatstone bridge circuit.
As AC and AD are equipotential:
(11.0)
With the galvanometer current being zero in a balanced state and considering the current
flow:
(11.1)
(11.2)
𝑆𝑤𝑖𝑡𝑐
𝐸𝑚𝑓
𝐴
𝐺
𝑅
𝑅
𝑅
𝑅 𝐵
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑎𝑟𝑚 𝑈𝑛𝑘𝑛𝑜𝑤𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐶 𝐷
𝐼
𝐼
𝐼
𝐼
𝑅𝑎𝑡𝑖𝑜 𝑎𝑟𝑚𝑠
Figure 15-1: The Wheatstone bridge (U.A. Bakshi; A.V. Bakshi, 2003)
Final Year Project (BEng) 2012
88
Substituting (11.2) and (11.1) into equation (11.0):
(
) (
2 4
) (11.3)
2 4 1 3 (11.4)
Expanding the brackets:
(11.5)
And finally, due to being equal on both sides:
(11.6)
Then:
(11.7)
Equation (11.7) is called the balance condition of the Wheatstone bridge (U.A. Bakshi; A.V.
Bakshi, 2003); if this balanced condition is no longer present in the bridge, a current is passed
through the galvanometer due to AC and AD not being equipotential.
For the Lab, preparation was begun by scoring perpendicular lines on the surface of the
Aluminium strip in order to align the strain gauges correctly, this was followed by gluing the
strain gauges to the aluminium strip and provide a contact by using a terminal in order to
solder the telephone wire to the strain gauges; Sellotape was used to insulate the strain gauge
contact from the Aluminium surface and two “dummy” strain gauges were used in order to
complete the Wheatstone bridge.
The gauges were finally checked using a Multimeter to ensure the resistance read 120 Ohms,
as stated by the manufacturer.
The finished strain gauge is illustrated in figure 15-2.
Final Year Project (BEng) 2012
89
15.1.2 Calibration of the strain gauge
In order to verify which loads correspond to a particular strain, the strain gauge was
calibrated by hanging weights directly from the aluminium strip using copper wire and a
chemistry clamp.
The results are illustrated in table 7.
Fig. 15-2: The finished strain gauge with top-side (Left) and underside (Right)
Fig. 15-3: Test setup for strain gauge calibration
𝐶 𝑒𝑚𝑖𝑠𝑡𝑟𝑦 𝑐𝑙𝑎𝑚𝑝
𝑆𝑡𝑟𝑎𝑖𝑛 𝑔𝑎𝑢𝑔𝑒
𝐶𝑜𝑝𝑝𝑒𝑟 𝑤𝑖𝑟𝑒
𝑊𝑒𝑖𝑔 𝑡 𝑎𝑛𝑔𝑒𝑟
𝐶𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 0.96𝑚𝑚
13. 6𝑚𝑚
Final Year Project (BEng) 2012
90
load (grams) Strain ( )
0 0
100 1
200 2
300 3
400 4
500 5
600 6
700 7
800 8
900 9
1000 10
Table 7: Strain calibration
15.1.3 The final physical test setup
As a corresponding strain had been obtained for a particular load, the physical prototype
could be clamped and connected to the strain gauge. This was achieved by filing a groove
into the moving cutter head, and looping the welding wire around the cutter head in order to
indirectly measure the reaction force as the cutting end moves throughout its travel.
The final test setup and cutter head wire loop are illustrated in figures 15-4 and 15-5
respectively.
Final Year Project (BEng) 2012
91
Fig. 15-4: The final test setup in order to test the physical model
Fig. 15-5: The cutter head wire loop in order to measure strain
Final Year Project (BEng) 2012
92
16 Results of testing the physical model
The following chapter presents the experimental findings using the method from chapter 15
and the test setup from figure 15-4. All associated raw data for chapter 15 is illustrated in
appendix 4.
Error bars for each graph have been generated using the standard uncertainty of the mean
or:
√ (12.0)
Where s is the standard deviation of the mean and n is the number of results for each data set.
The graph plots from experimentation are shown in figures 16-1, 16-2 and 16-3.
Final Year Project (BEng) 2012
93
Fig. 16-1: Strain vs. load for original configuration
-2
0
2
4
6
8
10
12
0 20 40 60 80 100 120
Str
ain
(μ
ε)
Applied load (grams)
Original input link position strain vs. load readings
Strain original 1st test"
Strain original 2nd test
Strain original 3rd test
Strain original averages
Final Year Project (BEng) 2012
94
Fig. 16-2: Strain vs. load for modified configuration
-2
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120
Str
ain
(μ
ε)
Applied load (grams)
Modified input link position strain vs. load readings
Strain modified 1st test"
Strain modified 2nd test
Strain modified 3rd test
Strain modified averages
Final Year Project (BEng) 2012
95
Fig. 16-3: Comparison of strain vs. load between original and modified configuration
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
0 20 40 60 80 100 120
Str
ain
(μ
ε)
Applied load (grams)
Original vs. modified input link position strain readings
Avg. Strain original
Avg. Strain modified
3mm offset marker
Final Year Project (BEng) 2012
96
16.1 Discussion
From figure 16-3, it is evident that the modified input link position yields higher output
forces upon applying larger masses (due to a decrease in cutter-head span when under
tension) and supports the project hypothesis whereby a larger output force is present within
the system due to the input link approaching a parallel condition to the cutter head blades and
a perpendicular condition to the input force; thus creating a maximum moment about the
point of rotation.
In other words, the main reason as to why the modified linkage configuration yields a higher
output force at greater applied loads is due to the modified input link fixed pivot position
allowing for the input link of the external mechanism to reach a parallel condition with the
cutting head in a shorter space of time when compared to the input link in the original
position.
It is also worth noting that the original configuration would appear to provide a greater output
force at increased cutter head spans; one of the main objectives of GEOMEDTM
whereby the
patented linkage configuration is intended to maximise the cutting force at larger cutter head
spans in order to shear higher gauge wires. However another explanation as to why the
original configuration yields a higher output force at lower applied loads could be due to the
original position of the input link fixed pivot providing a 45 degree incident angle which
provides a greater amount of rotation on the input link of the internal mechanism. The
modified position on the other hand, starts in a lower position than the original configuration
and therefore does not provide the same amount of rotation, but allows the mechanism to
reach a toggle position more quickly; yielding a higher maximum output force.
Above a loading of 50 grams however, when the cutter head jaws are allowed to travel when
overcoming friction, the revised input link configuration yields substantially higher strain
values than the original configuration whereby the differences in strain value become larger
as the mass (and therefore cutter-head travel) is increased; thus producing functions in the
form of a polynomial, as suggested by Phelan (1988).
16.2 Comparing results with theory
In order to gauge the reliability of the results obtained, let us consider the aluminium test strip
under tension, whereby the equivalent tensile force can be calculated from experimental
strain.
Final Year Project (BEng) 2012
97
With the aluminium strip having a cross-sectional area of 13.86mmx0.96mm and a Young’s
Modulus of 70Gpa (Efunda, 2012), then the maximum force applied in order to cause 10
(for the original configuration) is:
(12.1)
Then:
( 13. 6 10 0.96 10 10 10 0 10 ) (12.2)
9.314 949 (12.3)
Which corresponds closely to the weight added (100grams, where the theoretical mechanical
advantage was calculated as being 10.93), indicating the experiment was carried out in an
accurate and sensible manner with a minimal deviation from the theoretical values; the slight
loss in mechanical advantage of the system would be due to friction in the mechanism.
Additionally, for completeness, calculating the maximum output force using the strain value
obtained for the modified linkage position
( 13. 6 10 0.96 10 13. 10 0 10 ) (12.4)
12. 6 1300 (12.5)
Equation (12.5) illustrates a strong correlation to the theoretical Working ModelTM
calculations (see table 6) whereby the predicted mechanical advantage in the modified
position was calculated to be 1600N as opposed to 1188N using the original configuration,
yielding a percentage increase of 34.7%.
With the experimental data, the percentage increase from 949grams to 1300grams is:
100 (1300 949
949) 3 .0 (12.6)
thus confirming the experimental data to match that of the maximum predicted value using
working model, and that of the theoretical calculation from chapter 7.
Final Year Project (BEng) 2012
98
16.3 Fair test factors
It is worth mentioning that several considerations were made to ensure the investigation was
carried out in a fair and sensitive manner in order to obtain reliable data.
These considerations include:
Ensuring the same area of testing was used for each repeat using the same equipment
Using an area away from sources of draft which could potentially alter strain readings
due to temperature changes
Using 2 G-clamps to lock the model to a planar surface to minimize/eliminate rotation
of the model between tests
Re-setting the strain gauge display between tests to eliminate sources of residual
strain / heat changes
Using the most sensitive equipment available with digital displays in order to
eliminate parallax error
Calibrating the strain gauges before use
Repeating each experiment 3 times
16.4 Anomalous results and limitations of the experimental procedure
From figures 16-1 and 16-2, the majority of data points lie outside of the experimental error
bars indicating that, despite obtaining results which match the theory, that the experiment
could further be improved in order to obtain data points situated closer to the mean, and
hence trend line; the most obvious way of achieving this would be to carry out further tests in
order to increase the test sample size , thus reducing the standard uncertainty.
However, it must be remembered that the high sensitivity of the equipment used would make
it increasingly difficult to obtain the same value of strain for subsequent repeats of the same
test. Additionally, despite using an area with minimal fluctuation in ambient temperature,
some sporadic strain values had been recorded in preliminary measurement whereby strains
were displayed without having added any weights to the system; thus subjecting the
experiment to compounded errors combined with friction between contact linkages and
friction between the pin joints (M2.5 bolts).
Final Year Project (BEng) 2012
99
17 Conclusions
From the theoretical and practical data obtained, the project can be deemed a complete
success due to the modified linkage configuration yielding an increased maximum
mechanical advantage of 34.7% and 37.0% for the theoretical and experimental analyses
respectively, compared to the standard configuration produced by GEOMEDTM
for the
Hercules Gold-cut wire cutting pliers. This means that the product could in theory be scaled
by a factor of 0.73 the overall size of the original product in order to maintain an equivalent
mechanical advantage as the existing product, potentially saving manufacturing and material
costs for the manufacturer.
However, from the results obtained, the original linkage configuration provides a higher
output force with minimal cutter-head travel, as opposed to the revised linkage configuration
which yields a higher maximum output force, although at greater cutter-head displacements;
thus making the revised linkage configuration more suitable for similar or smaller gauge
wires of a higher stiffness or shear modulus. Additionally, with each linkage configuration,
an increase in cutter-head displacement (with the cutters approaching a shear condition or
3mm offset) directly correlated to an increase in mechanical advantage, as predicted in the
project hypothesis (from the work of Phelan, 1988) due to the coupler and output links of the
internal mechanism approaching a parallel condition. It was also proven (although obvious
from inspection) that the internal compounded mechanism does not conform to Grashof’s
criterion, due to the input link not being able to act as a crank, making the compounded
linkage configuration significantly powerful over small displacements.
To conclude, the project has successfully:
Reverse engineered the GEOMEDTM
Hercules Gold-cut wire cutting pliers from
preliminary measurement, followed by testing a physical prototype
Managed to obtain an almost identical mechanical advantage for the standard patented
internal linkage configuration through theoretical calculation
Obtained values of mechanical advantage from practical testing which closely
correlate to the theoretical data
Carried out a Finite Element Analysis of the original and revised linkage
configurations in order to indirectly identify the flow of the force from input to output
Final Year Project (BEng) 2012
100
Created a linkage configuration which yields a higher maximum output force than the
original product.
17.1 Recommendations
The project could be continued further by considering an alternative method of transferring
an input force from the handles to the cutting end other than using rigid members in the form
of links. The project has shown that the patented internal linkage configuration of the
Hercules Gold-cut wire cutting pliers can be deemed as “perfect” due to the input link
becoming parallel to the coupler link as the output link approaches a perpendicular condition
to the coupler when cutting 2-3mm wires; it is therefore the case that other potential
modification with the implementation of rigid bodies is limited by using similar arrangements
without increasing the size of the product.
In terms of testing, the experiment could be improved by using a material which is stiffer
than acrylic, meaning that thinner sheet could be used to further minimize friction between
the pin-joints (M2.5 bolts) and each link; this would improve readings when using a lower
weight and allow for more sensitive data plots at increase cutter head spans, rather than only
being able to measure the maximum output force upon reaching the point of cutting (2-3mm
offset).
Final Year Project (BEng) 2012
101
18 References
Accrington surgical. (2011). Surgical wire cutting products [Images online], available at:
http://www.accringtonsurgical.co.uk/Surgical-Instruments/i-tc-needle-holders/tc-wire-
cutters/tc-wire-cutters-682.html [Accessed 21 October 2011]
Ajuria, G et al. (2010). Optimum synthesis of planar linkages using a strain–energy error
function under geometric constraints. Journal of Mechanism and Machine theory [e-journal]
45 (1), January 2010, pp. 65-79. Available through Science Direct
[Accessed 26 November 2011]
Alt, H. (1932). Der uebertragungswinkel und seine bedeutung fuer das konstruieren
periodischer getriebe. Werkstatttechnik, 26(1), pp.61-64
Ambekar, A.G. (2007). Mechanism and Machine theory. New Delhi: Prentice-Hall
Anoop, M.R. (2009). Optimal Synthesis of Spatial Mechanism Using Genetic Algorithm.
10th National Conference on Technological Trends, [Online] Available at:
http://117.211.100.42:8180/jspui/bitstream/123456789/682/1/ME-MD-02.PDF
[Accessed 26 November 2011]
Balli, A., Chand, S. (2002). Transmission angle in mechanisms, Journal of mechanism and
machine theory, 37(2), pp. 175-195
Baratz, M et al. (1999). Orthopaedic surgery: the essentials. New York: Thieme Medical
Publishers, Inc
Bakshi, U.A., Bakshi, A.V. (2003). Electrical Machines and Instruments. 2nd
ed. Pune:
Technical publications
British Stainless Steel association. (2010). Selection of Stainless Steels for Surgical
Instruments. [Online] Available at:
http://www.bssa.org.uk/topics.php?article=132
[Accessed 29 November 2011]
Final Year Project (BEng) 2012
102
British Standards Institution. (1996). BS 3087-7:1996 Pliers and nippers – Specification for
dimensions of lever assisted side cutting pliers, end and diagonal cutting nippers. London:
BSI
British Standards. (2011). What is a standard? [Online] Available at:
http://www.bsigroup.com/en/Standards-and-Publications/About-standards/What-is-a-
standard/
[Accessed 28 November 2011]
British Standards Institution. (2001). BS 5194-1:1991 Surgical instruments – Metallic
materials: Stainless Steel. London: BSI
Broadbooks, P., Haws, T.L and Hull, C.A. (1902). Pliers. US. Pat. 699,909
Brunschwig, H. (1971). Dis ist das Buch der Cirurgia: Hantwirchung der Wund Artzny. New
York: Medicina Rara Ltd.
Buchholz, B., Armstrong, T.J. (1992). A kinematic model of the Human hand to evaluate its
prehensile capabilities. Journal of Biomechanics, 25 (2), pp. 149-162
Caravello, P. (2008). Adjustable compound cutters or grippers. US. Pat. US 2008/0168870
(Patent application publication)
Chang, W.T., Lin, C.C and Wu, L.I. (2005). A note on Grashof’s theorem. Journal of Marine
Science and Technology, 14 (4), pp. 239-248
Chang, W.T., Lin, C.C. (2002). The force transmissivity index of planar mechanisms.
Journal of Mechanism and Machine theory, 37 (1), pp. 1465-1485
Chondros T. G. (2010). Archimedes life works and machines. Journal of Mechanism and
Machine Theory , 45 (1) , pp. 1766-1775
Eckhardt, H.D. (1998). Kinematic design of machines and mechanisms. New York: McGraw-
Hill
Final Year Project (BEng) 2012
103
Edgren, C.S., Radwin, R.G and Irwin, C.B. (2004). Grip force vectors for varying handle
diameters and hand sizes. Journal of Human Factors [e-journal], summer issue, 42 (6), pp.
244-251. Available through Mendeley
[Accessed 27 November 2011]
Efunda (2012). Properties of common solid materials. [Online] Available at:
http://www.efunda.com/materials/common_matl/Common_Matl.cfm?MatlPhase=solid&Matl
Prop=Mechanical
[Accessed 28th
February 2012]
Enika surgical. (2011). Surgical wire cutting products [Images online], available at:
http://www.enika.com/dental/products.asp?MsID=2&SubID=116
[Accessed 21 October 2011].
Ferguson, E.S. (1962). Kinematics of Mechanisms from the time of Watt. United States
National Museum, Bulletin 228, Smithsonian Institution, Washington DC, 27(1). pp. 185-230
Geomed Medizin Technik GmbH & Co, No named inventor. (2003). Surgical pliers. DE. Pat.
20,207,785
Geomed Medizin Technik. (2011). Hercules Wire Cutters. [Online] Available at:
http://www.geomed.de/index.php?id=58&L=1
[Accessed 29 November 2011]
Hall. S. A. (1961). Kinematics and Linkage Design. Prentice-Hall, Englewood Cliffs, NJ
Keenan, J.P. (2006). The Best Test Preparation for the ASVAB. 6th
ed. NJ: Research and
Education Association, Inc.
Key surgical. (2011). Surgical wire cutting products [Images Online] available at:
http://www.keysurgical.com/products/?cat=7&prod=4#item4 [Accessed 21 October 2011].
Kirkup, J. (1993). From flint to stainless steel: observations on surgical instrument
composition. Annals of The Royal College of Surgeons of England, 75 (1), pp.365-374
Final Year Project (BEng) 2012
104
Kirkup, J. (1998). The history and evolution of surgical instruments: Scissors and related
pivot-controlled cutting instruments. Annals of The Royal College of Surgeons of England, 80
(1), pp. 422-432
Koeth, E.D.C., Brown, F and Haynes, R. (1905). Combination tool. US. Pat. 791,917
Lindsay, J., Whitney J.A and Quetil, C.E. (1874). Improvement in griping at cutting tools.
US. Pat. 146,829
Matweb (2011). AISI Type 316L Stainless Steel, annealed strip. [Online] Available at:
http://www.matweb.com/search/DataSheet.aspx?MatGUID=dbae14dbb31c4049beb047e1dca
1527a
[Accessed 03 December 2011]
Matweb (2011). Tungsten Carbide, WC [Online] Available at:
http://www.matweb.com/search/DataSheet.aspx?MatGUID=e68b647b86104478a32012cbbd
5ad3ea
[Accessed 03 December 2011]
Mauersberger. K, Hanfried. K. (2009). A contribution to the history of cam mechanisms -
from Leonardo da vinci till today. Netherlands: Springer
Mcgorry, R.W. (2001). A system for the measurement of grip forces and applied moments
during hand tool use. Journal of Applied Ergonomics, 32(1), pp. 271-279
Midha. A et al. (1984). Mechanical Advantage of a Single Input and Multiple-Output Ports
Mechanical Device. Journal of Mechanisms, Transmissions, and Automation in Design, 106
(1), December 1984, pp. 462-467
Moon, F. (2007). The machines of Leonardo da Vinci and Franz Reuleaux: Kinematics of
machines from the Renaissance to the 20th
Century. Dordrecht: Springer
Mooney, A.J., H&M Enterprises, Inc. (1999). Wire cutting tool with integral holding means.
US. Pat. 5,920,990
Final Year Project (BEng) 2012
105
Norton. R (2004). Design of machinery: An introduction to the synthesis and analysis of
mechanisms and machines. New York: McGraw-Hill
Patel, T. (2011). Synthesis of Four Bar Mechanism for Polynomial Function Generation by
Complex Algebra. [Online] Ahmedabad, India: Nirma Institute of Technology. Available at:
http://www.bvmengineering.ac.in/docs/published%20papers/mechprod/mechprod/601018.pdf
Phelan, R.M. (1988). Fundamentals of mechanical design. 3rd
ed. New York: McGraw-Hill
Porter, H.K., Geddes, J.W. (1940). Wire cutter. US. Pat. 2,308,684
Porter, H.K., Humphrey, E and Porter, T.W. (1880). Bolt-cutter. US. Pat. 226,190
Rosen, L.J., Gaudet, R.A and Morgan, R.E. (1960). Endodontic cutter. US. Pat. 3,209,458
Rothenhofer, G., Walsh, C and Slocum, A. (2010). Transmission ratio based analysis and
robust design of mechanisms. Journal of precision engineering, 34 (1), pp. 790-797
Rowe, R.D., Smith, J.G., (1981). Hand tool for working with wire and cable. US. Pat.
4,224,067
Savigny, J.H. (1800). A Catalogue of Chirurgical Instruments. London: W. Bulmer and Co
Shirazi, K.H. (2007). Computer modelling and geometric construction for four-point
synthesis of 4R spherical linkages. Journal of Applied Mathematical Modelling [e-journal],
31 (9), September 2007, pp. 1874-1888. Available through: Science Direct
Shurtleff., W.F., Smith, A.L and Peters, J.C. (1975). Mild steel cutter. US. Pat. 3,913,227
Simplex medical. (2011). Surgical wire cutting products [Images online], available at:
http://www.simpexmedical.com/5152/9801.html
[Accessed] 21 October 2011]
Sirag surgical. (2011). Surgical wire cutting products [Images online], available at:
http://siragsurgicals.in/sirag/catelog.php?catgy=wire_cutter
[Accessed 21 October 2011].
Final Year Project (BEng) 2012
106
Smith, H., Smith, G.W and Durand, J.E. (1876) . Improvement in Pliers. US. Pat. 184,734
Spink, M.S. and Lewis, G.L. (1973). Albucasis on Surgery and Instruments. London:
Wellcome Institute of history and medicine
Suh, H.C and Radcliffe, W.C. (1978). Kinematics and mechanisms Design. New York: John
Wiley and Sons
Tippy, W., Smith, A.L and Beck, S.E. (1975). Cut and hold pliers. US. Pat. 3,922,781
Wang, S.L. (1996). "Mechanism simulation with Working Model," Frontiers in Education
Conference, 1996. FIE '96. 26th Annual Conference., Proceedings of , 3 (6-9). pp.1102-1106
Ward-Perkins, J.B., (1940). Medieval Catalogue of the London Museum. London: HMSO
Woodall, J. (1639). The surgeon’s mate. London: Bourne
Wu. L.I. (1990). Modified transmission angle of planar linkage mechanisms: Proceeding of
the ASME 21st Biennial Mechanism Conference, 1990, pp. 131–140.
Zhou. H, Cheung. H.M. E. (2004). Adjustable four-bar linkages for multi-phase motion
generation, Journal of mechanism and machine theory, 39 (3), pp. 261-279
Final Year Project (BEng) 2012
107
19 Appendix
Appendix 1- BS EN ISO7153-1:2001 (Metallic materials for surgical instruments)
Steel grade Chemical compositions (%)
Ref Grade No.
According tob
C Si
(max)
Mn
(max)
P
(max)
S Cr Mo Ni Other
Elements
ISO
4957
ISO
683-13
Martensitic Steels
A
B
C
D
E
F
G
—
27
28
—
—
—
—
3
4
5
—
—
—
—
0,09 to 0,15
0,16 to 0,25
0,26 to 0,35
0,42 to 0,50
0,47 to 0,57
0,6 to 0,7
0,65 to 0,75
1
1
1
1
0,5
0,5
1
1
1
1
1
1
1
1
0,04
0,04
0,04
0,04
0,03
0,03
0,04
0,03 max.
0,03 max.
0,03 max.
0,03 max.
0,025 max.
0,025 max
0,03 max.
11,5 to 13,5
12 to 14
12 to 14
12,5 to 14,5
13,7 to 15,2
12 to 13,5
12 to 14
—
—
—
—
—
—
0,5 max.
1 max.
1 max
1 max.
1 max.
0,5 max.
0,5 max.
1 max.
H
I
K
R
—
—
30
—
—
—
—
0,35 to 0,4
0,42 to 0,55
0,33 to 0,43
0,85 to 0,95
1
1
1
1
1
1
1
1
0,045
0,045
0,03
0,045
0,03 max.
0,03 max.
0,03 max
0,03 max.
14 to 15
12 to 15
15 to 17
17 to 19
0,4 to 0,6
0,45 to 0,9
1 to 1,5
0,9 to 1,3
—
—
1 max
—
V: 0,1 to 0,15
V: 0,1 to 0,15
—
V: 0,07 to
0,12
Ferritic Steels
L - 8a 0,08 max 1 1,5 0,06 0,15 to 0,35 16-18 0,6 max 1 max
Austenitic Steels
M
N
O
P
-
-
-
-
11
17
14
20
0,07 max
0,12 max
0,15 max
0,07 max
1
1
1
1
2
2
2
2
0,045
0,06
0,045
0,045
0,03
0,15 to 0,35
0,03 max
0,03 max
17 to 19
17 to 19
16-18
16,5 to 18,5
- c
2 to 2,5
8 to 11
8 to 10
6 to 8
10,6 to 13,5
a The reference letters are used for the purpose of cross-referencing.
b The grade numbers are provisional and will be subject to alteration when the relevant International Standards are published.
c The manufacturer has the option of adding molybdenum up to 0,7 %.
Final Year Project (BEng) 2012
108
Appendix 2 – Full derivation of the four bar kinematic constraint equation
With reference to figure 4-2 and using the following rules of Trigonometry:
Let us also call 180 where 180 = radians (allowing for simplification) and also substitute
( for A and for B:
Then:
2
2
2
And finally for lengths a and b:
2
Then for lengths c and d:
2 2
2
Due to geometry for figure 27, 0, then:
0 2 2
2
2 ( ( ) ( )
)
Then finally:
2 2 2 0
Final Year Project (BEng) 2012
109
Appendix 3 – Four bar linkage force transmission ratio table data
Theta 1
(radians)
Theta 2
(radians)
Transmission
ratio
Theta 1
(degrees)
Theta 2
(degrees) T2/T1
1.19 2.35 0.616 68 134.50 1.62
1.17 2.34 0.597 67 133.50 1.68
1.15 2.33 0.578 66 132.50 1.73
1.13 2.32 0.559 65 131.50 1.79
1.12 2.31 0.541 64 130.50 1.85
1.10 2.30 0.522 63 129.50 1.91
1.08 2.29 0.504 62 128.50 1.98
1.06 2.28 0.486 61 127.50 2.06
1.05 2.27 0.468 60 126.50 2.14
1.03 2.26 0.451 59 125.50 2.22
1.01 2.25 0.433 58 124.50 2.31
0.99 2.24 0.416 57 123.50 2.40
0.98 2.23 0.399 56 122.50 2.51
0.96 2.22 0.382 55 121.50 2.62
0.94 2.21 0.365 54 120.50 2.74
0.93 2.20 0.348 53 119.50 2.88
0.91 2.19 0.331 52 118.50 3.02
0.89 2.18 0.315 51 117.50 3.18
0.87 2.17 0.298 50 116.50 3.35
0.86 2.16 0.282 49 115.50 3.55
0.84 2.15 0.266 48 114.50 3.77
0.82 2.14 0.249 47 113.50 4.01
0.80 2.14 0.233 46 112.50 4.29
0.79 2.13 0.217 45 111.50 4.60
0.77 2.12 0.201 44 110.50 4.96
0.75 2.11 0.186 43 109.50 5.39
0.73 2.10 0.170 42 108.50 5.88
0.72 2.09 0.154 41 107.50 6.48
0.70 2.08 0.139 40 106.50 7.20
0.68 2.07 0.123 39 105.50 8.11
0.66 2.06 0.108 38 104.50 9.27
0.65 2.05 0.093 37 103.50 10.80
0.63 2.04 0.077 36 102.50 12.93
0.61 2.03 0.062 35 101.50 16.10
0.59 2.02 0.047 34 100.50 21.28
0.58 2.01 0.032 33 99.50 31.34
0.56 2.00 0.017 32 98.50 59.20
0.54 1.99 0.002 31 97.50 516.72
0.52 1.98 -0.013 30 96.50 -77.13
0.51 1.97 -0.028 29 95.50 -35.96
Final Year Project (BEng) 2012
110
0.49 1.96 -0.043 28 94.50 -23.47
0.47 1.95 -0.057 27 93.50 -17.44
0.45 1.94 -0.072 26 92.50 -13.88
0.44 1.93 -0.087 25 91.50 -11.54
0.42 1.92 -0.101 24 90.50 -9.88
0.40 1.91 -0.116 23 89.50 -8.64
0.38 1.90 -0.130 22 88.50 -7.68
0.37 1.89 -0.145 21 87.50 -6.91
0.35 1.88 -0.159 20 86.50 -6.28
0.33 1.87 -0.173 19 85.50 -5.76
0.31 1.86 -0.188 18 84.50 -5.33
0.30 1.86 -0.202 17 83.50 -4.95
0.28 1.85 -0.216 16 82.50 -4.62
0.26 1.84 -0.230 15 81.50 -4.34
0.24 1.83 -0.245 14 80.50 -4.09
0.23 1.82 -0.259 13 79.50 -3.87
0.21 1.81 -0.273 12 78.50 -3.67
0.19 1.80 -0.287 11 77.50 -3.49
0.17 1.79 -0.301 10 76.50 -3.33
0.16 1.78 -0.315 9 75.50 -3.18
0.14 1.77 -0.329 8 74.50 -3.04
0.12 1.76 -0.342 7 73.50 -2.92
0.10 1.75 -0.356 6 72.50 -2.81
0.09 1.74 -0.370 5 71.50 -2.70
0.07 1.73 -0.384 4 70.50 -2.61
0.05 1.72 -0.397 3 69.50 -2.52
0.03 1.71 -0.411 2 68.50 -2.43
0.02 1.70 -0.425 1 67.50 -2.35
Final Year Project (BEng) 2012
111
Appendix 4 – Raw data for stress vs. strain when loading physical model
Original input link position
mass (g) με
1st test 2nd test 3rd test stdev u Average xq 1st xq 2nd xq 3rd
0 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
10 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
20 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
30 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
40 1 1 2 0.58 0.33 1.3 0.3 0.3 0.7
50 3 3 2 0.58 0.33 2.7 0.3 0.3 0.7
60 4 4 4 0.00 0.00 4.0 0.0 0.0 0.0
70 6 7 6 0.58 0.33 6.3 0.3 0.7 0.3
80 6 7 6 0.58 0.33 6.3 0.3 0.7 0.3
90 8 9 8 0.58 0.33 8.3 0.3 0.7 0.3
100 9 11 10 1.00 0.58 10.0 1.0 1.0 0.0
Modified input link position
mass (g) με
1st test 2nd test 3rd test Stdev u Average xq 1st xq 2nd xq 3rd
0 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
10 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
20 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
30 0 0 0 0.00 0.00 0.0 0.0 0.0 0.0
40 1 0 0 0.58 0.33 0.3 0.7 0.3 0.7
50 2 3 2 0.58 0.33 2.3 0.3 0.7 0.3
60 4 4 4 0.00 0.00 4.0 0.0 0.0 0.0
70 8 8 7 0.58 0.33 7.7 0.3 0.3 0.3
80 9 8 9 0.58 0.33 8.7 0.3 0.7 0.3
90 11 11 12 0.58 0.33 11.3 0.3 0.3 0.3
100 13 14 14 0.58 0.33 13.7 0.7 0.3 0.7
Final Year Project (BEng) 2012
112
Appendix 5 - COSMOS Finite Element Analysis Report
Model Information
Model name: Planar wire cutter
Current Configuration: Default
Solid Bodies
Document Name and
Reference Treated As Volumetric Properties
Document Path/Date
Modified
Body.3
Solid Body
Mass:0.00634121 kg
Volume:7.92651e-007 m^3
Density:8000 kg/m^3
Weight:0.0621438 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\cutterightdepthc
orrect.SLDPRT
Feb 04 19:12:52 2012
Body.2
Solid Body
Mass:0.00634142 kg
Volume:7.92677e-007 m^3
Density:8000 kg/m^3
Weight:0.0621459 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\cutterleftdepthc
orrect.SLDPRT
Feb 04 19:14:06 2012
Model Information
Final Year Project (BEng) 2012
113
PartBody
Solid Body
Mass:0.0245649 kg
Volume:3.07061e-006 m^3
Density:8000 kg/m^3
Weight:0.240736 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\cutterright.SLD
PRT
Feb 04 19:11:50 2012
PartBody
Solid Body
Mass:0.0670188 kg
Volume:8.37734e-006 m^3
Density:8000 kg/m^3
Weight:0.656784 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\lefthandlepart.S
LDPRT
Feb 05 11:04:16 2012
PartBody
Solid Body
Mass:0.0257342 kg
Volume:3.21677e-006 m^3
Density:8000 kg/m^3
Weight:0.252195 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\link1hundredmi
ll.SLDPRT
Feb 05 11:04:16 2012
PartBody
Solid Body
Mass:0.0066088 kg
Volume:8.261e-007 m^3
Density:8000 kg/m^3
Weight:0.0647662 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\link2.SLDPRT
Feb 05 11:04:16 2012
PartBody
Solid Body
Mass:0.00936136 kg
Volume:1.17017e-006 m^3
Density:8000 kg/m^3
Weight:0.0917413 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\link3.SLDPRT
Feb 04 19:17:28 2012
Boss-Extrude1
Solid Body
Mass:0.000502655 kg
Volume:6.28319e-008 m^3
Density:8000 kg/m^3
Weight:0.00492602 N
G:\Uni Level 3\Final
year project\2d part
files in Catia for laser
cutter\FOR SOLID
WORKS
2012\wire.SLDPRT
Feb 04 19:52:16 2012
Final Year Project (BEng) 2012
114
Study Properties
Study name Study 1
Analysis type Static
Mesh type Mixed Mesh
Thermal Effect: On
Thermal option Include temperature loads
Zero strain temperature 298 Kelvin
Include fluid pressure effects from
SolidWorks Flow Simulation
Off
Solver type FFEPlus
Inplane Effect: Off
Soft Spring: Off
Inertial Relief: Off
Incompatible bonding options Automatic
Large displacement Off
Compute free body forces On
Friction Off
Use Adaptive Method: Off
Result folder SolidWorks document
(c:\users\ryan\appdata\local\temp)
Units
Unit system: SI (MKS)
Length/Displacement mm
Temperature Kelvin
Angular velocity Rad/sec
Pressure/Stress N/m^2
Final Year Project (BEng) 2012
115
Material Properties, loads and fixtures
Model Reference Properties Components
Name: AISI 316 Annealed
Stainless Steel Bar
(SS) Model type: Linear Elastic
Isotropic Default failure
criterion: Max von Mises
Stress Yield strength: 1.37895e+008
N/m^2 Tensile strength: 5.5e+008 N/m^2 Elastic modulus: 1.93e+011 N/m^2
Poisson's ratio: 0.3 Mass density: 8000 kg/m^3
Thermal expansion
coefficient: 1.6e-005 /Kelvin
SolidBody
1(Body.3)(cutterightdept
hcorrect-1),
SolidBody
1(Body.2)(cutterleftdepth
correct-2),
SolidBody
1(PartBody)(cutterright-
1),
SolidBody
1(Imported1)(latestmodif
iedhandlereadyfortesON
EHOLE-1),
SolidBody
1(PartBody)(lefthandlepa
rt-1),
SolidBody
1(PartBody)(link2-2),
SolidBody
1(PartBody)(link3-1),
SolidBody 1(Boss-
Extrude1)(modifiedinputl
ink-2),
SolidBody 1(Boss-
Extrude1)(wire-1)
Curve Data:N/A
Final Year Project (BEng) 2012
116
Model Reference Connector Details Strength Details
Pin Connector-1
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) 0 0 13.242 13.242
Shear Force (N) -42.237 -534.16 0 535.82
Torque (N-m) -0 -0 -1.2565e-012 -1.2565e-012
Bending moment (N-m) -0.55729 -0.26937 0 0.61898
Pin Connector-9
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) 0 0 53.63 53.63
Shear Force (N) -500.97 -41.942 0 502.73
Torque (N-m) 0 0 1.4413e-012 1.4413e-012
Bending moment (N-m) -0.42284 0.088695 0 0.43204
Pin Connector-10
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Final Year Project (BEng) 2012
117
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) -0 -0 -66.997 -66.997
Shear Force (N) 411.13 548.91 0 685.8
Torque (N-m) 0 0 1.4413e-012 1.4413e-012
Bending moment (N-m) 0.80581 -0.98481 0 1.2725
Pin Connector-11
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) -0 -0 66.998 -66.998
Shear Force (N) -411.12 -548.91 0 685.8
Torque (N-m) -0 -0 7.2671e-013 -7.2671e-013
Bending moment (N-m) 0.78348 -0.2055 0 0.80998
Pin Connector-12
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) 0 0 -183.06 183.06
Shear Force (N) 1239.5 538.61 0 1351.5
Torque (N-m) -0 -0 7.2672e-013 -7.2672e-013
Bending moment (N-m) -1.2934 2.1145 0 2.4787
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
No Data
Final Year Project (BEng) 2012
118
Pin Connector-13 Units: SI
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) -0 -0 -4.0973 -4.0973
Shear Force (N) 201.66 24.543 0 203.15
Torque (N-m) 0 0 9.596e-018 9.596e-018
Bending moment (N-m) 0.067476 -0.59503 0 0.59884
Pin Connector-14
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) 0 0 0.93239 0.93239
Shear Force (N) 169.29 -46.199 0 175.48
Torque (N-m) -0 -0 -9.7603e-017 -9.7603e-017
Bending moment (N-m) -0.14186 -0.51699 0 0.5361
Pin Connector-15
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) -0 -0 -20.075 -20.075
Shear Force (N) 91.532 24.709 0 94.808
Torque (N-m) 0 0 9.3458e-013 9.3458e-013
Bending moment (N-m) 0.047157 -0.023154 0 0.052534
Final Year Project (BEng) 2012
119
Pin Connector-16
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) -0 -0 -16.253 -16.253
Shear Force (N) 129.46 -9.8637 0 129.84
Torque (N-m) 0 0 7.9454e-013 7.9454e-013
Bending moment (N-m) 0.0029973 -0.058384 0 0.058461
Pin Connector-21
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) 0 0 13.383 13.383
Shear Force (N) 89.3 -506.95 0 514.75
Torque (N-m) -0 -0 -1.7166e-012 -1.7166e-012
Bending moment (N-m) -0.41604 -0.21312 0 0.46745
Pin Connector-22
Entities: 2 face(s) Type: Pin
Connection type: With retaining
ring (No
translation) Rotational stiffness
value: 0
Units: SI
No Data
Connector Forces
Type X-Component Y-Component Z-Component Resultant
Axial Force (N) -0 -0 -13.367 -13.367
Shear Force (N) -89.848 506.96 0 514.86
Final Year Project (BEng) 2012
120
Torque (N-m) -0 -0 -1.7166e-012 -1.7166e-012
Bending moment (N-m) 1.813 0.45891 0 1.8702
Load name Load Image Load Details
Force-4
Entities: 1 face(s)
Reference: Face< 1 >
Type: Apply torque
Value: -13.384 N-m
Fixture name Fixture Image Fixture Details
Fixed-1
Entities: 1 face(s)
Type: Fixed Geometry
Resultant Forces
Components X Y Z Resultant
Reaction
force(N) 132.089 27.2037 0.125037 134.862
Reaction
Moment(N-m) -1.08504 2.48097 0.00245652 2.70787
Final Year Project (BEng) 2012
121
Contact Information
Contact Contact Image Contact Properties
Contact Set-1
Type: Bonded
contact pair
Entites: 3 face(s)
Contact Set-2
Type: Bonded
contact pair
Entites: 3 face(s)
Global Contact
Type: Allow
Penetration
Components: 1
component(s)
Mesh Information
Mesh type Mixed Mesh
Mesher Used: Standard mesh
Automatic Transition: Off
Include Mesh Auto Loops: Off
Jacobian points 4 Points
Jacobian check for shell On
Element Size 1.50839 mm
Tolerance 0.0754193 mm
Mesh Quality High
Remesh failed parts with incompatible mesh Off
Final Year Project (BEng) 2012
122
Mesh Information - Details
Total Nodes 66647
Total Elements 36630
Time to complete mesh(hh;mm;ss): 00:00:41
Computer name: Staffordshire IS Labs
Resultant & Reaction forces
Selection set Units Sum X Sum Y Sum Z Resultant
Entire Model N 132.089 27.2037 0.125037 134.862
Reaction Moments
Selection set Units Sum X Sum Y Sum Z Resultant
Entire Model N-m -1.08504 2.48097 0.00245652 2.70787
Final Year Project (BEng) 2012
123
Study Results
Name Type Min Max
Stress1 VON: von Mises
Stress
0 N/m^2
Node: 40028
9.43181e+007
N/m^2
Node: 39713
Assem1-Study 1-Stress-Stress1
Name Type Min Max
Displacement1 URES: Resultant
Displacement
0 mm
Node: 7309
0.0217917 mm
Node: 46722
Final Year Project (BEng) 2012
124
Assem1-Study 1-Displacement-Displacement1
Name Type Min Max
Strain1 ESTRN: Equivalent
Strain
0
Element: 23313
0.000423608
Element: 23251
Final Year Project (BEng) 2012
125
Assem1-Study 1-Strain-Strain1
Image – Stress concentration close-up (with deformation, modified input link
position)
Final Year Project (BEng) 2012
126