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1. A.K.Kapse, Dr. C. C. Handa / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue4, July-August 2012, pp.1871-1573
A Generalized Approach For Measurement Of Performance Of
Planar Mechanism Using Relative Velocity Method.
1
A.K.Kapse, 2Dr. C. C. Handa
1
P.G Student, Department of Mechanical Engg, K.D.K.C.E, Nagpur, India
2
Professor & Head, Department of Mechanical Engg, K.D.K.C.E, Nagpur, India
Abstract
Mechanism are designed for desired The concept that velocity of any point on a link with
output or required performance for specified respect to another point on same link is always
input. Error in link length results in variation in perpendicular to the line joining this point on the
the performance of mechanism. Machines are space diagram. The present research work attempt to
consisting of mechanism for their successful arrange the link of four bar chain mechanism in
operations. The link length inaccuracies are due to descending order of sensitivity that is ratio of change
no. of factors like machining errors deflection of in output performance to change in link length. To
link, clearances in joint etc. Due to manufacturing obtain desired performance close tolerances will be
defects & clearances, the link length varies. This provided on some sensitive links and normal on
variations in link length causes variations in remaining links to optimize the cost. Relative
designed performance of mechanism. In this velocity method is used for the analysis of the four
paper a simple class I four bar mechanism is bar mechanism. Which is a graphical method and
analyzed, assuming that links are rigid. Design easy to check complete solution to the problem.
engineer wants tight tolerances for accurate
performance; while on other hand manufacturing 3. Performance
engineer prefer loose tolerances. This paper Performance of mechanism is expressed in
proposes an approach to identify the effect of term of desired output, position and location. In case
change in link length on the performance of the when the mechanism has to work as force or torque
mechanism, using relative velocity method. manipulator the performance can be expressed as
ratio of effort & load. In this performance of
Keyward: Mechanism, Keyward2: Relative mechanism is defined by at any angular position of
Velocity Analysis, Keyward3: Performance crank. This maximum torque can be specified as the
ideal performance. If variation in the performance of
1. Introduction fabricated mechanism is with in tolerance limit
If a number of links are assembled in such a mechanism should be accepted. However if the
way that motion of one cause constrained and variation is not within the limit further performance
predictable motion to other it is called as mechanism. analysis is required.
A mechanism transmites a motion, force, tourage Angular velocity ratio is inversely
etc. A machine is a mechanism or combination of proportional to torque ratio. If Input torque is known
mechanisms, which apart from imparting definite output torque can be determine. Performance using
motion to the parts, also transmit available mechnical angular velocity ratio is given by equation,
energy into some kind of desired work. Thus T4 W2
mechanism is a fundamental unit for motion =
transmition. Generally mechanism used in machine is
T2 W4
responsible for the performance of machine and
required output. A mechanism with four link is called 4. Approach
as simple four bar chain mechanism. The analysis of four bar mechanism using
Many research has been carried out on performance relative velocity method can be divided into three
evaluation of mechanism due to inadequate tolerance phases
on link length and clearance in joint. In this links are a) Position analysis
assumed as rigid. For this purposes, graphical b) Velocity analysis
approach is used, but analytical approach is also an c) Performance analysis
alternate method.
a) Position analysis : Checking the Grashof
2. Relative velocity method condition
Relative velocity method for determining It is useful to determine class of mechanism
the velocity of different points in the mechanism may L max + L min P + Q – Class I mechanism
be used to any configuration Diagrams. It is based on
1871 | P a g e

2. A.K.Kapse, Dr. C. C. Handa / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue4, July-August 2012, pp.1871-1573
L max + Lmin P + Q – Class II mechanism
Links Nomenclature Dimensions
AB (Link 2) Crank 40
where, BC (Link 3) Coupler 150
L max = maximum length link CD (Link 4) Follower 80
L min = minimum length link AD (Link 1) Frame 150
P & Q = Remaining two links
Input angle () = 600, Input torgue (T2) = 50 Nm.
Calculating output angle :
Output angle can the calculated using relation POSITION ANALYSIS
Position analysis is divided in to two stages -
Φ1,2= 2 tan-1[ Check The Grashof Condition:
Grashof condition is useful to determine the class of
where,  = Input angle the mechanism whether it is Class I or Class II
mechanism. It is given by,
A = (1-K2) cos  – K1 + K3
B = -2 sin 
C = K1 – (1 + K2) cos  + K3 Where,
d
K1 =
a P & Q = Remaining two links
d Above condition is satisfied. Thus, given
K2 = mechanism is Class I mechanism.
c
a 2 - b2 + c 2 + d 2 Output Angle Calculations :
K3 = Output angle of four bar mechanism can be
2ac calculated using the equation,
a, b, c, d, are length of links respectively.
b) Velocity analysis :
Graphical approach is used for velocity analysis of
four bar mechanism. Where,
2p N 2
W2 = (rad / sec)
60
where , w2 = angular velocity of crank
N2 = angular speed of crank Where,
v2 = length of crank x w2
v2= velocity of crank (m/s)
Using velocity of crank drawing velocity diagram &
measuring velocity of coupler (v3) & follower (v4)
resp.
To calculate angular velocity of follower or output
link.
V4 = length of follower x w4
V4
W4 =
lenght Of Follower
W4 = angular velocity of follower.
c) Performance analysis : Velocity analysis
W4 ang.Velocity of o/p link We use graphical approach for velocity
RV = = analysis of the four bar mechanism which is more
W2 ang.Velocity of i/p link accurate.
Torque on o/p link T4
M.A. = =
Torque on i/p link T2 Where, is angular velocity of the crank
T4 W2 Is angular speed of the crank
=
T2 W4
5. Mathamatical Calculation
The four bar mechanism which is selecting
for analysis purpose it's dimension are as follows We have,
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3. A.K.Kapse, Dr. C. C. Handa / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue4, July-August 2012, pp.1871-1573
Where, is the velocity of link 2
Result
Table shows the values obtained of Angular
velocity ratio, Mechanical advantage and percentage
variation in the performance from standard
performance for crank length mm.
Conclusion
The proposed analytical method is useful in
determining performance variation of any planar four
bar mechanism cause due to dimensional
inaccuracies. Computer aid can help in easy workput
of possible variation in link dimension.
References:
Figure shows a Crank Rocker Four Bar [1] C. C. Handa, H. T. Thorat, “A Generalized
Mechanism alongwith Its Velocity Diagram Approach in Anticipating the Effect of link
length Tolerances on performance of
Measure from the velocity diagram. Mechanism using Instantaneous
center”,Advances in Machines and
Mechanisms; Proceeding 9th NaCoMM
To calculate angular velocity of output link 1999,, December 16-17,1999
[2] M. Y. Lee, A. G. Erdman, S. Faik, “A
Where, . Generalized Performance Sensitivity
Synthesis Methodology for Four Bar
Mechanisms”, Mechanism and Machine
Theory vol. 34, pp 1127-1139, 1999
[3] C. C. Handa, H. T. Thorat, “A Generalized
Approach in Identifying Control Link
PERFORMANCE ANALYSIS : Tolerances and its Effect on Design
Angular Velocity Ratio = w4/w2 Tolerances of Mechanisms Using
Instantaneous Center”, NaCoMM 2003
Rv = 0.3799 [4] P. L. Bhagwat & Dr. B. M. Domkundwar,
“Sensitivity Analysis by Graphical
Mechanical Advantage = T4/T2 Approach.” Pune.A. M. Vaidya And P. M.
Padole, “A Performance Evaluation of Four
bar Mechanisms Considering Flexibility of
Links and Joint Stiffness” The Open
Mechanical Engineering Journal, 2010, 4, pp
Output Torgue T4, 16-28
[5] P.S.Thakare, Dr. C.C. Handa, “A
Generalised Approach for Sensitivity
Analysis of Four Bar Mechanism and
Identifying Sensitive Links Tolerances
Using Relative Velocity Method”,
International Journal of Applied Research in
Mechanical Engineering, Vol.1, 2011.
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