This document discusses modeling, simulating, and analyzing the dynamic forces of a four-bar planar mechanism using CATIA V5 software. The document begins with an introduction to four-bar mechanisms and their importance. It then describes the mathematical modeling of displacement, velocity, and acceleration analysis of four-bar linkages. Next, it explains how to model a four-bar mechanism using different CATIA tools. The document presents results of the simulation in CATIA including graphs of link angle, speed, and acceleration over time. It concludes that CATIA allows simulation of link motion at different positions and validation of analytical equations, providing a valuable tool for mechanism analysis and design optimization.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
444
MODELING, SIMULATION & DYNAMIC ANALYSIS OF FOUR-BAR
PLANAR MECHANISMS USING CATIA V5R21
Chikesh ranjan*; Dr R. P. Sharma **
* Dept. of Mechanical Engineering, RTC Institute of Technology, Anandi, Ormanjhi,
Ranchi, 835213, India
** Dept. of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215
India.
ABSTRACT
The four-bar linkage is the most basic chain of pin-connected links that allows
relative motion between links. Although a simple mechanism, the four-bar linkage
Mechanism is very versatile and used in thousands of applications. To study the motion of a
four bar mechanism, knowledge of velocity and acceleration analysis is required. The
analysis of velocity and acceleration depend upon the graphical as well as analytical methods.
The graphical approach is suitable for finding out the velocity and acceleration of the links of
a mechanism in one or two positions of the crank. However, if it is required to find these
values at various configurations of the mechanism or to find the maximum values of
maximum velocity or acceleration, it is not convenient to draw velocity and acceleration
diagrams again and again.so that we are approaches to find out velocity and acceleration of
four bar mechanism using software.
The main themes of this paper are the modelling, computer-aided dynamic force analysis and
simulation of four-bar planar mechanisms composed of rigid bodies and massless force and
torque producing elements. Modelling of planar four-bar mechanisms will be done by using
the CATIAV5R21 software. By this software we can simulate their link at different positions
and find the velocity and acceleration graph and compared with analytical equations.
Keyword- CATIA, CAD, simulation.
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 2, March - April (2013), pp. 444-452
© IAEME: www.iaeme.com/ijmet.asp
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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1.0 INTRODUCTION AND LITERATURE SURVEY
A mechanical system is made-up of several components, which can be divided into
two major groups namely links and joints. The functionality of a joint relies upon the relative
motion allowed between the connected components. This implies the existence of a clearance
between the mating parts.In the analysis and design of mechanisms, kinematic quantities such
as velocities and accelerations are of great engineering importance. Velocities and
displacements give an insight into the functional behaviour of the mechanism. The
accelerations, on the other hand, are related to forces by Newton’s principle which
themselves are related to stresses and deformations in the mechanism’s components. In the
kinematic analysis, the mechanism is assumed to be made up of rigid bodies. Actually the
machine member is moving and the applied forces are not always constant for different
configurations of the machine, as in case of four bar mechanisms. However, these forces can
be considered as constant forces acting on the respective links for a particular configuration.
To study motion of a four bar mechanism, knowledge of velocity and acceleration analysis is
necessary. For this purpose, graphical approach is generally used. But values of velocity and
acceleration changes with respect to time for different positions of the crank.So analytical
approach is alternate method and preferable than graphical to save time and cost. For that, a
computer program is prepared to solve this problem and to get the values of velocity and
analysis at different positions of the crank.Traditionally, the only way to study such motion
was to design and manufacture a physical prototype and run it in the lab. In this setting, the
displacements, velocities, accelerations and forces had to be measured. This physical
simulation is inflexible in terms of mechanisms parameters and more importantly, due to
costs and space limitations, the variety of mechanisms available for the study is limited. In
addition, the study of mechanisms in a physical lab is usually done in groups, which limits a
student’s personal experience due to time constraints. To overcome this problem it is desired
to use the modern available tools and resources. Computer in terms of tool and design
software as resources will give a solution to above mentioned problem.
During the last quarter century, rigid body dynamics has received considerable
attention due to the central role it plays in robot simulation, control, design, and computer
animation. A great number and variety of formalisms have been developed for rigid body
systems despite the fact that all of them can be derived from a few fundamental principles of
mechanics. What is commonly known as the Newton-Euler method includes the constraint
forces acting on all bodies of the system, which results in redundant equations with more
equations than unknowns. Brian TavisRundgren[1] “Optimized Synthesis of Dynamically
Based Force Generating Planar Four-bar Mechanism”, have advocated a technique for
designing planar four-bar linkages by coupling optimization, dynamics and kinematics.
MekonnenGebreselassie[2] “Computer-Aided Synthesis, Kinematic Analysis and Simulation
of Planar Mechanisms“ have presented the kinematic synthesis and analysis of four, five, and
six-bar mechanisms by using the complex number approach.R. Brent Gillespie [3]“Kane’s
Equations for Haptic Display of Multibody Systems” have discussedin other formulations,
such as Lagrange’s and Kane’s method. The constraint forces are eliminated by using
D’Alembert’s principle. Efficient simulation algorithms were developed based on these
formulations for systems with different structures. A. M. Vaidyaand P. M. Padole [4]“A
Performance Evaluation of Four Bar Mechanism Considering Flexibility of Links and Joints
Stiffness” has deals with the study of joint clearance on kinematics of mechanism and bearing
stiffness along with links flexibility on modal analysis at higher frequency The method of

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
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calculating clearance at joints, checking for orientation of linkages and estimation of exact
mechanical error using sensitivity analysis is discussed. Manish Mehtaa and P M George
[5]“Rigid Dynamics Analysis Of Four Bar Mechanism InAnsys And C++ Programme” have
discussed a systematic approach is mention for dynamic force analysis of four bar linkage by
considering rigid link. Prof. N. G. Alvi, Dr.S.V.Deshmukhet.al.[6] has proposed analytical
method using computer programming is useful in determining the values of velocity and
acceleration analysis at different positions of the crank. On the basis of result and analysis, it
is seen that this present method is very fast and less laborious and very efficient than
graphical method. Also errors due to the graphical method are eliminated by this present
method which gives better result.
From a critical review of the literature on “modeling, simulation & dynamic
analysisof four-bar planar mechanisms using CATIA”.it is apparent that further studies are
warranted to provide better understanding and error free result using CATIA software.
2.0MATHEMATICAL MODELING
2.1 Mathematical Modeling
The modeling process itself is (or should be) most often an iterative process. The
following are the assumptions and restrictions imposed for getting solution.
1. Global deformations are not allowed when a rigid body is exposed to varying force
fields.
2. Point contact is assumed to simplify the modeling process.
3. Mass of each body is assumed to be concentrated at its canter of gravity and
connection elements like springs, dampers, actuators and joints are assumed to be
massless.
4. Impulse is not allowed to formulate system dynamics.
5. All friction effects are neglected in the analysis.
To different the values of velocity and acceleration at different positions of a crank, analytical
expressions in terms of general parameters are derived.
Figure2.0 -Four bar chain mechanism
Let,
Link AB – a- Crank Link ,BC – b – Coupler Link, CD – c- Rocker Link, AD – d- Fixed link
θ – Input angle, Ø – Output angle

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As, O/P angle is a function of I/P angle, we have
Ø=ƒ (a, b, c, d, θ) …………………… (1)
Thus, if values of a, b, c, d and θ are known, we can find out relationship between θ and Ø.
To determine the relationship between O/P and I/P links, we will use expressions of
displacement, velocity and acceleration.
Displacement Analysis:
Position of the O/P link given by Ø can be calculated using equation (2)
Ø=2tan-1{[-B±√B2 - 4AC]/2A}……… (2)
Where,
A= k-[a* (d-c) *cos θ] – c*d
B = -2*a*c *sin θ
C = K-[a (d+c)cos θ] +c*d 2k =a2-b2+c2+d2.
A relationship between the coupler link position β and I/P link θ can also be found using eqn
(3)
C*sinØ= a sin θ + b sin β………… (3)
Velocity Analysis:
Let, ωa, ωb, ωc be the angular velocities of the links AB, BC and CD respectively. Value of
ωa is given, value of ωb and ωc can be calculated using eqn (4.1 & 4.2)
Wb = -a*Wa*sin (Ø – θ) / b* sin (θ-β)……………………… (4.1)
Wc = a* Wa*sin (β – θ) / c*sin (β–Ø)… (4.2)
Acceleration Analysis:
Let αa , αb, αc be angular acceleration of links AB, BC, CD respectively. As per data given in
the problem, link AB rotates at uniform angular velocities. In this case, acceleration of input
linkwillbe zero i.e. there is no need to calculate it. αb, αc can be calculated using equations-
αb=[a* αa*sin(Ø – θ) – {a*(Wa2)*cos(Ø – θ)}-{b*(Wb2)*cos(Ø – β)}+ c*Wc2] b *sin(β –
Ø)
αb=[a* αa*sin(β - θ) – {a*(Wa2)*cos(β – θ)}- b*Wb2 + c*(Wc2)cos(β Ø – )] c*sin(β – Ø)
3. MODELING USING CATIA
CATIA V5, developed by DassaultSystemes, France, is a completely re-
engineered, next-generation family of CAD/CAM/CAE software solutions for Product
Lifecycle Management. Through its exceptionally easy-to-use state of the art user interface,
CATIA V5 delivers innovative technologies for maximum productivity and creativity,
from concept to the final product. CATIA V5 reduces the learning curve, as it allows
the flexibility of using feature-based and parametric designs.

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March
3.1Modeling of four bar links using CATIA
Figure
Figure
Figure
Figure
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
448
four bar links using CATIA
Figure 3.0- Isometric view of Link 1
Figure 3.1- Isometric view of Link 2
Figure 3.2- Isometric view of Link 3
Figure 3.3- Isometric view of Link 4
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
April (2013) © IAEME

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
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3.2 Assembly of four-bar mechanism using CATIA
Figure 3.4
A specification of four bar linkage for analysis is as follows:
4. FOLLOWING STEPS USED IN DIGITAL MOCK
SIMULATION WITH LAW TO GET THE RESULT
1. Assembly
2. Enter DMU workbench
3. Auto Constraints conversion (n/n to 0/n)
4. Convert joint into Angle driven and Length driven
5. Simulation
6. Simulation with law
7. Formula ʄ(x)
8. Speed and acceleration
9. Trace
10. Save all
5. Result and Discussion
In this paper four bar mechanisms are
the result at different position of links. During that different nature of graph in CATIA on
angle of link, speed of link and angular acceleration verses time in both clock wise and
anticlockwise movement of links
software.The nature of the graph is
and data needed to explore design alternatives and increase product innovation.
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
449
bar mechanism using CATIA
3.4-Assembly of four-bar mechanism
A specification of four bar linkage for analysis is as follows:
Link No. Length(m)
1(Ground) 1.241
2 1.241
3 1.200
4 1.200
FOLLOWING STEPS USED IN DIGITAL MOCK-UP KINEMATICS USING
TION WITH LAW TO GET THE RESULT
3. Auto Constraints conversion (n/n to 0/n)
4. Convert joint into Angle driven and Length driven
In this paper four bar mechanisms are modelled, assembled and simulated
the result at different position of links. During that different nature of graph in CATIA on
angle of link, speed of link and angular acceleration verses time in both clock wise and
anticlockwise movement of links are studied and following graphs are obtained from
The nature of the graph is linear, constant and variables.It provides the critical time
and data needed to explore design alternatives and increase product innovation.
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
April (2013) © IAEME
INEMATICS USING
, assembled and simulated to obtain
the result at different position of links. During that different nature of graph in CATIA on
angle of link, speed of link and angular acceleration verses time in both clock wise and
are obtained from
variables.It provides the critical time

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March
Fig5.0-Output plot of angle of link versus time.
Fig5.1-Output plot of angular speed of link versus time
(Clock & Anticlockwise link movement)
Fig5.2-Output plot of angular acceleration of link versus time
(Clock &Anticlockwise link movement)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
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Output plot of angle of link versus time.
Output plot of angular speed of link versus time
(Clock & Anticlockwise link movement)
Output plot of angular acceleration of link versus time
lock &Anticlockwise link movement)
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
April (2013) © IAEME

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March
Fig5.3-Output plot of angular acceleration of link
(Anticlockwise link movement)
6. CONCLUSION
In this paper, an attempt has
softwares. By this software we can simulate their link at different positions and find the
velocity and acceleration graph. On the basis of result and analysis, DMU Kinematics
Simulator provides users the ability to define
the mechanisms. During mock-up design review, users do not only need to view simulated
kinematics but also analyse the mechanism's consistency with the functional specifications.
DMU Kinematics Simulator p
computing the minimum distance. A 'stop on collision' option freezes the motion for detailed
analysis. The simulating softwares DMU CATIA Kinematics Simulator is very fast and less
laborious and very efficient than graphical and analytical methods. Also errors due to the
graphical and analytical methods are eliminated by this present method which gives better
result.
The study reveals following conclusions:
• For four bar mechanism the coupler point
by joint clearances and flexibility in linkages.
• Errors due to the graphical and analytical methods are eliminated by this present
method which gives better result.
7. REFERENCES
1. Brian TavisRundgren,( 2001) “
Generating Planar Four-bar Mechanism
Polytechnic Institute and State University, Virginia,.
2. MekonnenG.Selassie, Thesis of Master of Science on(2002) “
Synthesis and Analysis of Planar Mechanisms
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976
6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
451
Output plot of angular acceleration of link versus time
(Anticlockwise link movement)
attempt has been made to study on four bars mechanism by CATIA
softwares. By this software we can simulate their link at different positions and find the
velocity and acceleration graph. On the basis of result and analysis, DMU Kinematics
Simulator provides users the ability to define a point in a moving part and generate it trace for
up design review, users do not only need to view simulated
the mechanism's consistency with the functional specifications.
DMU Kinematics Simulator performs interference and clearance checking as well as
computing the minimum distance. A 'stop on collision' option freezes the motion for detailed
analysis. The simulating softwares DMU CATIA Kinematics Simulator is very fast and less
fficient than graphical and analytical methods. Also errors due to the
graphical and analytical methods are eliminated by this present method which gives better
The study reveals following conclusions:
For four bar mechanism the coupler point location and output angle is greatly affected
by joint clearances and flexibility in linkages.
Errors due to the graphical and analytical methods are eliminated by this present
method which gives better result.
Brian TavisRundgren,( 2001) “Optimized Synthesis of Dynamically Based Force
bar Mechanism”, thesis on Masters of Science,Virginia
Polytechnic Institute and State University, Virginia,.
MekonnenG.Selassie, Thesis of Master of Science on(2002) “Computer
Synthesis and Analysis of Planar Mechanisms” Mechanical Engineering Dept., AAU,.
International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
April (2013) © IAEME
on four bars mechanism by CATIA
softwares. By this software we can simulate their link at different positions and find the
velocity and acceleration graph. On the basis of result and analysis, DMU Kinematics
a point in a moving part and generate it trace for
up design review, users do not only need to view simulated
the mechanism's consistency with the functional specifications.
erforms interference and clearance checking as well as
computing the minimum distance. A 'stop on collision' option freezes the motion for detailed
analysis. The simulating softwares DMU CATIA Kinematics Simulator is very fast and less
fficient than graphical and analytical methods. Also errors due to the
graphical and analytical methods are eliminated by this present method which gives better
location and output angle is greatly affected
Errors due to the graphical and analytical methods are eliminated by this present
timized Synthesis of Dynamically Based Force
”, thesis on Masters of Science,Virginia
Computer-Aided
” Mechanical Engineering Dept., AAU,.

9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
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3. R. Brent Gillespie,(2003)” Kane’s Equations for Haptic Display of Multibody
Systems”,University of Michigan, Dept. of Mech. Eng’g, Haptics-e, Vol.3.No.2.,
http://www.haptics-e.org.
4. A. M. Vaidya and P. M. Padole (2010)“A Performance Evaluation of Four Bar
Mechanism Considering Flexibility of Links and Joints Stiffness” published in aOpen
Mechanical Engineering Journal,
5. Manish Mehta And P M George (2012) “Rigid Dynamics Analysis Of Four Bar
Mechanism In Ansys And C++ Programme” published in a journal International
Journal of Mechanical and Production Engineering Research and Development
(IJMPERD) 2 June.
6. Prof. N. G. Alvi,Dr. S. V. Deshmukh and Ram.R.Wayzode(2012) “Computer Aided
Analysis of Four bar Chain Mechanism” published in a International Journal of
Engineering Research and Applications (IJERA)..
7. Bhagyesh Deshmukh and Dr. Sujit Pardeshi, “Study of Various Compliant
Micromechanism and Introduction of a Compliant Micromotion Replicating
Mechanism”, International Journal of Mechanical Engineering & Technology (IJMET),
Volume 3, Issue 3, 2012, pp. 574 - 582, ISSN Print: 0976 – 6340, ISSN Online: 0976 –
6359