Modeling and simulation of four bar planar mechanisms using adams

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
429
MODELING AND SIMULATION OF FOUR-BAR PLANAR
MECHANISMS USING ADAMS
Dr R. P. Sharma *; Chikesh ranjan **
* Dept. of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215
India.
** Dept. of Mechanical Engineering, RTC Institute of Technology, Anandi, Ormanjhi,
Ranchi, 835213
ABSTRACT
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. Various methods including finite element method, lump mass
method, substructure method and continuum mechanics method have been discussed by
various researchers. In this paper, the analysis of a four-bar mechanism is undertaken. 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 .The main theme 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 ADAMS software. By this software we can simulate their link at
different positions and find the velocity and acceleration graph and compared with analytical
equations. Motions of the rigid bodies are predicted by numerically integrating Differential-
Algebraic Equations (DAEs). ADAMS is more reliable software because it considers masses,
center of mass location and inertia properties on the links.
Keyword- ADAMS, 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. 429-435
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI)
www.jifactor.com
IJMET
© I A E M E

430
1.0 LITERATURE SURVEY
Mechanisms are used in a great variety machines and devices. The simplest closed-loop
linkage is the four-bar linkage, which has three moving links, one fixed link (a linkage with one
link fixed is a mechanism) and four revolute.
J. García de Jalon et. al.[1]“Improved Dynamic Formulations for the Dynamic Simulation
of Multibody Systems”, The ideas behind these improvements of global formulations are used to
improve the topological formulations when they are applied to closed-loop Multibody systems.
Waseem A. Khan[2]“Distributed Dynamics of Systems with Closed Kinematic Chains”, have
examined the formulation of modular and distributed models and evaluated their performance as
applied to mechanical systems with closed kinematic chains. Bryan J. Bergelin and Philip A.
Voglewede [3] 2012 “Design of an Active Ankle-Foot Prosthesis Utilizing a Four-Bar
Mechanism” have discussed the design and testing of powered ankle prosthesis. Chikesh ranjan
and. Sharma R P[4] 2013 “Modeling, Simulation & DynamicAnalysis Of Four-Bar Planar
Mechanisms Using Catia V5r21” have discussed Modelling of planar four-bar mechanisms using
the CATIAV5R21 software. V.K. Gupta[7](1974) in his paper “Dynamic Analysis of Multi-
Rigid-Body Systems” have presented a method for formulating and solving the Newton-Euler
equations of motion of a system of interconnected rigid bodies.
R. R. Allen et.al.[8](1982) have presented “Connection Force Analysis of Mechanisms
Described by Explicit Equations of Motion in Generalized Coordinates” they clearly found that
the connection forces acting at the joints of a kinematic mechanism.
2.0 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

431
Let,
Link AB – a- Crank Link ,BC – b – Coupler Link, CD – c- Rocker Link, AD – d- Fixed link
θ – Input angle, Ø – Output angle
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
linkwill be 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)

432
3.0 MODELING AND SIMULATION OF FOUR BAR LINKS USING ADAMS
ADAMS stands for Automatic Dynamic Analysis of Mechanical Systems and was
originally developed by Mechanical Dynamic Inc.(MDI).Models are built in text format and
then submitted into ADAMS/Solver. In the early 90’s, ADAMS/View was released which
allowed users to build, simulate and examine results in a single Graphical User Environment
(GUI). Today, MSC produces many general engineering analysis packages like
MSC.NASTRAN, MSC.PATRAN, MSC.DYTRAN etc. and also packages which cater to
industry specific users like MSC.ADAMS/Car, MSC.ADAMS/Rail, and
MSC.ADAMS/Engine etc. In this thesis however, we’ll be dealing with MSC.ADAMS alone.
MSC.ADAMS™ Simulation Package is a powerful modeling and simulating environment
that lets one build, simulate, refine, and ultimately optimize any mechanical system, from
automobiles and trains to VCRs and backhoes. This tutorial is intended as an introduction to
using MSC.DAMS, specifically in the context of robotics, although it’s applications are much
more wider. Figure -3.0 shows modeling of link 2, Figures -3.1 shows modeling of link
3,Figure -3.2 shows modeling of link 4, Figures -3.3 shows modeling of link 1. Figure -3.4
assembly of link four link through ADAMS.
Figure -3.0 Adams GUI with link1 Figures -3.1 Adams GUI with link 2
Figure -3.2 Adams GUI with link 3 Figures -3.3 Adams GUI with link 4

433
Figure -3.4 Adams GUI with Geometry
A specification of four bar linkage for analysis is as follows:
Link No. Length(m) Center of Mass(m) Mass(Kg) Inertia(Kgm2)
1(Ground) 1.241 -NA- -NA- -NA-
2 1.241 1.2 20.15 9.6
3 1.200 0.6 8.25 0.06
4 1.200 0.6 8.25 0.06
The initial configuration of the mechanism is when the driven link is at 10°. The mechanism
is driven by a preloaded torsion spring of stiffness 0.1N/radian kept at the driving joint
between link 1 (ground) and link 2. The preload is 1.96Nm and as the mechanism is released,
the spring starts unwinding. The requirement is to compute the motion of the mechanism till
(or just before) the mechanism reaches it next singular configuration.
4.0 FOLLOWING STEPS USED PROCESS OF PERFORMING A MODEL
SIMULATION IN ADAMS
1. Create a New ADAMS Database
2. Define the Units and Working Grid size
3. Import or Create the Geometry
4. Define moving parts in the Model
5. Connect the moving parts with Joint connections
6. Apply motion to a Joint
7. Run a Kinematic Simulation
8. Animate Simulation Results
9. Plot result values from the Simulation run
5.0 RESULT AND DISCUSSION
In this paper four bar mechanisms are modelled, assembled and simulated to obtain
the result at different position of links. During that different nature of graph in ADAMS 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
software. We get that the graph movement will be linear. Figures -5.2, constant, Figure -5.3

434
and Figure-5.4 are variables . It provides the critical time and data needed to explore design
alternatives and increase product innovation. it considers masses, center of mass location,
inertia properties on the links.
Figure-5.1 Figures -5.2
Figure -5.3 Figures -5.4
Figure -5.5

435
6. CONCLUSIONS
On the basis of result and analysis, it is concluded that its result is more reliable than
other softwares like CATIA because it considers masses, center of mass location, inertia
properties on the links. The simulating software ADAMS 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 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.
7. REFERENCES
1. J. Garcia de Jalon, E. Alvarez, F. A. de Ribera, (2000) “Improved Dynamic
Formulations for the Dynamic Simulation of Multibody Systems”.
2. Waseem A. Khan, (2002) “Distributed Dynamics of Systems with Closed
Kinematic Chains”.
3. Bryan J. Bergelin and Philip A. Voglewede “Design of an Active Ankle-Foot Prosthesis
Utilizing a Four-Bar Mechanism” published in a journal ASME JUNE 2012.
4. Chikesh ranjan and DR.R.P Sharma “Modeling, Simulation & DynamicAnalysis Of
Four-Bar Planar Mechanisms Using Catia V5r21 published in a journal IJMET 2013.
5. R.Gurpude and Prof.P.Dhopte “Design Synthesis & Simulation of Four Bar Mechanism
for Wheels for Climbing” published in a journal IJCTEE 2012.
6. Manish Mehta and P M George(2012), “Rigid Dynamics Analysis Of Four Bar
Mechanism InAnsys And C++ Programme” published in a journal International Journal
of Mechanical and Production Engineering Research and Development (IJMPERD )2
June.
7. V.K. Gupta,“Dynamic Analysis of Multi-Rigid-Body Systems”, Journal of Engineering
for Industry, Trans. ASME, pp. 886-891, 1974.
8. R. R. Allen and Harrell, J. P., “ Connection Force Analysis of Mechanisms Described
by Explicit Equations of Motion in Generalized Coordinates”, Journal of Mechanical
Design, Trans. ASME, Vol. 104, pp. 168-174, 1982.

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