Modeling, simulation & dynamic analysis of four bar planar

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Modeling, simulation & dynamic analysis of four bar planar

  1. 1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME444MODELING, SIMULATION & DYNAMIC ANALYSIS OF FOUR-BARPLANAR MECHANISMS USING CATIA V5R21Chikesh 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, 835215India.ABSTRACTThe four-bar linkage is the most basic chain of pin-connected links that allowsrelative motion between links. Although a simple mechanism, the four-bar linkageMechanism is very versatile and used in thousands of applications. To study the motion of afour bar mechanism, knowledge of velocity and acceleration analysis is required. Theanalysis 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 ofa mechanism in one or two positions of the crank. However, if it is required to find thesevalues at various configurations of the mechanism or to find the maximum values ofmaximum velocity or acceleration, it is not convenient to draw velocity and accelerationdiagrams again and again.so that we are approaches to find out velocity and acceleration offour bar mechanism using software.The main themes of this paper are the modelling, computer-aided dynamic force analysis andsimulation of four-bar planar mechanisms composed of rigid bodies and massless force andtorque producing elements. Modelling of planar four-bar mechanisms will be done by usingthe CATIAV5R21 software. By this software we can simulate their link at different positionsand find the velocity and acceleration graph and compared with analytical equations.Keyword- CATIA, CAD, simulation.INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERINGAND 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.aspJournal Impact Factor (2013): 5.7731 (Calculated by GISI)www.jifactor.comIJMET© I A E M E
  2. 2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME4451.0 INTRODUCTION AND LITERATURE SURVEYA mechanical system is made-up of several components, which can be divided intotwo major groups namely links and joints. The functionality of a joint relies upon the relativemotion allowed between the connected components. This implies the existence of a clearancebetween the mating parts.In the analysis and design of mechanisms, kinematic quantities suchas velocities and accelerations are of great engineering importance. Velocities anddisplacements give an insight into the functional behaviour of the mechanism. Theaccelerations, on the other hand, are related to forces by Newton’s principle whichthemselves are related to stresses and deformations in the mechanism’s components. In thekinematic analysis, the mechanism is assumed to be made up of rigid bodies. Actually themachine member is moving and the applied forces are not always constant for differentconfigurations of the machine, as in case of four bar mechanisms. However, these forces canbe 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 isnecessary. For this purpose, graphical approach is generally used. But values of velocity andacceleration changes with respect to time for different positions of the crank.So analyticalapproach is alternate method and preferable than graphical to save time and cost. For that, acomputer program is prepared to solve this problem and to get the values of velocity andanalysis at different positions of the crank.Traditionally, the only way to study such motionwas to design and manufacture a physical prototype and run it in the lab. In this setting, thedisplacements, velocities, accelerations and forces had to be measured. This physicalsimulation is inflexible in terms of mechanisms parameters and more importantly, due tocosts and space limitations, the variety of mechanisms available for the study is limited. Inaddition, the study of mechanisms in a physical lab is usually done in groups, which limits astudent’s personal experience due to time constraints. To overcome this problem it is desiredto use the modern available tools and resources. Computer in terms of tool and designsoftware as resources will give a solution to above mentioned problem.During the last quarter century, rigid body dynamics has received considerableattention due to the central role it plays in robot simulation, control, design, and computeranimation. A great number and variety of formalisms have been developed for rigid bodysystems despite the fact that all of them can be derived from a few fundamental principles ofmechanics. What is commonly known as the Newton-Euler method includes the constraintforces acting on all bodies of the system, which results in redundant equations with moreequations than unknowns. Brian TavisRundgren[1] “Optimized Synthesis of DynamicallyBased Force Generating Planar Four-bar Mechanism”, have advocated a technique fordesigning planar four-bar linkages by coupling optimization, dynamics and kinematics.MekonnenGebreselassie[2] “Computer-Aided Synthesis, Kinematic Analysis and Simulationof Planar Mechanisms“ have presented the kinematic synthesis and analysis of four, five, andsix-bar mechanisms by using the complex number approach.R. Brent Gillespie [3]“Kane’sEquations for Haptic Display of Multibody Systems” have discussedin other formulations,such as Lagrange’s and Kane’s method. The constraint forces are eliminated by usingD’Alembert’s principle. Efficient simulation algorithms were developed based on theseformulations for systems with different structures. A. M. Vaidyaand P. M. Padole [4]“APerformance Evaluation of Four Bar Mechanism Considering Flexibility of Links and JointsStiffness” has deals with the study of joint clearance on kinematics of mechanism and bearingstiffness along with links flexibility on modal analysis at higher frequency The method of
  3. 3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME446calculating clearance at joints, checking for orientation of linkages and estimation of exactmechanical error using sensitivity analysis is discussed. Manish Mehtaa and P M George[5]“Rigid Dynamics Analysis Of Four Bar Mechanism InAnsys And C++ Programme” havediscussed a systematic approach is mention for dynamic force analysis of four bar linkage byconsidering rigid link. Prof. N. G. Alvi, Dr.S.V.Deshmukhet.al.[6] has proposed analyticalmethod using computer programming is useful in determining the values of velocity andacceleration analysis at different positions of the crank. On the basis of result and analysis, itis seen that this present method is very fast and less laborious and very efficient thangraphical method. Also errors due to the graphical method are eliminated by this presentmethod which gives better result.From a critical review of the literature on “modeling, simulation & dynamicanalysisof four-bar planar mechanisms using CATIA”.it is apparent that further studies arewarranted to provide better understanding and error free result using CATIA software.2.0MATHEMATICAL MODELING2.1 Mathematical ModelingThe modeling process itself is (or should be) most often an iterative process. Thefollowing are the assumptions and restrictions imposed for getting solution.1. Global deformations are not allowed when a rigid body is exposed to varying forcefields.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 andconnection elements like springs, dampers, actuators and joints are assumed to bemassless.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, analyticalexpressions in terms of general parameters are derived.Figure2.0 -Four bar chain mechanismLet,Link AB – a- Crank Link ,BC – b – Coupler Link, CD – c- Rocker Link, AD – d- Fixed linkθ – Input angle, Ø – Output angle
  4. 4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME447As, O/P angle is a function of I/P angle, we haveØ=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 ofdisplacement, 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*dB = -2*a*c *sin θC = 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 ofωa 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 inthe problem, link AB rotates at uniform angular velocities. In this case, acceleration of inputlinkwillbe 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 CATIACATIA V5, developed by DassaultSystemes, France, is a completely re-engineered, next-generation family of CAD/CAM/CAE software solutions for ProductLifecycle 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 allowsthe flexibility of using feature-based and parametric designs.
  5. 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March3.1Modeling of four bar links using CATIAFigureFigureFigureFigureInternational Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766359(Online) Volume 4, Issue 2, March - April (2013) © IAEME448four bar links using CATIAFigure 3.0- Isometric view of Link 1Figure 3.1- Isometric view of Link 2Figure 3.2- Isometric view of Link 3Figure 3.3- Isometric view of Link 4International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –April (2013) © IAEME
  6. 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March3.2 Assembly of four-bar mechanism using CATIAFigure 3.4A specification of four bar linkage for analysis is as follows:4. FOLLOWING STEPS USED IN DIGITAL MOCKSIMULATION WITH LAW TO GET THE RESULT1. Assembly2. Enter DMU workbench3. Auto Constraints conversion (n/n to 0/n)4. Convert joint into Angle driven and Length driven5. Simulation6. Simulation with law7. Formula ʄ(x)8. Speed and acceleration9. Trace10. Save all5. Result and DiscussionIn this paper four bar mechanisms arethe result at different position of links. During that different nature of graph in CATIA onangle of link, speed of link and angular acceleration verses time in both clock wise andanticlockwise movement of linkssoftware.The nature of the graph isand data needed to explore design alternatives and increase product innovation.International Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766359(Online) Volume 4, Issue 2, March - April (2013) © IAEME449bar mechanism using CATIA3.4-Assembly of four-bar mechanismA specification of four bar linkage for analysis is as follows:Link No. Length(m)1(Ground) 1.2412 1.2413 1.2004 1.200FOLLOWING STEPS USED IN DIGITAL MOCK-UP KINEMATICS USINGTION WITH LAW TO GET THE RESULT3. Auto Constraints conversion (n/n to 0/n)4. Convert joint into Angle driven and Length drivenIn this paper four bar mechanisms are modelled, assembled and simulatedthe result at different position of links. During that different nature of graph in CATIA onangle of link, speed of link and angular acceleration verses time in both clock wise andanticlockwise movement of links are studied and following graphs are obtained fromThe nature of the graph is linear, constant and variables.It provides the critical timeand data needed to explore design alternatives and increase product innovation.International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –April (2013) © IAEMEINEMATICS USING, assembled and simulated to obtainthe result at different position of links. During that different nature of graph in CATIA onangle of link, speed of link and angular acceleration verses time in both clock wise andare obtained fromvariables.It provides the critical time
  7. 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, MarchFig5.0-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 09766359(Online) Volume 4, Issue 2, March - April (2013) © IAEME450Output 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 timelock &Anticlockwise link movement)International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –April (2013) © IAEME
  8. 8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, MarchFig5.3-Output plot of angular acceleration of link(Anticlockwise link movement)6. CONCLUSIONIn this paper, an attempt hassoftwares. By this software we can simulate their link at different positions and find thevelocity and acceleration graph. On the basis of result and analysis, DMU KinematicsSimulator provides users the ability to definethe mechanisms. During mock-up design review, users do not only need to view simulatedkinematics but also analyse the mechanisms consistency with the functional specifications.DMU Kinematics Simulator pcomputing the minimum distance. A stop on collision option freezes the motion for detailedanalysis. The simulating softwares DMU CATIA Kinematics Simulator is very fast and lesslaborious and very efficient than graphical and analytical methods. Also errors due to thegraphical and analytical methods are eliminated by this present method which gives betterresult.The study reveals following conclusions:• For four bar mechanism the coupler pointby joint clearances and flexibility in linkages.• Errors due to the graphical and analytical methods are eliminated by this presentmethod which gives better result.7. REFERENCES1. Brian TavisRundgren,( 2001) “Generating Planar Four-bar MechanismPolytechnic Institute and State University, Virginia,.2. MekonnenG.Selassie, Thesis of Master of Science on(2002) “Synthesis and Analysis of Planar MechanismsInternational Journal of Mechanical Engineering and Technology (IJMET), ISSN 09766359(Online) Volume 4, Issue 2, March - April (2013) © IAEME451Output plot of angular acceleration of link versus time(Anticlockwise link movement)attempt has been made to study on four bars mechanism by CATIAsoftwares. By this software we can simulate their link at different positions and find thevelocity and acceleration graph. On the basis of result and analysis, DMU KinematicsSimulator provides users the ability to define a point in a moving part and generate it trace forup design review, users do not only need to view simulatedthe mechanisms consistency with the functional specifications.DMU Kinematics Simulator performs interference and clearance checking as well ascomputing the minimum distance. A stop on collision option freezes the motion for detailedanalysis. The simulating softwares DMU CATIA Kinematics Simulator is very fast and lessfficient than graphical and analytical methods. Also errors due to thegraphical and analytical methods are eliminated by this present method which gives betterThe study reveals following conclusions:For four bar mechanism the coupler point location and output angle is greatly affectedby joint clearances and flexibility in linkages.Errors due to the graphical and analytical methods are eliminated by this presentmethod which gives better result.Brian TavisRundgren,( 2001) “Optimized Synthesis of Dynamically Based Forcebar Mechanism”, thesis on Masters of Science,VirginiaPolytechnic Institute and State University, Virginia,.MekonnenG.Selassie, Thesis of Master of Science on(2002) “ComputerSynthesis and Analysis of Planar Mechanisms” Mechanical Engineering Dept., AAU,.International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –April (2013) © IAEMEon four bars mechanism by CATIAsoftwares. By this software we can simulate their link at different positions and find thevelocity and acceleration graph. On the basis of result and analysis, DMU Kinematicsa point in a moving part and generate it trace forup design review, users do not only need to view simulatedthe mechanisms consistency with the functional specifications.erforms interference and clearance checking as well ascomputing the minimum distance. A stop on collision option freezes the motion for detailedanalysis. The simulating softwares DMU CATIA Kinematics Simulator is very fast and lessfficient than graphical and analytical methods. Also errors due to thegraphical and analytical methods are eliminated by this present method which gives betterlocation and output angle is greatly affectedErrors due to the graphical and analytical methods are eliminated by this presenttimized Synthesis of Dynamically Based Force”, thesis on Masters of Science,VirginiaComputer-Aided” Mechanical Engineering Dept., AAU,.
  9. 9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME4523. R. Brent Gillespie,(2003)” Kane’s Equations for Haptic Display of MultibodySystems”,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 BarMechanism Considering Flexibility of Links and Joints Stiffness” published in aOpenMechanical Engineering Journal,5. Manish Mehta And P M George (2012) “Rigid Dynamics Analysis Of Four BarMechanism In Ansys And C++ Programme” published in a journal InternationalJournal 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 AidedAnalysis of Four bar Chain Mechanism” published in a International Journal ofEngineering Research and Applications (IJERA)..7. Bhagyesh Deshmukh and Dr. Sujit Pardeshi, “Study of Various CompliantMicromechanism and Introduction of a Compliant Micromotion ReplicatingMechanism”, International Journal of Mechanical Engineering & Technology (IJMET),Volume 3, Issue 3, 2012, pp. 574 - 582, ISSN Print: 0976 – 6340, ISSN Online: 0976 –6359

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