Modeling and simulation of four bar planar mechanisms using adams


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Modeling and simulation of four bar planar mechanisms using adams

  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) © IAEME429MODELING AND SIMULATION OF FOUR-BAR PLANARMECHANISMS USING ADAMSDr R. P. Sharma *; Chikesh ranjan *** Dept. of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, 835215India.** Dept. of Mechanical Engineering, RTC Institute of Technology, Anandi, Ormanjhi,Ranchi, 835213ABSTRACTA 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. Various methods including finite element method, lump massmethod, substructure method and continuum mechanics method have been discussed byvarious researchers. In this paper, the analysis of a four-bar mechanism is undertaken. In theanalysis and design of mechanisms, kinematic quantities such as velocities and accelerationsare of great engineering importance. Velocities and displacements give an insight into thefunctional behaviour of the mechanism. The accelerations, on the other hand, are related toforces .The main theme of this paper are the modelling, computer-aided dynamic forceanalysis and simulation of four-bar planar mechanisms composed of rigid bodies andmassless force and torque producing elements. Modelling of planar four-bar mechanisms willbe done by using the ADAMS software. By this software we can simulate their link atdifferent positions and find the velocity and acceleration graph and compared with analyticalequations. 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, simulationINTERNATIONAL JOURNAL OF MECHANICAL ENGINEERINGAND TECHNOLOGY (IJMET)ISSN 0976 – 6340 (Print)ISSN 0976 – 6359 (Online)Volume 4, Issue 2, March - April (2013), pp. 429-435© IAEME: 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) © IAEME4301.0 LITERATURE SURVEYMechanisms are used in a great variety machines and devices. The simplest closed-looplinkage is the four-bar linkage, which has three moving links, one fixed link (a linkage with onelink fixed is a mechanism) and four revolute.J. García de Jalon et. al.[1]“Improved Dynamic Formulations for the Dynamic Simulationof Multibody Systems”, The ideas behind these improvements of global formulations are used toimprove the topological formulations when they are applied to closed-loop Multibody systems.Waseem A. Khan[2]“Distributed Dynamics of Systems with Closed Kinematic Chains”, haveexamined the formulation of modular and distributed models and evaluated their performance asapplied 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-BarMechanism” have discussed the design and testing of powered ankle prosthesis. Chikesh ranjanand. Sharma R P[4] 2013 “Modeling, Simulation & DynamicAnalysis Of Four-Bar PlanarMechanisms Using Catia V5r21” have discussed Modelling of planar four-bar mechanisms usingthe 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-Eulerequations of motion of a system of interconnected rigid bodies.R. R. Allen[8](1982) have presented “Connection Force Analysis of MechanismsDescribed by Explicit Equations of Motion in Generalized Coordinates” they clearly found thatthe connection forces acting at the joints of a kinematic mechanism.2.0 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 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 connectionelements 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, analyticalexpressions in terms of general parameters are derived.Figure2.0 -Four bar chain mechanism
  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) © IAEME431Let,Link AB – a- Crank Link ,BC – b – Coupler Link, CD – c- Rocker Link, AD – d- Fixed linkθ – Input angle, Ø – Output angleAs, 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 inputlinkwill 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)
  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) © IAEME4323.0 MODELING AND SIMULATION OF FOUR BAR LINKS USING ADAMSADAMS stands for Automatic Dynamic Analysis of Mechanical Systems and wasoriginally developed by Mechanical Dynamic Inc.(MDI).Models are built in text format andthen submitted into ADAMS/Solver. In the early 90’s, ADAMS/View was released whichallowed users to build, simulate and examine results in a single Graphical User Environment(GUI). Today, MSC produces many general engineering analysis packages likeMSC.NASTRAN, MSC.PATRAN, MSC.DYTRAN etc. and also packages which cater toindustry specific users like MSC.ADAMS/Car, MSC.ADAMS/Rail, andMSC.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 environmentthat lets one build, simulate, refine, and ultimately optimize any mechanical system, fromautomobiles and trains to VCRs and backhoes. This tutorial is intended as an introduction tousing MSC.DAMS, specifically in the context of robotics, although it’s applications are muchmore wider. Figure -3.0 shows modeling of link 2, Figures -3.1 shows modeling of link3,Figure -3.2 shows modeling of link 4, Figures -3.3 shows modeling of link 1. Figure -3.4assembly of link four link through ADAMS.Figure -3.0 Adams GUI with link1 Figures -3.1 Adams GUI with link 2Figure -3.2 Adams GUI with link 3 Figures -3.3 Adams GUI with link 4
  5. 5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME433Figure -3.4 Adams GUI with GeometryA 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 9.63 1.200 0.6 8.25 0.064 1.200 0.6 8.25 0.06The initial configuration of the mechanism is when the driven link is at 10°. The mechanismis driven by a preloaded torsion spring of stiffness 0.1N/radian kept at the driving jointbetween 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 MODELSIMULATION IN ADAMS1. Create a New ADAMS Database2. Define the Units and Working Grid size3. Import or Create the Geometry4. Define moving parts in the Model5. Connect the moving parts with Joint connections6. Apply motion to a Joint7. Run a Kinematic Simulation8. Animate Simulation Results9. Plot result values from the Simulation run5.0 RESULT AND DISCUSSIONIn this paper four bar mechanisms are modelled, assembled and simulated to obtainthe result at different position of links. During that different nature of graph in ADAMS 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 fromsoftware. We get that the graph movement will be linear. Figures -5.2, constant, Figure -5.3
  6. 6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME434and Figure-5.4 are variables . It provides the critical time and data needed to explore designalternatives and increase product innovation. it considers masses, center of mass location,inertia properties on the links.Figure-5.1 Figures -5.2Figure -5.3 Figures -5.4Figure -5.5
  7. 7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME4356. CONCLUSIONSOn the basis of result and analysis, it is concluded that its result is more reliable thanother softwares like CATIA because it considers masses, center of mass location, inertiaproperties on the links. The simulating software ADAMS is very fast and less laborious andvery efficient than graphical and analytical methods. Also errors due to the graphical andanalytical 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 affectedby 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. J. Garcia de Jalon, E. Alvarez, F. A. de Ribera, (2000) “Improved DynamicFormulations for the Dynamic Simulation of Multibody Systems”.2. Waseem A. Khan, (2002) “Distributed Dynamics of Systems with ClosedKinematic Chains”.3. Bryan J. Bergelin and Philip A. Voglewede “Design of an Active Ankle-Foot ProsthesisUtilizing a Four-Bar Mechanism” published in a journal ASME JUNE 2012.4. Chikesh ranjan and DR.R.P Sharma “Modeling, Simulation & DynamicAnalysis OfFour-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 Mechanismfor Wheels for Climbing” published in a journal IJCTEE 2012.6. Manish Mehta and P M George(2012), “Rigid Dynamics Analysis Of Four BarMechanism InAnsys And C++ Programme” published in a journal International Journalof Mechanical and Production Engineering Research and Development (IJMPERD )2June.7. V.K. Gupta,“Dynamic Analysis of Multi-Rigid-Body Systems”, Journal of Engineeringfor Industry, Trans. ASME, pp. 886-891, 1974.8. R. R. Allen and Harrell, J. P., “ Connection Force Analysis of Mechanisms Describedby Explicit Equations of Motion in Generalized Coordinates”, Journal of MechanicalDesign, Trans. ASME, Vol. 104, pp. 168-174, 1982.