Computer Simulation Approach For Solving Jacobian And Kinematic Of Mechanisms And Application

The Jacobian matrix is not only an important parameter for describing thecharacteristic of the mechanisms, but also an important index for measuring theperformance of kinematics and dynamics. It has close connect with thesingularity and dexterity analysis of the mechanisms. The analysis and design ofspatial mechanisms is difficult, which is the reason why it is limited in use. Atpresent, the analytics which is used widely is high accuracy but needs hugecalculation, and sometimes it is hard to establish the related mathematicalmodels. So, to find a novel simple and convenient method to simplify thecalculation, we present a novel computer simulation approach to calculate theJacobian matrix and analyze the kinematics of spatial mechanisms.In the paper, the theory basis and realization steps of the computersimulation approach are discussed. By using the geometric constraint, thedimension constraint, the dimension equation and the dimension drivingtechniques of CAD, the simulation mechanisms are created. After that, createthe Jacobian simulation mechanisms and the velocity simulation mechanismswith two close same simulation mechanisms, and add correct dimensionconstraint equations, and then the Jacobian and velocity are solved. Create theacceleration simulation mechanisms with two close velocity simulationmechanisms, and the acceleration of mechanisms is solved.The Jacobian of some typical mechanisms of serial and parallel planarmechanisms and spatial serial mechanisms are solved by this method. We alsocalculate the Jacobian by analytics, and compare their results. At last, thevelocity and acceleration of the spatial serial mechanisms are solved by thecomputer simulation approach. Also, we validate its result through comparisonwith the result of analytics.The computer simulation approach is not only visual but also obtains theclosely same accuracy of the analytics without boring calculation. Since thismethod would not be limited by the mechanism's complication, the morecomplicated mechanism it used for the more effective you will find it be. It isespecially suitable for complicated multi-DOF mechanisms and new designedmechanisms.