Kane’s Method-Based Simulation and Modeling Robots with Elastic Elements, Using Finite Element Method

Abstract

The Lagrange’s equation remains the most used method by researchers to determine the finite element motion equations in the case of elasto-dynamic analysis of a multibody system (MBS). However, applying this method requires the calculation of the kinetic energy of an element and then a series of differentiations that involve a great computational effort. The last decade has shown an increased interest of researchers in the study of multibody systems (MBS) using alternative analytical methods, aiming to simplify the description of the model and the solution of the systems of obtained equations. The method of Kane’s equations is one possibility to do this and, in the paper, we applied this method in the study of a MBS applying finite element analysis (FEA). The number of operations involved is lower than in the case of Lagrange’s equations and Kane’s equations are little used previously in conjunction with the finite element method (FEM). Results are obtained regardless of the type of finite element used. The shape functions will determine the final form of the matrix coefficients in the equations. The results are applied in the case of a planar mechanism with two degrees of freedom.