Elastodynamic analysis of multibody systems and parametric mass matrix derivation

Abstract

One important aspect of the dynamic performance evaluation of a parallel manipulator is the elastodynamic analysis which calls for the calculation of the stiffness and mass matrices. In the elastodynamic analysis, the motors are assumed to be locked, and thus, the system’s mass matrix should be obtained based on the small-amplitude elastic motion caused by the flexible components. As a sequel to the efficient methodology for the calculation of the stiffness matrix of a multibody system which was introduced in our previous work, the focus of this article is to develop a similar mathematical framework to compute the mass matrix of a rigid-flexible multibody system parametrically. This similarity helps an analyst to readily obtain the kinetic and strain energies with the same set of generalized coordinates, and consequently, the mass and stiffness matrices with the same dimensions. Therefore, the elastodynamic analysis of complicated multibody systems can be conducted with no burden. Moreover, the resultant mass matrix can be obtained parametrically which can be used for optimization and sensitivity analysis purposes. The proposed framework is applied for the elastodynamic analysis of a Delta parallel robot, and the results will be verified by means of a finite element analysis software package.