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.

摘要

并联机械手动态性能评估的一个重要方面是需要计算刚度和质量矩阵的弹性动力学分析。在弹性动力学分析中，假设电机处于锁定状态，因此，系统的质量矩阵应基于柔性部件引起的小幅度弹性运动得到。作为我们之前工作中介绍的用于计算多体系统刚度矩阵的有效方法的续集，本文的重点是开发一个类似的数学框架来计算刚柔多体系统的质量矩阵参数化。这种相似性有助于分析人员轻松获得具有同一组广义坐标的动能和应变能，因此，具有相同尺寸的质量和刚度矩阵。因此，可以轻松进行复杂多体系统的弹性动力学分析。此外，所得质量矩阵可以参数化获得，可用于优化和灵敏度分析目的。所提出的框架应用于 Delta 并联机器人的弹性动力学分析，结果将通过有限元分析软件包进行验证。