基于万有D'Alembert原理的机械手动力学分析与计算实现

本文用建立方法的 Gauss 变分原理导出了 Kane 动力学方程和 Rober-son—Wittenburg 方法中的动力学普遍方程,认为从广义的角度讲,上述方法的出发点都是万有 D' Alembert 原理,它们之间存在着内在联系。文章还介绍了作者根据方法编写的求解具有任意自由度数和任意关节形式的单式开链机械手动力学两类问题的通用程序,以及对 Stanford 六自由度机械手的求解过程。

Dynamic Analysis and Computer Implementation of Manipulators Based on Generalized D'Alembert's Principle

Since 1960 the dynamic methods of multi-rigid-body manipulators havebecome more and more developed1]8].Thus far,it is generally recognizedthat various methods may be divided into two categories1]5].One categoryderives dynamic equations using vector mechanics or analytical mechanics,suchas Kane method1]6]and Roberson-Wittenburg method1].Another category,such as Popov method3],searches the constrained extremum of system func-tional using variational principles.To the author's best knowledge,no paper inthe open literature has attempted to deal with the two categories with an unifiedapproach.This paper applies Gauss principle,the very principle on whichPopov method is established,to deduce the dynamic equations of Kane and RWmethods;Thus,the above three methods are all based on the generalizedD'Alembert's principle.In addition,this paper gives the computer program for dynamic analysisof the direct and inverse problems of manipulators.