Development of a Simulator for a Dynamic Analysis of a Multi-Rigid-body System

本文提出了用螺旋理论、张量代数和李代数对多刚体系统进行统一分析的方法，以便在计算机上进行机构的动力学仿真。首先，对于矢量分析公式的表示，表示扭转的基由机构的被动关节轴组成，其对偶基用于表示机构中的扳手。建立了统一的分析算法。它不受机构运动空间的限制，也不受开环机构、闭环机构、并联机构以及连杆上有环或约束的并联机构等机构类型的影响。在此基础上，建立了适用于多种机构的分析算法。分析表明，该方法可以方便地建立多刚体系统的统一程序，并在此基础上推导出了开环机构、具有一个或多个回路的闭环机构、连接链中有回路或约束的并联机构的仿真分析程序。编制了动力学模拟器的计算机程序，结果表明，该程序可以模拟目前使用的机构的运动。

The unified analysis method of multi-rigid-body systems using the screw theory, the tensor algebra and the Lie algebra has been developed for the dynamic simulation of mechanisms by a computer. First, for the expression of the vector analysis formula, the basis for expressing twists is composed of passive joint axes of the mechanism and its dual basis is used for expressing wrenches in a mechanism. The unified analysis algorithm has been developed. It is free from the kind of motion spaces of mechanisms and from the types of mechanisms such as open loop mechanisms, closed loop mechanisms, parallel mechanisms, and parallel mechanisms with loops or constraints in its connecting chains. Based on this method, the analysis algorithm which is applicable to many types of mechanisms has been established. It is shown by the analysis that the building of a unifying program for multi-rigid-body systems can be easily performed by this method.Based on this algorithm, an analysis procedure for the simulation of open loop mechanisms, closed loop mechanism having one or more loops, the parallel mechanism which has a loop or a constraint in its connection chain had been derived. The computer program for the dynamic simulator has been developed and it is shown that the motion of the mechanisms which are used at present can be simulated by this program.