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Unified Theory for Kinematic and Dynamic Analysis System of Mechanisms

机构运动动力学分析系统统一理论

基本信息

批准号：
11650269
负责人：
SUGIMOTO Koichi
金额：
$ 2.24万
依托单位：
Kagawa University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2001
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11650269/
关键词：
Motion Analysis Equation of Motion Mechanism Screw Theory Lie Algebra Multi-Body System Kinematics Force Analysis 機構運動学ロボット

项目摘要

Unified theory for the kinematic and dynamic analysis of the multiple rigid body system based on the Lie algebra has been studied. The algorithm has been developed which is applicable to both of the open and the closed loop mechanisms and the closed loop mechanism and the algorithm is improved in order to reduce the computational cost of a computer program. It is clarified that, for the unifying motion simulator of mechanisms, a simulator for a closed loop mechanism can be constructed over that for an open loop mechanism by connecting tips of the tree structure of an open loop mechanism. Based on this theory, the inertia matrix can be expressed by closed form equations and the recursive computation method for an inertia matrix of mechanisms is derived. Moreover, in order to derive the equations for analyzing the constraint in each loop, simple expression can be obtained by utilizing the basis composed of passive joints for representing velocities and its dual basis for forces. This method can also make it possible to analyze a mechanism with loops of different motion spaces by the same procedure as that for a mechanism with loops of same motion spaces. The algorithm has thus versatility and is also directly applied to the multi-body system such as free flying object in space. These results will be utilized for developing the unified motion simulator of multi-body systems.

研究了基于李代数的多刚体系统运动学和动力学分析的统一理论。提出了一种既适用于开环机构又适用于闭环机构的算法，并对算法进行了改进，以降低计算机程序的计算量。阐明了对于机构统一运动模拟器，通过连接开环机构树形结构的顶端，可以在开环机构模拟器的基础上构造出闭环机构的模拟器。在此基础上，将机构的惯性矩阵表示为闭合形式的方程，并推导出机构惯性矩阵的递推计算方法。此外，为了推导出分析各回路中约束的方程，可以利用被动关节组成的速度基和力的对偶基来得到简单的表达式。这种方法还可以用与分析具有相同运动空间回路的机构相同的步骤来分析具有不同运动空间回路的机构。该算法具有通用性，也可直接应用于空间自由飞行物体等多体系统。这些结果将用于开发多体系统的统一运动模拟器。