Unified Theory for Kinematic and Dynamic Analysis System of Mechanisms

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。本文提出了一种既适用于开环机构又适用于闭环机构的算法，并对闭环机构进行了改进，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尖端，可以在开环机构的基础上构造一个闭环机构模拟器。在此基础上，导出了机构惯量矩阵的递推计算方法，并将惯量矩阵用闭式方程表示。此外，为了推导出分析各环约束的方程，可以利用被动关节组成的速度基和力的对偶基得到简单的表达式。该方法还可以用与具有相同运动空间的回路的机构相同的程序来分析具有不同运动空间的回路的机构。该算法具有通用性，可直接应用于空间自由飞行物体等多体系统。这些结果将用于多体系统统一运动模拟器的开发。

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.