Unified Theory for Kinematic and Dynamic Analysis System of Mechanisms

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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.