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

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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.