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The dynamics after that of the Newton-Euler method uses the symmetric property between a momentum vector and a velocity vector, or between a force vector and a velocity vector. The usage of the symmetric property makes the expression of the kinematic and dynamic analysis independent from the choice of a coordinates system. In this paper, it is clarified that this concept can be applied to the analysis of multi-rigid-body systems and mechanisms, using the concept of tangent and cotangent vectors based on the screw coordinates of joint axes. And the procedures of analyses of the closed loop mechanisms and parallel mechanisms are derived. An outline of the algorithm of the simulator for closed loop mechanism and parallel mechanisms is also described and the simulation results of parallel mechanisms are illustrated.

Dynamic Simulator of Mechanisms Based on the Tangent and Cotangent Vectors