A three-dimensional motion simulation model of an open-loop kinematically constrained mechanical system is developed to simulate the motion response of a robotic arm to externally applied static loads. The general system consists of N rigid bodies connected together by (N-1) kinematic pairs. The class and type of kinematic pairs may be selected from a set of twelve physically realizable kinematic pairs. Six equations of force equilibrium are written for an ith body. A variational method is used to linearize these equations for incremental values of displacement and to incorporate the generalized parameters of the kinematic pairs and characteristics of the internal driving forces. Five applications of the proposed simulation model are discussed.

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