A Recursive Formulation for Constrained Mechanical System Dynamics: Part I. Open Loop Systems

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Abstract
A recursive formulation of the equations of motion of spatial constrained mechanical systems is derived, using tools of variational and vector calculus. Position, virtual displacement, velocity, and acceleration relations are developed, using relative coordinates between kinematically coupled bodies. Graph theoretic definition of connectivity of systems with tree structure is used to define computational sequences for formulation and solution of the equations of motion that is efficient and well suited for parallel computation. Using a variational form of the equations of dynamics, inertia and right-side terms are reduced from outboard bodyjcentroidal reference frames to an inboard body centroidal reference frame. A recursive algorithm is developed to reduce equations of motion to a base body. A robot arm is analyzed to illustrate use and efficiency of the method.