Department of Mechanical Engineering, Robotic Mechanical Systems Laboratory, McGill Research Centre for Intelligent Machines, McGill University, Montreal, Quebec, Canada H3A 2A7. Manuscript received by ASME Applied Mechanics Division, June 1, 1987; final revision September 2, 1987. coupled by holonomic constraints. Several approaches to the problem have been proposed, aimed at separating independent from dependent generalized coordinates (Nikravesh and Haug, 1982; Kammam and Huston, 1984; Singh and Likins, 1985; Kim and Vanderploeg, 1986-1. 2). A comprehensive discussion of the problem at hand, and various formulations proposed to solve it appear in Jerkovsky (1978), whereas Casey (1983) presents a tensor treatment of rigid-body dynamics that is particularly useful in this context. Proposed in this note is a method that allows the elimination of the constraint forces by multiplication of the unconstrained dynamical equations by a suitably defined orthogonal complement of the matrix of linear velocity constraints. Although the method presented here bears many items in common with the formulation presented by Jerkovsky (1978), the said method differs from the latter in various respects, as described next.

2 Preliminary Definitions A system of r holonomically-coupled rigid bodies is the subject of this study. The twist of the system's/th rigid body, undergoing an arbitrary motion in the three-dimensional space, t,-, is defined here in terms of its angular velocity,«,-, and the velocity of its mass center, c,-: