Determination of joint reaction forces in a symbolic form in rigid multibody systems

This paper presents an algorithm for determination of joint reaction forces in a symbolic form in planar and spatial tree structure rigid multibody systems. The frictionless revolute and prismatic joints are taken into consideration. The algorithm is based on the use of Kaneʹs equations with undetermined multipliers of constraints. The expressions for the reaction forces and the torques of reaction couples in the joints are obtained in a form that does not require matrix inversion and allows an easy and straightforward implementation in programming environments for symbolic computations (like Mathematica, Maple etc.). The application of the proposed algorithm to the problem of determination of static friction forces in locked Coulomb friction joints is indicated. The algorithm has been illustrated by using both a gymnast on a trampoline and a Puma manipulator.