Constraint Forces and the Method of Auxiliary Generalized Speeds

Abstract

This paper deals with noncontributing forces, usually called constraint forces or reaction forces, arising in simple, nonholonomic multibody systems. These forces are related to two kinds of constraints, namely, kinematical constraints—derived from kinematical requirements, and auxiliary constraints, introduced for the purpose of constraint forces determination. Here, the method of “auxiliary generalized speeds” is used to bring into evidence constraint forces related to the two kinds of constraints. It is shown that auxiliary generalized speeds can always be chosen in a way that gives rise to additional equations each having one measure number of a constraint force as an unknown. Motion equations can thus be generated and solved without regard to constraint forces determination; and constraint forces can be determined with no matrix inversion, at a minimal computational cost.