Modeling Mechanisms with Nonholonomic Joints Using the Boltzmann-Hamel Equations

Abstract

This article describes a new technique for deriving dynamic equations of motion for serial chain and tree topology mech anisms with common nonholonomic constraints. For each type of nonholonomic constraint, the Boltzmann-Hamel equations produce a concise set of dynamic equations. These equations are similar to Lagrange's equations and can be applied to mechanisms that incorporate that type of constraint. A small library of these equations can be used to efficiently analyze many different types of mechanisms. Nonholonomic constraints are usually included in a La grangian setting by adding Lagrange multipliers and then eliminating them from the final set of equations. The ap proach described in this article automatically produces a minimum set of equations of motion that do not include La grange multipliers.