Modeling mechanisms with nonholonomic joints using the Boltzmann-Hamel equations

This article describes a new technique for deriving dynamic equations of motion for serial chain and tree topology mechanisms 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 Lagrangian setting by adding Lagrange multipliers and then eliminating them from the final set of equations. The approach described in this article automatically produces a minimum set of equations of motion that do not include Lagrange multipliers.