Contact/Impact in Hybrid Parameter Multiple Body Mechanical Systems

Abstract

The multiple motion regime (free/constrained) dynamics of hybrid parameter multiple body (HPMB) systems is addressed. Impact response has characteristically been analyzed using impulse-momentum techniques. Unfortunately, the classical methods for modeling complex HPMB systems are energy based and have proven ineffectual at modeling impact. The problems are exacerbated by the problematic nature of time varying constraint conditions. This paper outlines the reformulation of a recently developed HPMB system modeling methodology into an impulse-momentum formulation, which systematically handles the constraints and impact. The starting point for this reformulation is a variational calculus based methodology. The variational roots of the methodology allows rigorous equation formulation which includes the complete nonlinear hybrid differential equations and boundary conditions. Because the methodology presented in this paper is formulated in the constraint-free subspace of the configuration space, both holonomic and nonholonomic constraints are automatically satisfied. As a result, the constraint-addition/deletion algorithms are not needed. Generalized forces of constraint can be directly calculated via the methodology, so the condition for switching from one motion regime to another is readily determined. The resulting equations provides a means to determine after impact velocities (and velocity fields for distributed bodies) which provide the after collision initial conditions. Finally the paper demonstrates, via example, how to apply the methodology to contact/impact in robotic manipulators and structural systems.