On the efficacy of pseudo-coordinates—Part 2: moving boundary constraints

Abstract

In this paper an argument is presented in favor of utilizing felicitous or natural coordinates in the model formulation of complex hybrid parameter multiple body mechanical systems (HPMBS). Specifically for this paper, HPMBS that consist of continuua that are subjected to spatially and temporally varying non-holonomic boundary conditions. This is the second paper of a two part series of papers that is presented to clarify the novelty and usefulness of a recently developed Gibbs–Appell type projection based HPMBS modeling tool. The purpose of the paper is to show that with the novel use of pseudo-coordinates and speeds (as defined by the author) it is completely natural to provide minimal configuration space dimensionality yet still retain rigorous analytical formulation tractability. Presented in this work, as a demonstrative arguing point, is the development of the hybrid parameter motion equations for a rolling flexible-disk material cutting device. This device consists of a circular flexible continuum (the cutter) along with the requisite mounting rigid hub and handle. This non-holonomically constrained device is modeled executing spatial motion constrained to the plane via moving constraints applied to the boundary of the planar continuum. Also included in this work are numerical results bolstering the claims made herein. These numerical results demonstrate that the methodology elucidated provides low-order models suitable for modeling complicated devices. These low-order models are in contrast to the current modeling trend of ever-increasing degrees of freedom.