Elastic impact of a pendulum on frictional surface

Abstract

Constrained impacts with friction frequently exist in mechanical systems such as robotic arms, hard disk drives and other mechanisms. Such discontinuous contacts, if not designed and analysed properly, can lead to malfunctions. In particular, for the analysis of problems that involve eccentric collisions and reversal of friction force, use of stereomechanical impact theory with coefficient of restitution can produce paradoxical energy increase. Alternatively, continuum models, which provide more detailed analysis for such problems, can be used, however they are computationally tedious. Instead, here, contact is described by compliant elements with friction and applied to a physical pendulum. In this thesis, impact-momentum relations for general three-dimensional free collisions are modified for a pendulum which exemplifies an impact with friction and constraint. Inclusion of tangential compliance to model enables the model to demonstrate tangential force reversals and their transition between stick and slip, which is demonstrated using a sphere and a slender rod obliquely colliding with a rough massive plane. Use of compliant elements to describe impact by a planar pendulum produces differences in the behavior of a constrained system compared with free impacts. For instance, in free collisions an impact that starts with an initial sticking, is always followed by sliding. However, in a pendulum if the contact begins by sticking, it continues to stick throughout the duration of impact. Another difference appears when contact starts with an initial sliding. In free impact, sliding is followed by sticking and sliding, then the body rebounds unless the collision is inelastic. However, in the constrained case wedging of the pendulum is observed if initial angle of collision is below a critical value for a specified friction coefficient.