|dc.description.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