In this lecture the group of rigid body motions is introduced via its representation on standard three dimensional Euclidian space. The relevance for robotics is that the links of a robot are usually modelled as rigid bodies. Moreover the payload of a robot is also usually a rigid body and hence much of robotics is concerned with understanding rigid… (More)
In this work we construct a simple dynamical model for vibratory bowl feeders. The symmetrical arrangement of the springs supporting the bowl allow us to predict a simple structure for the stiffness matrix of the system. The cylindrical symmetry of the bowl itself then means that the linearized rigid body dynamics of the system can be simplified to a… (More)
—The Cayley map for the rotation group SO(3) is extended to a map from the Lie algebra of the group of rigid body motions SE(3) to the group itself. This is done in several inequivalent ways. A close connection between these maps and linear line complexes associated with a finite screw motions is found.
Three rather different problems in robotics are studied using the same technique from screw theory. The first problem concerns systems of springs. We differentiate the potential function in the direction of an arbitrary screw to find the equilibrium position. The second problem is almost identical in terms of the computations, we seek the least squares… (More)
This work looks at several problems concerned with interpolating rigid-body motions and their application in robotics. Two recently proposed interpolation methods are shown to produce the same results. We also discuss how it might be possible to control a robot in such a way as to follow one of these interpolated motions