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)
—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)