This paper deals with the trajectories of points embedded in a moving rigid body being guided by a linkage having extra or "redundant" motion parameters. A new method for the kinematic use of redundancy is presented. The method is based on the concept of a metric and differs from the typically used pseudo-inverse formulation. It is shown how the redun dancy can be used to alter first-order properties such as the shape of the velocity ellipse (or the ellipsoid) and a scalar measure of transmission ratio or effectiveness. It is shown how such local use of the redundancy leads to some global results such as determining the alterable regions and the boundaries of the trajectories. An example of a planar 3R manipulator illustrates these new techniques.
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