Analysis of Instantaneous Kinematic Properties regarding the Shape of Robotic Mechanisms

We demonstrate the general formulation of a method for conducting a kinematic analysis regarding the shape formed by multiple reference links on robotic mechanisms. In contrast to the standard kinematic analysis of robot manipulators that assumes having a single hand link configuration with respect to the base link, the formulated kinematic analysis regarding the shape is free from this assumption. Consequently, an analysis without specifying base link and that about shape defined by multiple reference links are possible. Moreover, the kinematic properties, which are invariant from the switching of base and hand links, can be obtained. First, a method to decompose motions of multiple bodies into rigid and non-rigid components is formulated. Then, the method is generalized considering the weights for translational and angular velocities. Next, Jacobian matrices that relate active joint velocities and non-rigid motions (change in the shape) of specified reference links on the robotic mechanism are defined. Subsequently, certain measures for evaluating shape controllability are defined based on the measures for evaluating hand configuration controllability of robot manipulators. Finally, some application examples using the defined measures are demonstrated.