Statics of In-Parallel Manipulator Systems

In-parallel systems can have some active and some passive joints (i.e., joints with and without joint actuators). The questions that we address in this paper are: how to choose the active and passive joints, how to know whether a set of active joints is sufficient, redundant, or minimal to control the end-effector, and whether there exists a unique choice of active actuators. Our approach to study this problem is based on instantaneous properties of series chains as derived from the theory of screw systems. In this framework, we identify those screws that correspond to the joint actuators of the component series chains. Once the correspondence is made, the sought after actuator properties are deduced from the vector space properties of these screws.