Rate kinematics of in-parallel manipulator systems

The following questions are addressed: how to determine the joint rates and constraints on the end-effector rates and how to know which joint rates are instantaneously inactive and which can be driven independently. The approach is based on the instantaneous properties of series chains as derived from the theory of screw systems. In this framework, those screws that correspond to the joint rates of the constituent series chains are identified. Once the correspondence is determined, the sought-after kinematic properties can be deduced from the vector space properties of these screws