The constraint equations for a kinematic chain are obtained using rigid transformations to characterize the relative movement allowed at each joint and separate rigid transformations [X to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of "n" links connected in series has the kinematic equations,