Synthesis of spatial compliances with simple serial elastic mechanisms

We address the spatial elastic behavior that can be achieved through the use of a serial chain of revolute and prismatic elastic joints. We show that, regardless of the number of joints or the configuration of the links, there exists a subspace within the 21-dimensional compliance matrix space that cannot be reached by a simple serial elastic mechanism. This restriction is shown to be dual to the restriction on the stiffness matrices associated with simple parallel mechanisms. Although analogous to each other, the two restrictions correspond to different elastic behaviors. A procedure to synthesize any realizable compliance matrix with a simple serial mechanism is provided. The dualities and differences between the parallel and serial cases are discussed.