I. Introduction
The standard taxonomy of multibody systems by kinematic topology consists of serial chain structures, branching or tree-like structures, and graph or closed-loop structures [9] [19]. In the case of serial and branching structures a set of independent generalized coordinates is chosen. The kinematic constraints between the bodies are implied by the choice of these generalized coordinates. Since these generalized coordinates are independent (unconstrained) we will refer to the serial and branching structures as unconstrained with respect to configuration space. The equations of motion can then be derived by any number of methods [6] [15] [20].