Systematic reduction of multibody equations of motion to a minimal set

This paper presents a two-step process to convert the equations of motion for closed-loop systems from a large set of absolute coordinates to a minimal set of relative joint coordinates. Initially, absolute coordinates are used to define the position of each body, the kinematic joints, and the forces acting on the bodies. Before numerical integration of the equations of motion, the equations are converted to a minimal set to gain computational efficiency. A simple example is provided to illustrate the conversion steps. It is also shown that the equations of motion can be expressed in terms of the time derivative of the system momenta, instead of the accelerations, to reduce numerical integration error and gain computational stability.