A General Superelement Model on a Moving Reference Frame for Planar Multibody System Dynamics

This paper presents a mathematical formulation for a superelement on a moving reference frame. A group of constrained elements, forming a single degree-of-freedom with respect to some reference frame, is represented by one element. The configuration of a typical superelement is determined with respect to the reference frame using one parameter only. This reduces the number of generalized coordinates needed to define the configuration of the entire system. Energy relations and generalized force expressions are developed in terms of the reference coordinates and superelement parameters. An inverse dynamics approach is used to obtain the functions associated with a superelement. The differential equations of motion of a system consisting of one reference frame and several superelements are derived. Constraints internal to the superelements do not appear in the resulting differential equations. This reduces the dimensions of the problem and the computational time required to solutions. Two examples are considered to demonstrate the feasibility and the efficiency of the method.