Construction of the Equations of Motion for Multibody Dynamics Using Point and Joint Coordinates

Abstract

A systematic process for constructing the equations of motion for multibody systems containing open or closed kinematic loops is presented. We first illustrate a nonconventional method for describing the configuration of a body in space using a set of dependent point coordinates, instead of the more classical set of translational and rotational body coordinates. Based on this point-coordinate description, body mass and applied loads are distributed to the points. For multibody systems, the equations of motion are constructed as a large set of mixed differential-algebraic equations. For open-loop systems, based on a velocity transformation process, the equations of motion are converted to a minimal set of equations in terms of the joint accelerations. For multibody systems with closed kinematic loops, the equations of motion are first written as a small set of differential-algebraic equations. Then, following a second velocity transformation, these equations are converted to a minimal set of differential equations. The combination of point-and joint-coordinate formulations provides some interesting features.