A Unified Formulation of Multibody Kinematic Equations in Terms of Absolute, Joint, and Indirect Coordinates

This paper reviews some of the coordinate sets employed in multibody dynamic formulations, including absolute, joint, absolute angular, and indirect coordinates. Linear graph theory is then combined with the concept of a “virtual joint” to develop a unified modelling methodology that is capable of representing any of these coordinate sets. An algorithm is proposed and demonstrated for generating the kinematic constraint equations for dependent coordinates, plus kinematic transformations between coordinates (e.g. velocity transformations). The effects of different coordinates on the dynamic equations for a simple manipulator are shown.