Multibody simulation with body coordinates using a novel quaternion-based relative revolution constraint

Abstract

Multibody simulation has evolved significantly over the last decades but simultaneously has become a field of specialists and commercial software products. Body coordinates avoid complex simulation algorithms even for arbitrary system topology and simulation scenario, while exhibiting lower but in most practical cases still satisfactory computational efficiency. Currently, when body coordinates are used, special measures are required to robustly constrain the angle of relative revolution between two bodies to a predefined value. This constraint is required, e.g. for inverse dynamic simulation of a mechanism with rotational actuators. This paper presents a new formulation of this constraint, which is efficiently evaluated and makes special measures as mentioned above obsolete, thus increasing straightforwardness and simplicity of consequent multibody simulation. A multibody simulation program which is based on the new constraint formulation and provides a plain, universal, and adaptable simulation platform is presented in addition. The program is defined in Matlab and Octave, open source, freely accessible and was validated against the Matlab toolbox SimMechanics revealing similar simulation accuracy.