Simulation of Motion of Constrained Multibody Systems Based on Projection Operator

Abstract

This paper presents an efficient dynamic formulation for solvingDifferential Algebraic Equations (DAE) by using the notion of orthogonalprojection. Firstly, the constraint equations are expressed explicitlyat acceleration level by using the notion of the orthogonal projection.Secondly, the Lagrangian multiplier is eliminated from the dynamicsequation by the projection operator. Then, the resultant equations areconsolidated into one equation which explicitly correlates theacceleration to the generalized force through a so-called constraint mass matrix. It is proved that the constraint mass matrix isalways invertible and hence the acceleration can be computed in aclosed-form manner even with the presence of redundant constraints or asingular configuration. The equation of motion is given explicitly in arelatively compact form, which can lead to computational efficiency. Italso has a useful physical interpretation, as the component of thegeneralized force contributing to motion dynamics is readily derivedform the formulation. Finally, results obtained from numericalsimulation of motion of a five-bar mechanism is documented.