Inverse Dynamics of Constrained Multibody Systems

A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.