A MODELING PROCEDURE FOR LINEARIZED MOTIONS OF TREE-STRUCTURED MULTIBODIES .1. DERIVATION OF THE EQUATIONS OF MOTION

A modelling technique for linear time invariant non-gyroscopic rigid m ultibody systems with tree structure is stated. The equations of motio n are derived analytically on the basis of the Roberson-Wittenburg met hod. The interconnection structure between the bodies within the multi body is established by a directed system graph and the dynamics are ba sed on a variational analysis. The resulting differential equations ar e described with generalized Lagrangian coordinates. Several types of forces are formulated explicitly and mathematical expressions for each of them are derived. Formulae for the classical tire model and the ti re model of Crolla are incorporated in the equations of motion. As a r esult, each system matrix in the differential equations is written as a combination of simple and easily constructed matrices which are func tions of the geometry and the mechanical parameters of the mechanism.