Dynamics of an elastic multibody chain: Part B—Global dynamics

Abstract

Abstract In this the second paper in a series describing the dynamics of an arbitrary multibody system, the global dynamics of a topological chain of elasticbodies is considered in detail. The direct-path approach is used in the assignment of coordinate systems, interbody position vectors, connection matrices, and in the handling of mass properties, all in conjunction with a Newton-Euler, finite-element formulation. Nonlinear inertial effects, which can be important during rapid manoeuvres, are also identified. The equations are first collected in a form appropriate to a chain with unconstrained joints—a full six degrees of freedom are permitted at each interbody joint. Constraints are then selectively introduced and the associated constraint forces calculated using the concept of projection matrices. The associated control forces (to carry out robotics tasks, for example) are also calculated. Finally, a compact form of the motion equations is presented for a multibody chain with constrained-controlled interbody joints.