Dynamics analysis of a spatial rigid-flexible linkage model subjected to optimized programmed constraints

The article presents a spatial linkage composed of rigid and flexible links subjected to work dependent programmed constraints. The key tool used for the spatial linkage dynamics derivation is an automated computational procedure for constrained dynamics generation. It serves systems subjected to holonomic and first order nonholonomic constraints and proved its effectiveness to open chain models. The procedure results in final motion equations that are in the reduced state form, i.e., constraint reaction force are eliminated during derivation. This is the essential advantage of the procedure application since it provides the smallest set of dynamic equations, which may serve motion analysis and control. The article presents extension of the procedure on linkages composed of flexible links with closed-loop kinematics, for which a spanning tree can have a serial or tree structure. Also, a new optimization procedure is proposed for constraints that are imposed upon the linkage motion. The optimization procedure aims selection of the constraint ranges due to the additional system work regimes, e.g., available power sources or energy consumption. The theoretical development of automated generation of constrained dynamics as well as the constraint optimization procedure is illustrated by the linkage model example.