Motion spaces of machine–process combinations

Machines and mechanisms realize processes, from the shaping process of a milling machine to the motion process of an automotive system. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrarily many robot degrees of freedom on one given path degree of freedom resulting in a set for evaluating possible motion spaces, now supplemented also by constraint force spaces, helpful for design and optimization. For multidimensional processes, things become more complex but feasible. This paper presents a corresponding approach applying multibody system theory in combination with transformations from the machine side to the process side and vice versa. Practical aspects are discussed and examples given.