Optimal sliding mode control for cutting tasks of quick-return mechanisms

A solution of the constant cutting velocity problem of quick-return mechanisms is the main concern of this paper. An optimal sliding mode control in the task space is used to achieve uniform and accurate cuts throughout the workpiece. The switching hyperplane is designed to minimize the position error of the slider-dynamics in an infinite horizon.

A Jacobian compensator is used to exploit the mechanical advantage and ensure controllability. The velocity profile is constructed in terms of the mechanism and workpiece geometric properties. Stability of the closed-loop dynamics is verified with the Lyapunov stability theory. Experiments are carried out in a quick-return mechanism prototype to validate the proposal.