Inverse Dynamics of Redundantly Actuated Four-bar Mechanism Using an Optimal Control Formulation

Closed kinematic chain mechanisms are extensively used in several applications, from machine tools to biomechanical models. A few works however address the mechanics of these systems with redundant actuation, i.e., with more actuators than degrees of freedom. The inverse dynamics analysis of this kind of system does not possess an unique solution, and therefore optimization procedures should be applied to estimate net joint torques when a kinematics is previously imposed. Literature presents some methods to solve this undetermined problem, based on multi-body system dynamics approach. In this paper the inverse dynamics problem is formulated as an Optimal Control Problem (OCP): to find a set of controls that minimizes an integral state and control variables cost function, subjected to endpoint, trajectory, and control constraints, both equality and inequality. Some possible sets of constraints are explored to force a 3-link open chain system dynamics behave like a four bar mechanism with a crank rotating at a constant velocity. The controls calculated by OCP are assumed to be the input joint torques. The regular case with one torque actuator is solved and compared to the two and three actuators case.