Udwadia-Kalaba control approach for 3-DOF planar parallel manipulator

This paper aims to address the trajectory tracking control problem of a 3-degree-of-freedom (3-DOF) planar parallel manipulator which contains prismatic-prismatic-revolute (PPR) joint. Udwadia Kalaba approach which presents a concise and explicit equation of motion for constrained mechanical systems with holonomic or nonholonomic constraints is applied to obtain a closed-form expression for the control force required to precisely meet the trajectory requirements of the 3-PPR planar parallel manipulator. When the initial conditions do not satisfy the given constraints, a modified constraint equation is constructed. Numerical simulations are performed to demonstrate the simplicity, efficacy and accuracy of this control method.