Dynamic Modeling and Control of the Omega-3 Parallel Manipulator

Parallel manipulators are widely used in industrial applications due to their rigid structures and ability to perform automated tasks at high speeds. However, because the links on a parallel manipulator are mechanically coupled, solving its kinematics and dynamics equations can be more difficult than for its serial counterpart. Nevertheless, the inverse kinematics and inverse dynamics models are a critical component of a manipulator's controller. Specifically, a more computationally simple formulation of the inverse kinematics and dynamics is necessary to achieve efficient and fast manipulator control. In this paper, both the inverse kinematics and dynamics equations for the Omega-3, a three degree-of-freedom (3-DOF) parallel manipulator, are developed. For the inverse kinematics problem, the concept of loop closure equations is used to simplify the analysis. The virtual work principle is used to create a numerically simple inverse dynamics model. Using the inverse kinematics and dynamics model, a trajectory tracking controller is implemented on the manipulator and the resulting experiments reveal good tracking behavior.