Inverse dynamics of a 3-prismatic-revolute-revolute planar parallel manipulator using natural orthogonal complement

The performance of robotic systems with parallel kinematics can be evaluated by their kinematic, static, and dynamic properties. These properties are directly used in model-based controllers which potentially offer higher accuracy for robotic systems. Inverse dynamic solution is an essential part of these controllers. In the present work, the inverse dynamics model of a 3-PRR (prismatic-revolute-revolute) planar parallel manipulator based on the natural orthogonal complement (NOC) method is developed. To drive the NOC for the 3-PRR closed-loop systems, the explicit expressions of the loop constraints equations and the associated Jacobian matrices are first obtained. Next the NOC matrix, which is a velocity transformation matrix relating the Cartesian angular/translational velocities of various bodies to the motor joint rates, is calculated. Finally results of the NOC method are compared with simulation of a 3-PRR planar parallel manipulator using two commercial softwares: SimMechanics toolbox of Matlab and COSMOSMotion of SolidWorks. In order to verify the theoretical results, two different configurations for the robot are considered: a horizontal and a vertical. Results of the NOC method as well as the two simulations are compared for the two robot configurations.