Closed form solution for direct and inverse kinematics of a US-RS-RPS 2-DOF parallel robot

Parallel mechanisms with reduced degree of freedom (DOF) have grown in importancefor industry and researchers as they oer a simpler architecture and lower manufacturing/operating costs with great performance. In this paper, a two degree of freedomparallel robot is proposed and analyzed. The robot with a xed base, a moving platformand three legs achieve translational and rotational motion through actuation on prismaticand revolute joints, and can be applied on pick and place applications, vehicle simulatorsamong others. By making use of homogeneous transformation matrices and Sylvestersdialytic elimination method a closed form solution for direct kinematics is obtained forall possible assembly modes. Inverse kinematics was solved in closed form as well. Thisgreatly decreases computational time and proposed approach is optimal. A case studywas done to validate the solutions found and compared with a CAD model to corroborateresults. Finally, a workspace calculation was made for dierent geometrical parametersof the robot.