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 importance for industry and researchers as they offer a simpler architecture and lower
manufacturing/operating costs with great performance. In this paper, a two-degree-offreedom
parallel robot is proposed and analyzed. The robot with a xed base, a moving
platform, and three legs achieve translational and rotational motions through actuation
on prismatic and revolute joints and can be applied to pick-and-place applications, vehicle
simulators, etc. Through homogeneous transformation matrices and Sylvesters dialytic
elimination method, a closed-form solution for direct kinematics is obtained for all possible
assembly modes. Inverse kinematics is solved by the closed-form solution as well. This
greatly decreases computational time, suggesting the optimality of the proposed approach.
A case study is investigated to validate the solutions found and is compared with a CAD
model to corroborate the obtained results. Finally, a workspace calculation is carried out
for different geometrical parameters of the robot.