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

Document Type: Article


Department of Mechanical Engineering, Universidad del Norte, Km.5 Via Puerto Colombia, Barranquilla, Colombia


Parallel mechanisms with reduced degree of freedom (DOF) have grown in importance
for industry and researchers as they o er a simpler architecture and lower manufactur-
ing/operating costs with great performance. In this paper, a two degree of freedom
parallel robot is proposed and analyzed. The robot with a xed base, a moving platform
and three legs achieve translational and rotational motion through actuation on prismatic
and revolute joints, and can be applied on pick and place applications, vehicle simulators
among others. By making use of homogeneous transformation matrices and Sylvesters
dialytic elimination method a closed form solution for direct kinematics is obtained for
all possible assembly modes. Inverse kinematics was solved in closed form as well. This
greatly decreases computational time and proposed approach is optimal. A case study
was done to validate the solutions found and compared with a CAD model to corroborate
results. Finally, a workspace calculation was made for di erent geometrical parameters
of the robot.


Main Subjects