Kinematics and Statics of a 3UPU Robot in Screw Coordinates

Abstract

This paper investigates the kinematics and statics of a 3UPU robot in screw coordinates. According to the definition of a twist, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. The twist equation is established to calculate the position and posture of each joint. This equation can be applied directly to analyze the statics. According to the definition of a wrench, both the force and torque of the planar linkages are expressed in wrench components. As a result, the wrench equations are established to express the resultant action of a force system in one coordinate frame. Compared with the traditional Cartesian coordinate method, the wrench equation is free from complex algebraic manipulation and convenient to obtain wrench matrix by Plücker coordinates of each wrench. Numerical calculation is applied to solve the kinematics which can conveniently depict the position and posture of each joint in the absolute coordinate frame. Six unknown variables can be solved with each equation of wrench that contains three forces and three torques. The kinematics and static analysis of the 3−UPU robot validate this method.