Kinematics and Statics of a 3-UPURobot in Screw Coordinates

Abstract

This paper investigates kinematics and statics analysis of a 3-UPU 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. We therefore establish the twist equation (TE) 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 linkage are expressed in wrench components. As a result, we establish wrench equations (WE) to express the resultant action of a force system in one coordinate frame. With the definition of twist and wrench, we can associate the kinematics with statics by unit screws. Compared with the traditional Cartesian coordinate method, the WE 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 obtain the position and posture of each joint in absolute coordinate. Six unknown variables can be solved with each equation of wrench which contain 3 forces and 3 torques. The kinematics and static analysis of the 3-UPU robot validate this method.

Kinematics and Statics of the Gough-Stewart Platform

“…(6), (7), and (10), expressed in Section 3, the unit screw iu $ of each joint in the absolute coordinate system, which consists of position 0 i r and posture i e , could be obtained via an iterative procedure. And the solved kinematic parameters, which are expressed in screw form, can be directly employed in establishing the static equations based on Equation (26). The relationship and unified procedure of the kinematic and static modeling of a kinematic chain are given in Figure 6.…”

“…Screw theory is a convenient method to solve the kinematics and statics of parallel mechanisms. The expressions for the kinematics and statics could be simplified using screw theory, and some scholars have applied screw theory to solve the kinematics [23,24] and statics [25,26] in parallel mechanisms. Traditional static modeling methods, which are established in the Cartesian coordinate system, suffer from an unclear mechanism relationship using the dismantling method, and the vector method will introduce multiple variables, while the conventional methods start with displacement, and then solve the velocities and accelerations through first-and second-order numerical interpolation, respectively, which leads to high computational costs.…”

Kinematics and Dynamics Analysis of a 3UPS-UPU-S Parallel Mechanism

“…By using conventional kinematic modeling approaches to describe both rotational and translational motions, a suitable mathematical framework in a relatively general way is required. Screw coordinates have been proposed as a valuable tool to simplify the kinematic analysis of parallel mechanisms [1].…”