Dynamics for a 3-UPU Parallel Robot

Abstract

This paper investigates Newton-Euler dynamics in Plücker coordinates for a parallel robot. In classical mechanics, the Newton–Euler equations describe the dynamics of a rigid body by combining translations and rotations. In accordance to the definition of a screw, the angular velocity of a rigid body and its linear velocity at a point are represented in Plücker coordinates. With Plücker coordinates, we get the absolute displacement through numerical integration on the velocity solution and acceleration through numerical differential interpolation of velocity of each joint. The absolute accelerations and displacements calculated in kinematics are used to establish the force equation and toque equation directly. Since both the displacement and acceleration can be numerically expressed in terms of velocity of first order, the most prominent merit of the algorithm is that the dynamics can be iterated based on the velocities in Plücker coordinates including forward and inverse dynamics. The dynamics of a spatial 3-UPU parallel robot validates the algorithm. Although this paper only discusses the dynamics of 3-UPU parallel robot, it is also suited to developing numerical algorithms for kinematics and dynamics of a series mechanism and hybrid mechanism.