Higher-order kinematic analyses of a planar parallel robot based on screw theory

Abstract

This paper presents the higher-order kinematic analyses of a planar parallel robot, addressed by means of the theory of screws. The reduced velocity, acceleration, jerk and hyper-jerk state for the end-effector of robot was developed as a spatial vector by applying the concept of Lie algebra and helicoidal vector field. In order to verify the effectiveness of this theoretical development, the kinematics models obtained was solved and simulated in MATLAB environment, using Freeth's Nephroid trajectory as reference path for tracking with the end-effector. The simulation results proved that this type of spatial notation is convenient, because it allows us to quickly develop equations of motion and express them succinctly in symbolic form, reducing the volume of algebra, simplifying the modeling tasks, implementation and execution the algorithms used to solve kinematic problems in parallel robots. The major contribution of this work is the possibility of extended the classical kinematic analysis to a high order system; where the application of screw theory becomes a safe and reliable mathematical tool, which may be successfully used on parallel planar robots with singular configurations, represented with helicoidal vector field.