Mathematical modelling of linear motion error for Hexarot parallel manipulators

Hexarot is a robotic manipulator that belongs to the family of axis symmetric parallel mechanisms. The robot is able to move the robot platform or tool center point in six degrees of freedom (DOF). This paper presents the kinematics model of the robot including the inverse and forward kinematics, and its time derivatives. Then using the kinematics formulations, investigation of the nonlinear motion of the Hexarot robot for a desired linear motion path is performed. For this purpose, the concept of curvature of the robot path is used for measuring the nonlinearity of the actual motion of the robot. The nonlinear motion error of the robot is analyzed for the scenario where the platform moves on a linear path between two arbitrary points of the robot workspace. The effects of different parameters on the nonlinear motion error of the mechanism are demonstrated and strategies for motions with low error values are proposed.