Study on error sensibility of UPU parallel manipulator based on probability distribution

This paper takes the 3-UPU parallel manipulator which possesses 3 translational and 1 revolute (3T1R) motions as a studying case. The sensitivity of degree of freedom (DOF) characteristics and kinematic errors resulting from various kinds of torsion angle errors is observed. Kinematic model of the manipulator is established and typical torsion angle errors are enumerated. Based on the model and particular probability distribution, forward solutions are solved and discussed in two cases by numerical method. Firstly, the position and orientation error of end effector changing with time is presented when error fixed. Secondly, by using probability distribution theory, the influence of error amplitude on position and orientation error of manipulator in the particular time is assessed. With analyzing and comparing the numerical results and simulation illustrations, status of different torsion angle errors acting on moving platform are obtained. The error sources are estimated according to the sensitivity.