Forward Kinematics Analysis for A Nearly General Parallel Mechanism with Five Degrees of Freedom

This paper deals with the forward kinematics problem of a general platform-type parallel mechanism with five degrees of freedom (DOF). Such mechanism is composed of a movable platform connected to the base by five active limbs. Four of them are identical 6-DOF UPS limbs and the last one is a 5-DOF UPU limb which has the same DOF as that of the movable platform, thus resulting in the legs' topology 4-UPS/UPU. Based on the kinematics analysis, a reasonably procedure using the polynomial continuation methods presented in literature is introduced, which aims at obtaining all possible configurations of the mechanism effectively and efficiently. Through this process, a set of 58 solutions to the forward kinematics problem of the 4-UPS/UPU mechanism can be found, i.e. such mechanism may in general have at most 58 nonsingular configurations