Geometry Constraint and Branch Motion Evolution of 3-PUP Parallel Mechanisms with Bifurcated Motion

This paper investigates the interesting bifurcated motion property of a class of 3-PUP parallel mechanisms which are classified by the angle between two prismatic joints on the platform called platform angle. Based on the basic geometric constraint embedded in the loop closure equation, bifurcated rotations in two orthogonal directions are revealed systematically, indicating the full mobility of the mechanisms in two branches with a home position which is investigated using screw theory. While all the 3-PUP parallel mechanisms have a pure rotation in one branch, the other branch is a screw motion with inconstant pitch ± h when the platform angle is less or larger than π. A special case is that the platform angle equals to π and the branch screw motion becomes a pure rotation with pitch 0. Furthermore, the platforms possess a decoupled common translation at all configurations including the home position with constraint singularity. Actuation scheme is identified for the branch motion operation and constraint singularity avoidance with both forward and inverse kinematics obtained analytically.