Constraint analysis and bifurcated motion of the 3PUP parallel mechanism

This paper investigates the geometry properties and certain restrictions of stroke induced by the special assemblage of a 3PUP parallel mechanism which consists of a fixed base, a platform and three limbs. The constraints exerted on the platform by a general PUP limb are analyzed based on screw theory. The disposition and analytical expression of all the constraints applied by three PUP limbs are revealed according to the geometry of the parallel mechanism and reciprocity of screws. Geometric-constraints induced bifurcation of the platform is analyzed and motion characteristics corresponding to each bifurcated motion branch and the transitory position of two bifurcated motion branches are derived corresponding to distinct restrictions of actuated strokes. The study further reveals the practical application of the 3PUP parallel mechanism in developing rehabilitation device for sprained subtalar joint.

► A PUP limb exerts one constraint force and one couple on the platform.
► The platform has two bifurcated motion branches induced by distinct constraints.
► The platform can implement pure rotation and translation in one motion branch.
► The platform can implement screw motion and translation in another motion branch.
► The transitory position happens when the platform is parallel to the base.