Kinematic analysis of Hoberman's Linkages with the screw theory

This paper studies the Hoberman's linkage consisting of a series of scissor like elements connected by revolute joints. Because every Hoberman's angulated element subtends a constant angle during the motion, every angulated link was assumed as a PRRP linkage which has two prismatic joints and two revolute joints. Therefore, the two PRRP linkages of the Hoberman's angulated element are individually movable with a single degree of freedom. The mobility was investigated with the method based on the screw theory. It has been proved that the Hoberman's angulated element is movable because the terminal constraints exerted to the common joint by the two linkages are equal.

► Every angulated link was assumed as a PRRP linkage.
► The kinematics of Hoberman's linkage was studied based on the screw theory.
► The terminal constraints exerted to the common joint was given.
► The condition of the mobility of Hoberman's units was discussed.