Mobility analysis of generalized angulated scissor-like elements with the reciprocal screw theory

• The kinematics of every angulated link was studied based on the screw theory.
• The terminal constraints exerted to the common joint were given.
• The mobility of two types of GAEs was discussed.

This paper deals with the planar closed loop linkage consisting of a series of scissor-like elements connected by revolute joints. Because every generalized angulated element (GAE) 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 GAE are individually movable with a single degree of freedom. The mobility of two types of GAEs was investigated with the method based on the screw theory. It has been proven that both types of GAEs are movable because the terminal constraints exerted to the common joint by the two linkages are equal.