Analytical Reason for Smaller Lateral Sway in Angled-Plane Scissor Linkage

Abstract

Scissor linkages are widely used with scissor links arranged in two parallel planes. When small misalignment of revolute joint axes are permissible, the linkage can undergo lateral sway. This paper, using rigid-body kinematics and a modeling of misalignment, converts the task of finding lateral sway into a non-linear constrained optimization problem. Through linearization of the optimization problem, this paper analytically proves that (1) maximum lateral sway increases as the number of units in the parallel-plane scissor linkage increases whereas in angled-plane scissor linkage, the lateral sway tends to a finite limit as the number of units is increased and (2) the lateral sway is independent of connector length in parallel-plane scissor linkage whereas it is dependent on the length of the connector in angled-plane scissor linkage. These results are further substantiated with numerical solution of the non-linear optimization problem. The results imply that the angled-plane scissor linkage can substantially limit lateral sway in comparison to parallel-plane scissor linkage under similar conditions of joint misalignment. The analytical expression derived in this paper helps in identifying the influence of design parameters on lateral sway.