Kinematic Synthesis of RRSC Mechanisms for Multi-Phase Finite and Multiply Separated Positions

Abstract

This paper presents a new technique for synthesizing RRSC mechanisms to achieve phases of rigid body positions, velocities and accelerations using the same hardware. This work considers two-phase moving pivot problems with constant R-R and C-S link lengths. By specifying the R-R and C-S link joint axes, the constant length condition becomes the only design constraint for these links. The prescribed finite and multiply separated positions are then incorporated in the link constraint equations with respect to the prescribed coordinate frame for each link and the mechanism joint variables and driving link parameters calculated. The rigid body velocities and accelerations were prescribed using instant screw axis (ISA) parameters.

On the synthesis of spatial revolute—revolute—spherical—cylindrical motion generators with prescribed coupler loads

“…Lee et al [4] developed the quadratic input-output relation and the associated mobility condition for the RRSS mechanism. Russell and Sodhi [5] presented an instant screw axis-based synthesis method for the synthesizing RRSC mechanisms to approximate prescribed coupler poses and coupler point velocities and accelerations. Tong and Chang [6] presented the synthesis of four revolute spherical mechanisms via the pole method.…”

“…Equations (3) and (4) are unit vector constraints for the R-R link fixed and moving pivot revolute joint axes. Equations (5) and (6) are constant length constraints for the R-R link. Equation (7) defines the displacement of the coupler link given the x, y, and z components of four arbitrary coupler pose variables p, q, r, and s (where subscripts 1 and j in equation (7) denote the starting and displaced coupler poses, respectively).…”