A Closed-Form Solution of Spatial Sliders for Rigid-Body Guidance

Abstract

This paper presents a closed-form solution to the four-position synthesis problem by using a spatial slider, which is a spatial dyad of two perpendicularly intersected cylindrical joints. We utilize the dialytic elimination method to simplify the synthesis equations and to obtain a univariate ninth degree polynomial equation. Among the nine sets of solutions, two of them are infinite, and one is the displacement screw from the first position to the second position. Therefore, we have at most six real solutions that can be used to design spatial sliders for the four-position synthesis problem. A numerical example is provided in to demonstrate the validity of the solution procedure.