Configuration analysis of the Schatz linkage

Abstract

This paper investigates different configurations of the Schatz linkage based on the analysis of a reciprocal screw and of the relationship between the reciprocal screw and its stem-screw system, which consists of twists of freedom located at six revolute joints of the linkage. A new method of using cofactors of an augmenting screw is used to obtain the reciprocal screw. The stem-screw system of order 5 of the linkage is developed from the special geometry of the six revolute joints and closed-form displacement solutions are provided based on the stem-screw system. The screw surface representing the trajectory of the reciprocal screw with a chosen pitch is established. This surface is then used to characterize zero-pitch reciprocal screw configurations. The special relationship between the reciprocal screw and the stem-screw system is analysed and used to characterize the constraint wrench and configurations created by the changes of the constraint wrench with a non-zero pitch. Consequently, a set of configurations are presented in conjunction with a ruled surface produced by the progression of the constraint wrench when the linkage drive joint rotates from 5° to 85°.