A Triangular Nomogram for Spherical Symmetric Coupler Curves and its Application to Mechanism Design

Abstract

This paper presents a triangular nomogram for spherical symmetric coupler curves generated by a spherical crank-rocker with special dimensions. The paper also illustrates the application of this nomogram for spherical mechanism design. The expression of symmetric coupler curves traced by the spherical crank-rocker is derived. A computer program is developed to calculate the coordinates of the coupler curve points for the prescribed dimensions of the mechanism. According to the classified properties of coupler curves obtained, a triangular nomogram for spherical symmetric coupler curves can then be constructed by using three design parameters, i.e., length of crank, length of fixed link, and coupler angle. The triangular nomogram provides an alternative selection for dimensional synthesis of spherical path generators. The synthesized mechanisms can also be used to provide initial estimates for optimal synthesis of spherical path generators. A design example is presented.