Complex Number Synthesis of Four-Bar Path Generating Mechanisms Adjustable for Multiple Tangential Circular Arcs

Abstract

By combining complex number methods of synthesis [1] with graphical techniques, an adjustable, planar, four-bar path generating mechanism can be synthesized to produce symmetrical coupler curves that conform to a specified radius over a finite range. In this way the earlier works by Tao and Yan [2, 3] can be generalized for use by a large number of mechanism designers. The coupler point of the mechanism will trace any desired number of circular arcs that are tangential at a preselected point with prescribed radii of curvature (positive, negative, or infinite). In this development, components of this mechanism may be chosen freely or under certain parameters by one of three techniques presented here. Also available is an analysis to give coupler link rotation, output crank rotation, and coupler point location as a function of input crank rotation.