Optimization of parameters for specified path generation using an atlas of coupler curves of geared five-bar linkages

Abstract

An atlas containing 732 coupler curves traced by the symmetric geared five-bar linkage has been drawn by the authors. Gear ratios of +1, −1, +2, −2, have been used. The data are presented either six or twelve curves to a page, arranged in axonometric projection to illustrate the envelope of a family of curves of that particular linkage geometry as the gearset phase angle isvaried. Dots on the curve represent uniform intervals of input crank angular displacement in order to provide coupler point velocity information. Other curves for parameters lying between those illustrated can be visually interpolated. Optimization techniques can be applied to modify the geometrics of a linkage parameters selected from the atlas as an approximate solution to the path motion desired. The origincurves are drawn on 11 × 17 sheets in four colors with a Benson-Varian xy plotter. Optimization algorithms are then used in conjunction with the atlas of linkage coupler curves to refine an initial selection of a desired motion path to achieve a particular motion with minimum deviation. The geared five-bar linkage is used as an example and a straight line generator is designed with less than 1% position error.