Design of Spherical 4R Mechanisms: Function Generation for the Entire Motion Cycle

Abstract

Spherical 4R mechanisms are studied for which the crank is relatively smaller than the remaining links. The theory of small-crank mechanisms is applied to obtain approximate descriptions for the follower angular displacement in terms of the input crank angle. The follower angle is presumed to comprise a mean and a perturbational motion. This results in an approximate expression in which the follower displacement is given as a linear combination of simple harmonic functions of the first and second harmonics of the crank angle. The approximate equations are utilized for synthesis of spherical 4R mechanisms for function generation. In contrast to the conventional design procedures, the use of the approximate equations allows the synthesis of spherical mechanisms in which a prescribed function is satisfied for the entire motion of the mechanism. In addition to design examples, sample error charts are provided to assist the designer in ascertaining feasible ranges for design and corresponding orders of error.