The Synthesis of Function Generating Mechanisms for Periodic Curves Using Large Numbers of Double-Crank Linkages

Abstract

This paper presents a methodology for synthesizing planar linkages to approximate any prescribed periodic function. The mechanisms selected for this task are the slider-crank and the geared five-bar with connecting rod and sliding output (GFBS), where any number of double-crank (or drag-link) four-bars are used as drivers. A slider-crank mechanism, when comparing the input crank rotation to the output slider displacement, produces a sinusoid-like function. Instead of directly driving the input crank, a drag-link four-bar may be added to drive the crank from its output via a rigid connection between the two. Driving the input of the added four-bar results in a function that modifies the sinusoid-like curve. This process can be continued through the addition of more drag-link mechanisms to the device, progressively altering the curve toward any periodic function with a single maximum. For periodic functions with multiple maxima, a GFBS is used as the terminal linkage added to the chain of drag-link mechanisms. The synthesis process starts by analyzing one period of the function to design either the terminal slidercrank or terminal GFBS. MATLAB’s fmincon command is then utilized as the four-bars are added to reduce the structural error between the desired function and the input–output function of the mechanism. Mechanisms have been synthesized in this fashion to include a large number of links that are capable of closely producing functions with a variety of intriguing features