Reducing Structural Error in Function Generating Mechanisms via the Addition of Large Numbers of Four-Bar Mechanisms

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 drag-link (or double crank) 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 that drives 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 is less sinusoid-like. This process can be continued through the addition of more drag-link mechanisms to the device, slowly 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 slider-crank or terminal GFBS. A randomized local search is then conducted as the four-bars are added to minimize the structural error between the desired function and the input-output function of the mechanism. Mechanisms have been “grown” in this fashion to dozens of links that are capable of closely producing functions with a variety of intriguing features.