Hessein Ashour



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This research 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.

Publication Date


Project Designation

Graduate Research

Primary Advisor

Andrew P. Murray, David H. Myszka

Primary Advisor's Department

Mechanical and Aerospace Engineering


Stander Symposium project


Arts and Humanities | Business | Education | Engineering | Life Sciences | Medicine and Health Sciences | Physical Sciences and Mathematics | Social and Behavioral Sciences

Reducing Structural Error in Function Generating Mechanisms via the Addition of Large Numbers of Double-Crank Linkages