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Research Papers

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

[+] Author and Article Information
Hessein Ali

Department of Mechanical and
Aerospace Engineering,
University of Dayton,
Dayton, OH 45469
e-mail: ashourh1@udayton.edu

Andrew P. Murray, David H. Myszka

Department of Mechanical and
Aerospace Engineering,
University of Dayton,
Dayton, OH 45469

1Corresponding author.

Manuscript received March 21, 2016; final manuscript received January 22, 2017; published online March 20, 2017. Assoc. Editor: Philippe Wenger.

J. Mechanisms Robotics 9(3), 031002 (Mar 20, 2017) (8 pages) Paper No: JMR-16-1077; doi: 10.1115/1.4035985 History: Received March 21, 2016; Revised January 22, 2017

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 slider-crank 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.

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Figures

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Fig. 1

The vector loop of the offset slider-crank mechanism

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Fig. 2

The vector loop of the geared five-bar mechanism with a connecting rod and a sliding output

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Fig. 3

The vector loop of the drag-link mechanism

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Fig. 6

The desired function, the slider-crank output, and the curve generated using the proposed method resulting in the addition of nine drag-link mechanisms

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Fig. 7

A slider-crank driven by nine drag-link mechanisms to produce the desired function shown in Fig. 6

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Fig. 8

The desired function and the input–output functions generated for several GFBS cases

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Fig. 9

The desired function having four maxima using a gear ratio of −4:1

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Fig. 10

The desired function having four maxima using a gear ratio of −5:1. The arrow emphasizes the additional extreme due to the selected gear ratio.

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Fig. 11

(a) The desired piecewise-linear periodic function using the terminal slider-crank. (b) The desired piecewise-linear periodic function using the terminal GFBS. (c) A periodic function with two maxima. (d) Ten maxima periodic function.

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