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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Erdman, A. , Sandor, G. , and Kota, S. , 2001, Mechanism Design: Analysis and Synthesis, 4th ed., Prentice Hall, Upper Saddle River, NJ.
Norton, R. L. , 2012, Design of Machinery, 5th ed., McGraw Hill, New York.
McCarthy, J. M. and Soh, G. S. , 2011, Geometric Design of Linkages (Interdisciplinary Applied Mathematics), 2nd ed., Springer, New York.
Waldron, K. J. , and Kinzel, G. L. , 2004, Kinematics, Dynamics, and Design of Machinery, 2nd ed., Wiley, Hoboken, NJ.
Almandeel, A. , Murray, A. P. , Myszka, D. H. , and Stumph, H. E., III , 2015, “ A Function Generation Synthesis Methodology for All Defect-Free Slider-Crank Solutions for Four Precision Points,” ASME J. Mech. Rob., 7(3), p. 031020. [CrossRef]
Freudenstein, F. , 1954, “ An Analytical Approach to the Design of Four-Link Mechanisms,” Trans. ASME, 76, pp. 483–492.
Erdman, A. , Sandor, G. , and Kota, S. , 1984, Advanced Mechanism Design: Analysis and Synthesis, Vol. 2, Prentice Hall, Englewood Cliffs, NJ.
Freudenstein, F. , 1959, “ Structural Error Analysis in Plane Kinematic Synthesis,” J. Eng. Ind., 81(1), pp. 15–22.
Naik, D. , and Amarnath, C. , 1989, “ Synthesis of Adjustable Four Bar Function Generators Through Five Bar Loop Closure Equations,” Mech. Mach. Theory, 24(6), pp. 523–526. [CrossRef]
McGovern, J. F. , and Sandor, G. N. , 1973, “ Kinematic Synthesis of Adjustable Mechanisms—Part 1: Function Generation,” ASME J. Manuf. Sci. Eng., 95(2), pp. 417–422.
Soong, R.-C. , and Chang, S.-B. , 2011, “ Synthesis of Function-Generation Mechanisms Using Variable Length Driving Links,” Mech. Mach. Theory, 46(11), pp. 1696–1706. [CrossRef]
Subbian, T. , and Flugrad, D. , 1994, “ Six and Seven Position Triad Synthesis Using Continuation Methods,” ASME J. Mech. Des., 116(2), pp. 660–665. [CrossRef]
McLarnan, C. , 1963, “ Synthesis of Six-Link Plane Mechanisms by Numerical Analysis,” ASME J. Manuf. Sci. Eng., 85(1), pp. 5–10.
Dhingra, A. K. , Cheng, J. C. , and Kohli, D. , 1994, “ Synthesis of Six-Link, Slider-Crank and Four-Link Mechanisms for Function, Path and Motion Generation Using Homotopy and m-Homogenization,” ASME J. Mech. Des., 116(4), pp. 1122–1131. [CrossRef]
Dhingra, A. K. , and Mani, N. K. , 1993, “ Finitely and Multiply Separated Synthesis of Link and Geared Mechanisms Using Symbolic Computing,” ASME J. Mech. Des., 115(3), pp. 560–567. [CrossRef]
Al-Dwairi, A. F. , 2009, “ Design of Centric Drag-Link Mechanisms for Delay Generation With Focus on Space Occupation,” ASME J. Mech. Des., 131(1), p. 011015. [CrossRef]
Oleksa, S. A. , and Tesar, D. , 1971, “ Multiply Separated Position Design of the Geared Five-Bar Function Generator,” ASME J. Manuf. Sci. Eng., 93(1), pp. 74–84.
Erdman, A. G. , and Sandor, G. N. , 1971, “ Kinematic Synthesis of a Geared Five-Bar Function Generator,” ASME J. Manuf. Sci. Eng., 93(1), pp. 11–16.
Sultan, I. , and Kalim, A. , 2011, “ On the Kinematics and Synthesis of a Geared Five-Bar Slider-Crank Mechanism,” Proc. Inst. Mech. Eng. C, 225(5), pp. 1253–1261. [CrossRef]
Freudenstein, F. , and Primrose, E. , 1963, “ Geared Five-Bar Motion—Part I: Gear Ratio Minus One,” ASME J. Appl. Mech., 30(2), pp. 161–169. [CrossRef]
Primrose, E. , and Freudenstein, F. , 1963, “ Geared Five-Bar Motion—Part 2: Arbitrary Commensurate Gear Ratio,” ASME J. Appl. Mech., 30(2), pp. 170–175. [CrossRef]
Artobolevskii, I. I. , 1964, Mechanisms for the Generation of Plane Curves, Macmillan, New York.
Lui, Y. , and McCarthy, J. M. , 2016, “ Design of Mechanisms to Trace Plane Curves,” ASME Paper No. DETC2016-59689.
Sutherland, G. , and Roth, B. , 1975, “ An Improved Least-Squares Method for Designing Function-Generating Mechanisms,” ASME J. Manuf. Sci. Eng., 97(1), pp. 303–307.
Chen, F. , and Chan, V.-L. , 1974, “ Dimensional Synthesis of Mechanisms for Function Generation Using Marquardt's Compromise,” ASME J. Manuf. Sci. Eng., 96(1), pp. 131–137.
Sarganachari, S. G. , Math, V. B. , and Ali, S. A. , 2010, “ Synthesis of Planar Six-Bar Mechanism for Function Generation: A Variable Topology Approach,” Int. J. Appl. Eng. Res., 5(3), pp. 471–476.
Shariati, M. , and Norouzi, M. , 2011, “ Optimal Synthesis of Function Generator of Four-Bar Linkages Based on Distribution of Precision Points,” Meccanica, 46(5), pp. 1007–1021. [CrossRef]
Akcali, I. , and Dittrich, G. , 1989, “ Function Generation by Galerkin's Method,” Mach. Mech. Theory, 24(1), pp. 39–43. [CrossRef]
Ting, K.-L. , 1994, “ Mobility Criteria of Geared Five-Bar Linkages,” Mech. Mach. Theory, 29(2), pp. 251–264. [CrossRef]
Murray, A. P. , and Larochelle, P. , 1998, “ A Classification Scheme for Planar 4R, Spherical 4R, and Spatial RCCC Linkages to Facilitate Computer Animation,” ASME Paper No. DETC98/MECH-5887.


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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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