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Research Papers: Design of Mechanisms and Robotic Systems

Synthesis of Quasi-Constant Transmission Ratio Planar Linkages

[+] Author and Article Information
Giorgio Figliolini

Associate Professor
Department of Civil and Mechanical Engineering,
University of Cassino and Southern Lazio,
Via G. Di Biasio 43,
Cassino (Fr) 03043, Italy
e-mail: figliolini@unicas.it

Ettore Pennestrì

Department of Enterprise Engineering,
University of Rome “Tor Vergata,”
Via del Politecnico 1,
Rome 00133, Italy
e-mail: pennestri@mec.uniroma2.it

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 17, 2014; final manuscript received June 23, 2015; published online August 19, 2015. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 137(10), 102301 (Aug 19, 2015) (12 pages) Paper No: MD-14-1801; doi: 10.1115/1.4031058 History: Received December 17, 2014

The present paper deals with the formulation of novel closed-form algorithms for the kinematic synthesis of quasi-constant transmission ratio planar four-bar and slider–crank linkages. The algorithms are specific for both infinitesimal and finite displacements. In the first case, the approach is based on the use of kinematic loci, such as centrodes, inflection circle, and cubic of stationary curvature, as well as Euler–Savary equation. In the second case, the design equations follow from the application of Chebyshev min–max optimality criterion. These algorithms are aimed to obtain, within a given range of motion, a quasi-constant transmission ratio between the driving and driven links. The numerical examples discussed allow a direct comparison of structural errors for mechanisms designed with different methodologies, such as infinitesimal Burmester theory and the Chebyshev optimality criterion.

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Figures

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Fig. 1

Freudenstein theorem: four-bar linkage

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Fig. 2

Freudenstein theorem: slider–crank mechanism

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Fig. 3

Inflection circle and cubic of stationary curvature

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Fig. 4

Burmester theory: four-bar linkage

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Fig. 5

Burmester theory: four-bar linkage

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Fig. 6

Quasi-constant transmission ratio

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Fig. 7

Burmester theory: slider–crank mechanism

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Fig. 8

Slider–crank mechanism (continuous-line) and its auxiliary mechanism (dashed-line)

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Fig. 9

Burmester theory: slider–crank mechanism

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Fig. 10

Swinging-block circular path generator

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Fig. 11

Chebyshev theory: slider–crank mechanism

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Fig. 12

Chebyshev theory: four-bar linkage for τ > 0, a < 1, and t0 > 0

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Fig. 13

Chebyshev theory: four-bar linkage for τ > 0, a > 1, and t0 < 0

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Fig. 14

Four-bar linkage: quasi-constant transmission ratio

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Fig. 15

Swinging-block straight path generator

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Fig. 16

Slider–crank mechanism: quasi-constant transmission ratio

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Fig. 17

Design chart for slider–crank mechanisms with quasi-constant transmission ratio

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