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Research Papers: Design of Mechanisms and Robotic Systems

Kinematic Synthesis of Rotary Machines Generated by Regular Curve-Polygons

[+] Author and Article Information
Giorgio Figliolini

Associate Professor
DiCEM,
University of Cassino and Southern Lazio,
G. Di Biasio 43,
Cassino 03043, Italy
e-mail: figliolini@unicas.it

Pierluigi Rea

DiCEM,
University of Cassino and Southern Lazio,
G. Di Biasio 43,
Cassino 03043, Italy
e-mail: rea@unicas.it

Salvatore Grande

DiCEM,
University of Cassino and Southern Lazio,
G. Di Biasio 43,
Cassino 03043, Italy
e-mail: salvatore.grande@unicas.it

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 4, 2015; final manuscript received November 17, 2015; published online December 11, 2015. Assoc. Editor: David Myszka.

J. Mech. Des 138(2), 022301 (Dec 11, 2015) (9 pages) Paper No: MD-15-1068; doi: 10.1115/1.4032088 History: Received February 04, 2015; Revised November 17, 2015

The subject of this paper is the kinematic synthesis of volumetric rotary machines, also known as GeRotors (GEnerated ROTORs), which are based on the planetary motion of suitable regular curve-polygons. In particular, the outer and inner conjugate profiles of a generating regular curve-polygon with any number of lobes and different circumcircle and rounded corner radii were synthesized as envelope curves of the polycentric profiles. This also enabled a regular curve-polygon with cusp corners to be obtained, as in the case of the Reuleaux triangle. The proposed formulation was then implemented in a matlab code and validated by means of several significant examples of rotary machines.

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References

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Figures

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Fig. 1

Geometry of a regular curve-polygon (n = 4)

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Fig. 2

Kinematic synthesis of the polycentric profiles

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Fig. 3

Angular limits for the kinematic synthesis of the circular-arc profiles (n = 4)

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Fig. 4

Geometry and angular limits for the kinematic synthesis of the circular-arc profiles (n = 5)

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Fig. 5

Two-lobed curve-polygon with cusp corners

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Fig. 6

Two-lobed curve-polygon with rounded corners

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Fig. 7

Three-lobed curve-polygon with cusp corners

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Fig. 8

Three-lobed curve-polygon with rounded corners

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Fig. 10

Five-lobed curve-polygon with cusp (dotted line) and rounded corners

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Fig. 9

Four-lobed curve-polygon with cusp (dotted line) and rounded corners

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Fig. 11

Planetary motion of a curve-polygon

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Fig. 12

Fixed and moving centrodes

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Fig. 13

Epitrochoids that are traced by the vertices of the inner regular polygon: (a) for RO < Rλ, (b) RO = Rλ, and (c) RO > Rλ

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Fig. 14

Sketch to evaluate the inner and outer envelopes

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Fig. 15

Two-lobed curve-polygon with cusp corners

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Fig. 16

Two-lobed curve-polygon with rounded corners

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Fig. 17

Three-lobed curve-polygon with cusp corners

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Fig. 18

Three-lobed curve-polygon with rounded corners

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Fig. 19

Four-lobed curve-polygon with rounded corners

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Fig. 20

Five-lobed curve-polygon with rounded corners

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