0
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

## Abstract

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.

<>

## Figures

Fig. 1

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

Fig. 2

Kinematic synthesis of the polycentric profiles

Fig. 3

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

Fig. 4

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

Fig. 5

Two-lobed curve-polygon with cusp corners

Fig. 6

Two-lobed curve-polygon with rounded corners

Fig. 7

Three-lobed curve-polygon with cusp corners

Fig. 8

Three-lobed curve-polygon with rounded corners

Fig. 10

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

Fig. 9

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

Fig. 11

Planetary motion of a curve-polygon

Fig. 12

Fixed and moving centrodes

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

Fig. 14

Sketch to evaluate the inner and outer envelopes

Fig. 15

Two-lobed curve-polygon with cusp corners

Fig. 16

Two-lobed curve-polygon with rounded corners

Fig. 17

Three-lobed curve-polygon with cusp corners

Fig. 18

Three-lobed curve-polygon with rounded corners

Fig. 19

Four-lobed curve-polygon with rounded corners

Fig. 20

Five-lobed curve-polygon with rounded corners

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections