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.

References

References
1.
Hill
,
M. F.
,
1927
,
Kinematics of Gerotors
,
The Peter Reilly Company
,
Philadelphia, PA
.
2.
Giacosa
,
D.
,
2000
,
Motori Endotermici
, Hoepli,
Milan, Italy
.
3.
Beard
,
J. E.
,
Yannitell
,
D. W.
, and
Pennock
,
G. R.
,
1992
, “
The Effects of the Generation Pin Size and Placement on the Curvature and Displacement of Epitrochoidal Gerotors
,”
Mech. Mach. Theory
,
27
(
4
), pp.
373
389
.
4.
Gamez-Montero
,
P. J.
,
Castilla
,
R.
,
Khamashta
,
M.
, and
Codina
,
E.
,
2006
, “
Contact Problems of a Trochoidal-Gear Pump
,”
Int. J. Mech. Sci.
,
48
(
12
), pp.
1471
1480
.
5.
Mimmi
,
G.
, and
Bonandrini
,
G.
,
2006
, “
On Design and Performance of Internal Epitrochoidal Pumps
,”
ASME
Paper No. DETC2006-99487.
6.
Bonandrini
,
G.
,
Mimmi
,
G.
, and
Rottenbacher
,
C.
,
2010
, “
Theoretical Analysis of an Original Rotary Machine
,”
ASME J. Mech. Des.
,
132
(
2
), p.
024501
.
7.
Chen
,
B.
,
Zhong
,
H.
,
Liu
,
J.
,
Li
,
C.
, and
Fang
,
T.
,
2012
, “
Generation and Investigation of a New Cycloid Drive With Double Contact
,”
Mech. Mach. Theory
,
49
(
3
), pp.
270
283
.
8.
Bonandrini
,
G.
,
Mimmi
,
G.
, and
Rottenbacher
,
C.
,
2012
, “
Design and Simulation of Meshing of a Particular Internal Rotary Pump
,”
Mech. Mach. Theory
,
49
(
3
), pp.
104
116
.
9.
Tong
,
S.
, and
Yang
,
D. C. H.
,
2000
, “
On the Generation of New Lobe Pumps for Higher Pumping Flowrate
,”
Mech. Mach. Theory
,
35
(
7
), pp.
997
1012
.
10.
Yan
,
J.
,
Yang
,
D. C. H.
, and
Tong
,
S.
,
2008
, “
On the Generation of Analytical Noncircular Multilobe Internal Pitch Curves
,”
ASME J. Mech. Des.
,
130
(
7
), p.
092601
.
11.
Colbourne
,
J. R.
,
1974
, “
The Geometry of Trochoid Envelopes and Their Application in Rotary Pumps
,”
Mech. Mach. Theory
,
9
(
3–4
), pp.
421
435
.
12.
Maiti
,
R.
, and
Sinha
,
L.
,
1988
, “
Kinematics of Active Contact in Modified Epitrochoid Generated Rotary Piston Machines
,”
Mech. Mach. Theory
,
23
(
1
), pp.
39
45
.
13.
Shung
,
J. B.
, and
Pennock
,
G. R.
,
1994
, “
Geometry for Trochoidal-Type Machines With Conjugate Envelopes
,”
Mech. Mach. Theory
,
29
(
1
), pp.
25
42
.
14.
Litvin
,
F. L.
, and
Feng
,
P.-H.
,
1996
, “
Computerized Design and Generation of Cycloidal Gearings
,”
Mech. Mach. Theory
,
31
(
7
), pp.
891
911
.
15.
Demenego
,
A.
,
Vecchiato
,
D.
,
Litvin
,
F. L.
,
Nervegna
,
N.
, and
Mancò
,
S.
,
2002
, “
Design and Simulation of Meshing of a Cycloidal Pump
,”
Mech. Mach. Theory
,
37
(
3
), pp.
311
332
.
16.
Ivanovic
,
L.
, and
Josifovic
,
D.
,
2006
, “
Specific Sliding of Trochoidal Gearing Profile in the Gerotor Pumps
,”
FME Trans.
,
34
(
3
), pp.
121
127
.
17.
Bonandrini
,
G.
,
Mimmi
,
G.
, and
Rottenbacher
,
C.
,
2009
, “
Theoretical Analysis of Internal Epitrochoidal and Hypotrochoidal Machines
,”
Proc. Inst. Mech. Eng., Part C
,
223
(
6
), pp.
1469
1480
.
18.
Tong
,
S.-H.
,
Yan
,
J.
, and
Yang
,
D. C. H.
,
2009
, “
Design and Deviation-Function Based Gerotors
,”
Mech. Mach. Theory
,
44
(
8
), pp.
1595
1606
.
19.
Wang
,
P. Y.
,
Fong
,
Z. H.
, and
Fang
,
H. S.
,
2002
, “
Design Constraints of Five-Arc Roots Vacuum Pumps
,”
Proc. Inst. Mech. Eng., Part C
,
216
(
2
), pp.
225
234
.
20.
Kang
,
Y. H.
, and
Vu
,
H. H.
,
2014
, “
A Newly Developed Rotor Profile for Lobe Pumps: Generation and Numerical Performance Assessment
,”
J. Mech. Sci. Technol.
,
28
(
3
), pp.
915
926
.
21.
Hsieh
,
C. F.
,
Hwang
,
Y. W.
, and
Fong
,
Z. H.
,
2008
, “
Study on the Tooth Profile for the Screw Claw Type Pump
,”
Mech. Mach. Theory
,
43
(
7
), pp.
812
828
.
22.
Hwang
,
Y. W.
, and
Hsieh
,
C. F.
,
2006
, “
Geometry Design and Analysis for Trochoidal-Type Speed Reducers: With Conjugate Envelopes
,”
Trans. Can. Soc. Mech. Eng.
,
30
(
2
), pp.
261
278
.
23.
Hwang
,
Y. W.
, and
Hsieh
,
C. F.
,
2007
, “
Determination of Surface Singularities of a Cycloidal Gear Drive With Inner Meshing
,”
Math. Comput. Model.
,
45
(
4
), pp.
340
354
.
24.
Hwang
,
Y. W.
, and
Hsieh
,
C. F.
,
2007
, “
Geometric Design Using Hypotrochoid and Non-Undercutting Conditions for an Internal Cycloidal Gear
,”
ASME J. Mech. Des.
,
129
(
4
), pp.
413
420
.
25.
Figliolini
,
G.
,
Rea
,
P.
, and
Angeles
,
J.
,
2006
, “
The Pure-Rolling Cam-Equivalent of the Geneva Mechanism
,”
Mech. Mach. Theory
,
41
(
11
), pp.
1320
1335
.
26.
Figliolini
,
G.
, and
Angeles
,
J.
,
2003
, “
The Synthesis of Elliptical Gears Generated by Shaper-Cutters
,”
ASME J. Mech. Des.
,
125
(
4
), pp.
793
801
.
27.
Figliolini
,
G.
,
Stachel
,
H.
, and
Angeles
,
J.
,
2015
, “
The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes
,”
ASME J. Mech. Rob.
,
7
(
1
), p.
011003
.
28.
Figliolini
,
G.
,
Conte
,
M.
, and
Rea
,
P.
,
2012
, “
Algebraic Algorithm for the Kinematic Analysis of Slider-Crank/Rocker Mechanisms
,”
ASME J. Mech. Rob.
,
4
(
1
), p.
011003
.
29.
Figliolini
,
G.
,
Rea
,
P.
, and
Angeles
,
J.
,
2015
, “
The Synthesis of the Axodes of the RCCC Linkages
,”
ASME J. Mech. Rob.
,
8
(
2
), p.
021011
.
30.
Litvin
,
F. L.
,
1989
,
Theory of Gearing
, Washington, DC, NASA RP-1212, AVSCOM Technical Report 88-C-C035, pp.
83
86
.
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