The base circle of a circular gear is concentric with the pitch circle and tangent to the action line. However, in a noncircular gear the base curve is not known a priori and not easy to determine. In this study, the base curves of noncircular gear wheels are obtained as the geometrical locus of the singular points on the involute tooth profile. Singular points—points from which a second involute branch begins to form on the tooth profile—restrict the allowable tooth height and allow the minimum number of teeth required to be estimated. We discuss the influence of the curvature radius of the pitch curve on the allowable tooth height and present an example to illustrate the proposed method.

Issue Section:
Research Papers
Keywords:
gears, wheels, design engineering, geometry, noncircular gear, singular points, base curves, allowable tooth height
Topics:
Gears, Wheels
1.
Kuczewski
,
M.
, 1988, “
Designing Elliptical Gears
,”
Mach. Des.
0024-9114,
60
(
7
), pp.
116
–
118
.
2.
Olsson
,
U.
, 1953, “
Non-Circular Cylindrical Gears
,”
Acta Polytech. Scand., Mech. Eng. Ser.
0001-687X,
2
(
10
), pp.
1
–
217
.
3.
Lozzi
,
A.
, 2000, “
Non-Circular Gears Graphic Generation of Involutes and Base Outlines
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
214
(
4
), pp.
411
–
422
.
4.
Litvin
,
F. L.
, 1994,
Gear Geometry and Applied Theory
,
Prentice Hall
,
Englewood Cliffs, NJ
.
5.
Wu
,
L. I.
, and
Chang
,
S. L.
, 1995, “
Base Curves and Tooth Profiles of Involute Elliptical Gears
,”
J. Chin. Soc. Mech. Eng.
0257-9731,
16
(
2
), pp.
133
–
140
.
6.
Dooner
,
D. B.
, 1988, “
The Synthesis of Non-Circular Gears Incorporating Involute Profiles
,” Master’s thesis, Florida University.
7.
Figliolini
,
G.
, and
Angeles
,
J.
, 2003, “
The Synthesis of Elliptical Gears Generated by Shaper-Cutters
,”
ASME J. Mech. Des.
1050-0472,
125
(
4
), pp.
793
–
801
.
Crossref
Search ADS
 
8.
Figliolini
,
G.
, and
Angeles
,
J.
, 2005, “
Synthesis of Elliptical Gears Generated by Shaper-Cutters
,”
ASME J. Mech. Des.
1050-0472,
127
(
5
), pp.
997
–
1005
.
Crossref
Search ADS
 
9.
Dooner
,
D. B.
, and
Seireg
,
A. A.
, 1995,
The Kinematic Geometric of Gearing: A Concurrent Engineering Approach
,
Wiley
,
New York
.
10.
Quintero
,
H. F.
,
Cardona
,
S.
, and
Jordi
,
L.
, 2004, “
Estudio de la Curva Base en los Engranajes No-Circulares
,”
An. Ing. Mec.
,
15
(
3
), pp.
1705
–
1710
.
11.
Chang
,
S. L.
, and
Tsay
,
C. B.
, 1998, “
Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured With Shaper Cutters
,”
ASME J. Mech. Des.
1050-0472,
120
(
1
), pp.
92
–
99
.
Crossref
Search ADS
 
12.
Chang
,
S. L.
,
Tsay
,
C. B.
, and
Wu
,
L. I.
, 1996, “
Mathematical Model and Undercutting Analysis of Elliptical Gears Generated by Rack Cutters
,”
Mech. Mach. Theory
0094-114X,
31
(
7
), pp.
879
–
890
.
Crossref
Search ADS
 
13.
Bair
,
B. W.
, 2002, “
Computer Aided Design of Elliptical Gears
,”
ASME J. Mech. Des.
1050-0472,
124
(
4
), pp.
787
–
793
.
Crossref
Search ADS
 
14.
Bair
,
B. W.
, 2004, “
Computer Aided Design of Elliptical Gears With Circular-Arc Teeth
,”
Mech. Mach. Theory
0094-114X,
39
(
2
), pp.
153
–
168
.
Crossref
Search ADS
 
15.
Danieli
,
G. A.
, 2000, “
Analytical Description of Meshing of Constant Pressure Angle Teeth Profiles on a Variables Radius Gear and Its Applications
,”
ASME J. Mech. Des.
1050-0472,
122
(
1
), pp.
123
–
129
.
Crossref
Search ADS
 
16.
Cardona
,
S.
, and
Jordi
,
L.
, 2003, “
Aportación al Estudio de los Engranajes No-Circulares
,”
VI Congreso Iberoamericano de Ingeniería Mecánica
, Coimbra, Portugal, pp.
1291
–
1296
.
17.
Kreyszig
,
E.
, 2000,
Matemáticas Avanzadas Para Ingeniería
,
Editorial Limusa
,
México
.
18.
Quintero
,
H. F.
,
Cardona
,
S.
, and
Jordi
,
L.
, 2004, “
Leyes de Desplazamiento en los Engranajes No-Circulares
,”
Rev. Sci. Tech.
0253-1933,
25
, pp.
145
–
150
.
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 by American Society of Mechanical Engineers
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