This paper presents a method for defining the relationship between the angular coordinates of N-lobe noncircular gear wheels using Bézier and B-spline nonparametric curves. After designing the displacement law, conjugate pitch curves are obtained using an analytical method that takes the driver angular coordinate as an input variable. With N-lobe noncircular gears, the number of speed cycles per revolution can be increased. In addition, N-lobe noncircular gears are well balanced because they rotate around their geometric center. Bézier nonparametric curves and B-spline nonparametric curves are used to obtain the displacement laws of an N-lobe noncircular gear. Using these functions, an N-lobe noncircular gear that satisfies a given relationship between the rotation angles of the driving and driven wheels can be designed or a given transmission ratio can be obtained.

1.
Doege
,
E.
,
Meinen
,
J.
,
Nuemaier
,
T.
, and
Schaprian
,
M.
, 2001, “
Numerical Design of a New Forging Press Drive Incorporating Noncircular Gears
,”
Proc. Inst. Mech. Eng., Part B
0954-4054,
215
(
4
), pp.
465
471
.
2.
Dooner
,
D. B.
, 1997, “
Use of Noncircular Gears to Reduce Torque and Speed Fluctuations in Rotating Shafts
,”
J. Mech. Des.
1050-0472,
119
(
2
), pp.
299
306
.
3.
Yao
,
Y. A.
, and
Yan
,
H. S.
, 2003, “
A New Method for Torque Balancing of Planar Linkages Using Non-Circular Gears
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
217
(
5
), pp.
495
502
.
4.
Fam
,
Y. L.
,
Sang
,
C. M.
, and
Nan
,
J. J.
, 1994, “
Concurrent Mechanism and Control Design for the Slewing of Flexible Space Structures
,”
J. Mech. Des.
1050-0472,
116
(
3
), pp.
944
951
.
5.
Han
,
P. S.
,
Thomlinson
,
M. A.
, and
Tu
,
Y. S.
, 1991, “
Kinematics and Kinetics of a Noncircular Bicycle Drive System
,”
Mech. Mach. Theory
0094-114X,
26
(
4
), pp.
375
388
.
6.
Dooner
,
D. B.
, 1997, “
A Geared 2 DOF Mechanical Function Generator
,”
J. Mech. Des.
1050-0472,
121
(
3
), pp.
65
70
.
7.
Librovich
,
B. V.
, 2003, “
Dynamics of Rotary Vane Engine
,”
J. Mech. Des.
1050-0472,
125
(
3
), pp.
498
508
.
8.
Voelkner
,
W.
, 2000, “
Present and Future Developments of Metal Forming: Selected Examples
,”
J. Mater. Process. Technol.
0924-0136,
106
, pp.
236
242
.
9.
Vanegas
,
L. U.
,
Abdel
,
M. M.
, and
Parker
,
G. A.
, 2006, “
Design of Noncircular Gears to Minimise Shaft Accelerations
,” 8th Biennial ASME Conference on Engineering Systems Design and Analysis,
Proceedings of ESDA2006
, Torino, Italy, ASME Paper No. ESDA2006-95560.
10.
Litvin
,
F. L.
, 1994,
Gear Geometry and Applied Theory
,
Prentice Hall Inc
, Englewood Cliffs, NJ.
11.
Dooner
,
D. B.
, 1998, “
The Synthesis of Noncircular Gear Incorporating Involute Profiles
,” MS thesis, University of Florida, Gainesville, FL.
12.
Chang
,
S. L.
, and
Tsay
,
C. B.
, 1998, “
Computerized Tooth Profile Generation and Undercut Analysis of Noncircular Gears Manufactured with Shaper Cutters
,”
J. Mech. Des.
1050-0472,
120
(
1
), pp.
92
99
.
13.
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
.
14.
Bair
,
B. W.
, 2002, “
Computer Aided Design of Elliptical Gears
,”
J. Mech. Des.
1050-0472,
124
(
4
), pp.
787
793
.
15.
Bair
,
B. W.
, 2002, “
Computerized Tooth Profile Generation of Elliptical Gears Manufactured by Shaper Cutters
,”
J. Mater. Process. Technol.
0924-0136,
122
(
2-3
), pp.
139
147
.
16.
Bair
,
B. W.
, 2004, “
Computer Aided Design of Elliptical Gears With Circular-Arc Teeth
,”
Mech. Mach. Theory
0094-114X,
39
(
2
), pp.
153
168
.
17.
Danieli
,
G. A.
, 2000, “
Analytical Description of Meshing of Constant Pressure Angle Teeth Profiles on a Variable Radius Gear and its Applications
,”
J. Mech. Des.
1050-0472,
122
(
1
), pp.
123
128
.
18.
Danieli
,
G. A.
, and
Mundo
,
D.
, 2005, “
New Developments in the Theory of Variable Radius Gear With Constant Pressure Angle
,”
Mech. Mach. Theory
0094-114X,
40
(
2
), pp.
203
217
.
19.
Figliolini
,
G.
, and
Angeles
,
J.
, 2003, “
The Synthesis of Elliptical Gears Generated by Shaper-Cutters
,”
J. Mech. Des.
1050-0472,
125
(
4
), pp.
793
801
.
20.
Figliolini
,
G.
, and
Angeles
,
J.
, 2005, “
Synthesis of the Base Curve of N-Lobe Elliptical Gears
,”
J. Mech. Des.
1050-0472,
127
(
5
), pp.
997
1005
.
21.
Tong
,
S. H.
, and
Yang
,
D. C. H.
, 1998, “
Generation of Identical Noncircular Pitch Curves
,”
J. Mech. Des.
1050-0472,
120
(
2
), pp.
337
341
.
22.
Quintero
,
H. F.
,
Cardona
,
S.
, and
Jordi
,
L.
, 2004, “
Estudio sobre las leyes de desplazamiento en los engranajes no circulares
,”
Rev. Sci. Tech.
0253-1933,
24
, pp.
145
150
.
23.
Quintero
,
H. F.
,
Cardona
,
S.
, and
Jordi
,
L.
, 2004, “
Comparative Study of Some Angular Displacement Law for Noncircular Gears
,”
TMT 2004
, Boznia and Herzegovina, pp.
463
466
.
24.
Cardona
,
S.
, and
Clos
,
D.
, 2001,
Teoría de Mecanismos
,
Ediciones UPC
, Barcelona, Spain.
25.
Rogers
,
D. F.
, and
Adams
,
J. A.
, 1976,
Mathematical Elements for Computer Graphics
,
McGraw Hill
, New York.
26.
Ting
,
K.
,
Lee
,
N. L.
, and
Brandan
,
G. H.
, 1994, “
Synthesis of Polynomial and Other Curves With the Bezier Technique
,”
Mech. Mach. Theory
0094-114X,
29
(
6
), pp.
887
903
.
27.
Reyes
,
G.
, 2000, “
Técnicas de diseño geométrico asistido por ordenador para mecanismos levapalpador
,” Ph.D. thesis, Universidad Politécnica de Cataluña, Barcelona, Spain.
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