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TECHNICAL PAPERS

The Synthesis of Elliptical Gears Generated by Shaper-Cutters

[+] Author and Article Information
Giorgio Figliolini

DiMSAT, University of Cassino, G. Di Biasio 43, 03043 Cassino (Fr), ITALYe-mail: figliolini@unicas.it

Jorge Angeles

Dept. of Mechanical Engineering & CIM, McGill University, 817 Sherbrooke St., Montreal, Quebec H3A 2K6, Canadae-mail: angeles@cim.mcgill.ca

J. Mech. Des 125(4), 793-801 (Jan 22, 2004) (9 pages) doi:10.1115/1.1631573 History: Received May 01, 2002; Revised April 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
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References

Bloomfield,  B., 1960, “Noncircular Gears,” J. Product Engineering, 31, March 14, pp. 59–66.
Chironis, N. P., 1965, Mechanisms, Linkages, and Mechanical Controls, McGraw-Hill, New York, pp. 241–245.
Rappaport,  S., 1960, “Elliptical Gears for Cyclic Speed Variations,” J. Product Engineering, March 28, pp. 68–70.
Emura,  T., and Arakawa,  A., 1992, “A New Steering Mechanism Using Noncircular Gears,” JSME Int. J., Ser. III, 35(4), pp. 604–610.
Dooner,  D. B., 1997, “Use of Noncircular Gears to Reduce Torque and Speed Fluctuations in Rotating Shafts,” ASME J. Mech. Des., 119, pp. 299–306.
Cunningham,  F. E., and Cunningham,  D. S., 1973, “Rediscovering the Noncircular Gear,” J. Machine Design,November 1, pp. 80–85.
Figliolini,  G., Lanni,  C., and Ceccarelli,  M., 2000, “On the Kinematic Synthesis of Noncircular Gears,” Int. J. of Gearing and Transmissions,3, pp. 90–98.
Tong, S., and Yang, C. H., 1998, “On the Generation of Identical Noncircular Pitch Curves,” DETC98/MECH-5829, 25th ASME Biennial Mechanisms Conference, Atlanta.
Grant, B. G., 1958, A Treatise on Gear Wheels, Philadelphia GEAR Works Inc., Philadelphia, pp. 67–83.
Litvin, F. L., 1989, Theory of Gearing, NASA Reference Publication 1212, US Army Aviation Systems Command—Technical Report 88-C-035, Washington.
Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice Hall, Englewood Cliffs, New Jersey, pp. 346–381, Chap. 12.
Mac Cord, C. W., 1889, Kinematics, John Wiley & Sons., New York, pp. 223–231, Chap. 11.
Olsson, U., 1953, Noncircular Cylindrical Gears, Acta Polytechnica, Mechanical Engineering Series, Stockholm, pp. 125–163, Chap. 6.
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., 120, pp. 92–99.
Chang,  S. L., and Tsay,  C. B., 1995, “Mathematical Model of the Elliptical Gear Generated by Shapers,” J. Chinese Society of Mechanical Engineers,16(5), pp. 415–423.
Bair,  B. W., 2002, “Computerized Tooth Profile Generation of Elliptical Gears Manufactured by Shaper-Cutter,” J. Mater. Process. Technol., 122, pp. 139–147.
Migliozzi, P., 2000, “Sintesi Cinematica di Ruote Dentate Ellittiche,” University of Cassino, Cassino. (in Italian)
Wu, X., Wang, S., Wang, G., and Yang, A., 1991, “Noncircular Gear CAD/CAM Technology,” Eighth IFToMM World Congress on the Theory of Machines and Mechanisms, Prague, pp. 391–394.
Dooner, D. B., and Seireg, A. A., 1999, “An Interactive Approach to the Integrated Design and Manufacture of Gear Pairs,” 4th World Congress on Gearing and Power Transmission, Paris, 1 , pp. 317–322.
Figliolini, G., and Angeles, J., 1999, “On the Geometry of the Kinematic Synthesis of Spatial Gears With Skew Axes,” 31 , XIV AIMETA National Conference of the Italian Society of Theoretical and Applied Mechanics, Como.
González-Palacios,  M., and Angeles,  J., 1999, “The Design of a Novel Mechanical Transmission for Speed Reduction,” ASME J. Mech. Des., 121(4), pp. 538–551.
González-Palacios, M., and Angeles, J., 2000, “The Novel Design of a Pure-Rolling Transmission to Convert Rotational Into Translational Motion,” DETC00/MECH-14166, 26th ASME Biennial Mechanisms Conference, Baltimore.

Figures

Grahic Jump Location
Pitch curves of the elliptical gears and their rack
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Pitch curves and their evolute for rA=200 mm and n1=2: a) convex profile for rB=150 mm; b) convex profile for rB=100 mm; c) concave profile for rB=50 mm and n1=2; d) rack for the same parameters as c)
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Pitch curves and their evolute for rA=200 mm and n1=3: a) convex profile for rB=180 mm; b) convex profile for rB=155.55 mm; c) concave profile for rB=100 mm and n1=3; d) rack for the same parameters as c)
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Geometric model of the shaper-cutter
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Pure-rolling motion of the pitch circle PS of the shaper-cutter on the pitch curve P1 the pinion 1
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Elliptical gears for n1=n2=1,N1=N2=31,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20: a) α1=0 deg; b) α1=45 deg; c) α1=90 deg. The code produces: C=66 mm,m=2.07 mm,L1=L2=201.46 mm and: a) α2=0 deg; b) α2=−79.28 deg; c) α2=−126.87 deg.
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Prototype of the elliptical pair of gears of Fig. 6: a) α1=0 deg; b) α1=45 deg; c) α1=90 deg
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Elliptical gears for n1=1,n2=2,N1=31,N2=62,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−34.93 deg, c=96.19 mm,m=2.07 mm,L1=201.46 mm,L2=402.92 mm.
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Elliptical gears for n1=1,n2=3,N1=31,N2=93,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−22.25 deg, c=126.98 mm,m=2.07 mm,L1=201.46 mm,L2=604.38 mm.
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Elliptical gears for n1=1,n2=4,N1=31,N2=124,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−16.31 deg, c=157.94 mm,m=2.07 mm,L1=201.46 mm,L2=805.84 mm.
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Elliptical pinion-rack for n1=1,N1=31,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code yields Yr*=22.54 mm and m=2.07 mm.
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Elliptical pinion-rack for n1=3,N1=93,rA=44 mm,rB=22 mm, ϕ=20 deg, Ns=20,α1=30 deg. The code yields Yr*=19.81 mm and m=0.83 mm.
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Zoom-in of the elliptical pinion-rack of Fig. 12
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Elliptical gears for n1=2,n2=3,N1=62,N2=93,rA=74 mm,rB=52 mm, ϕ=20 deg, Ns=20,α1=45 deg. The code produces: α2=−35.54 deg, c=156.70 mm,m=2.06 mm,L1=401.74 mm,L2=602.61 mm.
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Tooth profiles of elliptical gears for n1=1,N1=15,rA=44 mm,rB=22 mm, ϕ=10 deg, Ns=20 (undercutting)
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Tooth profiles of elliptical gears for n1=1,N1=15,rA=44 mm,rB=22 mm, ϕ=40 deg, Ns=20 (overcutting)

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