Determin0ation of envelope to family of planar parametric curves and envelope singularities

Computer Methods in Applied Mechanics and Engineering

Volumn 175, Issue 1-2, 1999, Pages 175-187

  Argyris, John ^a   Litvin, Faydor L ^a   Lian, Qiming ^a   Lagutin, Sergey A ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; GEAR MANUFACTURE; GRAPH THEORY; MATRIX ALGEBRA; REGRESSION ANALYSIS; VECTORS;

ENVELOPE SINGULARITY; PLANAR PARAMETRIC CURVES; ROOT BLOWERS;

COMPUTATIONAL METHODS;

EID: 0032627785     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00367-3     Document Type: Article

References (12)

1. [1] J. Favard, Course of Local Differential Geometry (Gauthier-Villars, Paris, 1957) (in French, translated into Russian).
2. [2] G.A. Korn and T.M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd edition (McGraw-Hill, NY, 1968).
3. [3] F.L. Litvin, Theory of Gearing, 2nd edition (Nauka, Moscow, 1968) (in Russian).
4. [4] F.L. Litvin, Determination of envelopes to lines of contact for mutually enveloping surfaces, Proceedings of Universities. Mathematics, No. 10(161) (1975) 47-50 (in Russian).
5. [5] F.L. Litvin, Theory of gearing, NASA Reference Publication 1212, 1988.
6. [6] F.L. Litvin, Gear Geometry and Applied Theory (Prentice Hall, 1994).
7. [7] F.L. Litvin, Development of gear technology and theory of gearing, NASA Reference Publication 1406, 1998.
8. [8] F.L. Litvin, A.M. Egelja and M. De Donno, Computerized determination of singularities and envelopes to families of contact lines on gear tooth surfaces, Comput. Methods Appl. Mech. Engrg. 158 (1998) 23-34.
9. [9] F.L. Litvin and P.H. Feng, Computerized design and generation of cycloidal gearings, Mech. Math. Theory 31(7) (1996) 891-991.
10. [10] J.J. Stoker, Differential Geometry (Wiley-Interscience, a Division of John Wiley & Sons, 1969).
11. [11] V.A. Zalgaller, Theory of Envelopes (Publishing House Nauka, Moscow, 1975) (in Russian).
12. [12] V.A. Zalgaller and F.L. Litvin, Sufficient condition of existence of envelope to contact lines and edge of regression on the surface of the envelope to the parametric family of surfaces, Proceedings of Universities: Mathematics, No. 3(178) (1977) 20-23 (in Russian).