Differential-geometric structures defining higher order contact transformations

2011 ◽  
Vol 55 (9) ◽  
pp. 58-75
Author(s):  
A. K. Rybnikov
Keyword(s):  
Higher Order ◽  
Geometric Structures ◽  
Order Contact ◽  
Contact Transformations

scholarly journals Higher‐order Lagrangian systems: Geometric structures, dynamics, and constraints

1991 ◽  
Vol 32 (10) ◽  
pp. 2744-2763 ◽  
Author(s):  
X. Gràcia ◽  
J. M. Pons ◽  
N. Román‐Roy
Keyword(s):  
Higher Order ◽  
Lagrangian Systems ◽  
Geometric Structures ◽  
Higher Order Lagrangian

A THEORETICAL BASIS FOR THE ANALYSIS OF LOGIX GEARS

2006 ◽  
Vol 30 (4) ◽  
pp. 511-518
Author(s):  
Liu Guran ◽  
Liu Quanhong ◽  
Zhao Dongfu ◽  
Song Deyu ◽  
C.Y. Chan
Keyword(s):  
Stress Concentration ◽  
Theoretical Basis ◽  
Higher Order ◽  
Concentration Profiles ◽  
Gear Design ◽  
Geometric Methods ◽  
Novel Approach ◽  
Tooth Surfaces ◽  
Contact Parameters ◽  
Order Contact

A novel approach to gear design to produce so-called Logix gears is based on differential geometric methods and results in higher order contact parameters, i.e., reduced stress concentration. Profiles designed in this way admit concave-to-convex mating tooth surfaces and a simple two gear set with such properties is presented as an example. Once a pair of mating gears has been configured it is then shown how to design hobbing racks to cut these gears.

A higher-order contact formula for plane curves

1991 ◽  
Vol 19 (2) ◽  
pp. 479-508 ◽  
Author(s):  
Colley Susan Jane ◽  
Gary Kennedy
Keyword(s):  
Higher Order ◽  
Plane Curves ◽  
Order Contact
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