A generalisation of Noether's formula for the number of virtual double points to space curve singularities

1991 ◽  
Vol 56 (1) ◽  
pp. 96-99
Author(s):  
Jan Stevens
Keyword(s):  
Space Curve ◽  
Double Points ◽  
Curve Singularities

A classifier for simple space curve singularities

2014 ◽  
Vol 51 (1) ◽  
pp. 92-104
Author(s):  
Faira Janjua ◽  
Gerhard Pfister
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Plane Curve ◽  
Space Curve ◽  
Plane Curve Singularities ◽  
Curve Singularities

The classification of Bruce and Gaffney respectively Gibson and Hobbs for simple plane curve singularities respectively simple space curve singularities is characterized in terms of invariants. This is the basis for the implementation of a classifier in the computer algebra system singular.

Classification of simple space curve singularities

1999 ◽  
Vol 27 (8) ◽  
pp. 3993-4013 ◽  
Author(s):  
Anne Frühbis-Krüger
Keyword(s):  
Space Curve ◽  
Curve Singularities

The deformations of the simple space curve singularities

1998 ◽  
Vol 229 (4) ◽  
pp. 607-614 ◽  
Author(s):  
Caren Schröter ◽  
Sonja Schuba
Keyword(s):  
Space Curve ◽  
Curve Singularities

scholarly journals A Classiffier for Unimodular Isolated Complete Intersection Space Curve Singularities

2016 ◽  
Vol 24 (1) ◽  
pp. 95-119
Author(s):  
Deeba Afzal ◽  
Gerhard Pfister
Keyword(s):  
Complete Intersection ◽  
Normal Forms ◽  
Complete Classification ◽  
Space Curve ◽  
Complete List ◽  
Curve Singularities

AbstractC.T.C. Wall classified the unimodular complete intersection singularities. He indicated in the list only the μ-constant strata and not the complete classification in each case. In this article we give a complete list of space curve unimodular singularities and also the description of a classifier. Instead of computing the normal forms, the singularity is identified by certain invariants.

Geometry Design and Contact Ratio Analysis for Circular Arc Parallel-Axis Helical Gears

2016 ◽  
Author(s):  
Z. Chen ◽  
B. Lei ◽  
Q. Zhao
Keyword(s):  
Rolling Process ◽  
Helical Gear ◽  
Space Curve ◽  
Impact Factors ◽  
Contact Ratio ◽  
Circular Arc ◽  
Practical Applications ◽  
Geometry Design ◽  
Gear Mechanism ◽  
The Impact

Based on space curve meshing theory, in this paper, we present a novel geometric design of a circular arc helical gear mechanism for parallel transmission with convex-concave circular arc profiles. The parameter equations describing the contact curves for both the driving gear and the driven gear were deduced from the space curve meshing equations, and parameter equations for calculating the convex-concave circular arc profiles were established both for internal meshing and external meshing. Furthermore, a formula for the contact ratio was deduced, and the impact factors influencing the contact ratio are discussed. Using the deduced equations, several numerical examples were considered to validate the contact ratio equation. The circular arc helical gear mechanism investigated in this study showed a high gear transmission performance when considering practical applications, such as a pure rolling process, a high contact ratio, and a large comprehensive strength.

Sign in / Sign up

Export Citation Format

Share Document