scholarly journals Applying Projective Geometry in Design of Worm Manufacturing

2013 ◽  
Vol 581 ◽  
pp. 77-81 ◽  
Author(s):  
Zsuzsa Balajti ◽  
József Ábel
Keyword(s):  
Mechanical Engineer ◽  
Euclidean Space ◽  
Projective Space ◽  
Production Process ◽  
Grinding Wheel ◽  
Space Model ◽  
Constant Pitch ◽  
Kinematical Model ◽  
Engineer Work ◽  
Conical Worm

The mathematical describing of the production process in mechanical engineer work in the euclidean space model and the base of the analytical describing of the projective space model is practically identical in the form, which makes it reasonable to discuss of the production geometry to approach of the projective geometrical negotiation in the . It is a fact that in one of the cases, using the approach of a projective geometrical connection and the mathematical-kinematical model resulted in expansion in the field of production precision, specifically considering the examination of the production of the conical worm by grinding wheel. The abstraction of the production geometry on projective space model has a few results in case of conical worms. The elliptical errors in production of the conical worm with arched or anything profile by grinding wheel can be eliminated by this method way to achieve the constant pitch, the torsion of profile and others.

scholarly journals On the deficiencies of meromorphic mappings of Cn into PNC

1977 ◽  
Vol 67 ◽  
pp. 165-176 ◽  
Author(s):  
Seiki Mori
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Meromorphic Mapping ◽  
Meromorphic Mappings ◽  
Complex Euclidean Space ◽  
Complex Projective

Let f(z) be a non-degenerate meromorphic mapping of the n-dimensional complex Euclidean space Cn into the N-dimensional complex projective space PNC. A generalization of results of Edrei-Fuchs [2] for meromorphic mappings of C into PNC was given by Toda [5], and an estimate of K(λ) for meromorphic mappings of Cn into PNC was done by Noguchi [4]. In this note we generalize several results of Edrei-Fuchs [2] in the case of meromorphic mappings of Cn into PNC.

scholarly journals One Parametric Motion in Klein Spaces

1950 ◽  
Vol 1 ◽  
pp. 19-23
Author(s):  
Minoru Kurita
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Euclidean Plane ◽  
Parametric Motion ◽  
Fixed Curve ◽  
Fixed Center

On the euclidean plane one-parametric motion is in general a roulett motion, exceptions being a translation at each instant and a rotation with a fixed center; here we mean by a roulett motion a motion in which a certain curve rolls on another fixed curve without slipping. In this paper we extend this fact to the case of Klein spaces and investigate in detail especially the cases of the euclidean space and the projective space.

The Study on Conic Outline Correction Processing with Column Grinding Wheel

2011 ◽  
Vol 204-210 ◽  
pp. 1503-1508
Author(s):  
Yan Li ◽  
Hui Fan He ◽  
Yong Liu ◽  
Biao Dan Zhao
Keyword(s):  
Distributed Computing ◽  
Error Analysis ◽  
Production Process ◽  
Production Costs ◽  
Grinding Wheel ◽  
Interpolation Algorithm ◽  
Wheel Wear

In order to make more uniform wheel wear, save production and reduce production costs, we improve the production process and optimize the processing way with the interpolation algorithm and the speed distributed computing by making the error analysis. And then the production process is gradually developed into green, environmental, lower consumption, higher income process.

scholarly journals Some immersions of projective space in euclidean space

Topology ◽  
1963 ◽  
Vol 2 (1-2) ◽  
pp. 69-71 ◽  
Author(s):  
Michael Ginsburg
Keyword(s):  
Euclidean Space ◽  
Projective Space

Approximation by Rational Mappings, via Homotopy Theory

2006 ◽  
Vol 49 (2) ◽  
pp. 237-246 ◽  
Author(s):  
P. M. Gauthier ◽  
E. S. Zeron
Keyword(s):  
Euclidean Space ◽  
Projective Space ◽  
Complex Projective Space ◽  
Homotopy Theory ◽  
Continuous Mappings ◽  
Complex Euclidean Space ◽  
Complex Projective ◽  
Compact Subsets

AbstractContinuous mappings defined from compact subsets K of complex Euclidean space ℂn into complex projective space ℙm are approximated by rational mappings. The fundamental tool employed is homotopy theory.

Finishing production of spiroid worm shaft by varied centre distance and by appling grinding wheel banking angle correction

2016 ◽  
Vol 7 (1) ◽  
pp. 13-19
Author(s):  
I. Dudás ◽  
S. Bodzás ◽  
K. Bányai
Keyword(s):  
Production Technology ◽  
Grinding Wheel ◽  
Production Parameters ◽  
Angle Correction ◽  
Main Production ◽  
Conical Worm ◽  
Spiroid Worm ◽  
Banking Angle

The objectives of this publication are to present a production technology which is a finishing production of conical worm using changing of centre distance between the worm and the grinding wheel and banking angle correction at the same time. We will determine the necessary optimum grinding wheel profiles for the manufacturing in light of the production tolerances. We will determine the function connections between the main production parameters.

QUATERNIONIC (ALIAS Sp(2)) COHERENT STATE AND HILBERT CONNECTION

1990 ◽  
Vol 05 (22) ◽  
pp. 1765-1772 ◽  
Author(s):  
HIROSHI KURATSUJI ◽  
KENICHI TAKADA
Keyword(s):  
Euclidean Space ◽  
Coherent State ◽  
Projective Space ◽  
Gauge Field ◽  
Path Integral ◽  
Topological Invariant ◽  
Dimensional Euclidean Space ◽  
Quaternionic Projective Space ◽  
Yang Mills ◽  
State Path

The Hilbert (or quantum) connection defined via the quaternionic (or Sp(2)) coherent state is studied by using coherent state path integral. This gives a non-integrable phase associated with the Yang-Mills gauge field induced on the compactified 4-dimensional Euclidean space S4(≃ P1(H) quaternionic projective space). The topological invariant is also discussed.

scholarly journals Influence of grinding wheel parameters on the meshing performance of toroidal surface enveloping conical worm drive

2019 ◽  
Vol 10 (1) ◽  
pp. 199-211
Author(s):  
Chongfei Huai ◽  
Yaping Zhao
Keyword(s):  
Numerical Study ◽  
Tooth Surface ◽  
Grinding Wheel ◽  
Geometrical Parameters ◽  
Geometrical Shape ◽  
Numerical Result ◽  
Toroidal Surface ◽  
Conical Worm ◽  
Curvature Interference ◽  
Geometry Characteristic

Abstract. A new type of toroidal surface enveloping conical worm gearing is proposed in our recent work (Chongfei and Yaping, 2019b). According to its forming principle, the geometrical shape of the generating surface has an important influence on the geometry characteristic of the enveloping worm pair. To explore the reasonable principles for selecting the geometrical parameters of the grinding wheel, some numerical study examples are performed. In this process, the methods for the tooth crest width are developed. Simple strategies for estimating the risk of the worm tooth surface being located in the invalid area and the risk of the curvature interference on the tooth surface are proposed. The numerical result shows that increasing the radius of the toroidal-generating surface and the nominal pressure angle of the grinding wheel are beneficial to improve the engagement behavior of the conical worm pair, but the tooth crest sharpening of the conical worm may happen if they are too large. For the nominal radius of the grinding wheel, it has a negligible effect on the meshing characteristics of this worm set. In addition, the selection principle of the parameters is also suggested.

Sign in / Sign up

Export Citation Format

Share Document