Mathematical modelling of contact of ruled surfaces: theory and practical application

International Conference on Mechanical Engineering, Automation and Control Systems 2015

机械制造;无线电电子学;计算机科学

Panchuk, K.L.^1 ; Niteyskiy, A.S.^1

Omsk State Technical University, Department of Engineer's Geometry and CAD, Omsk

644050, Russia^1

关键词: Differential geometry;    Dual number;    Dual vector;    Practical use;    Ruled surfaces;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/124/1/012083/pdf
DOI  :  10.1088/1757-899X/124/1/012083

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

In the theory of ruled surfaces there are well known researches of contact of ruled surfaces along their common generator line (Klein image is often used [1]). In this paper we propose a study of contact of non developable ruled surfaces via the dual vector calculus. The advantages of this method have been demonstrated by E. Study, W. Blaschke and D. N. Zeiliger in differential geometry studies of ruled surfaces in space R3over the algebra of dual numbers. A practical use of contact is demonstrated by the example modeling of the working surface of the progressive tool for tillage.