Mathematical model of the formation of cyclic and channel surfaces based on nonlinear rotation
This work is a continuation of the series of works by the authors devoted to the issues of shaping surfaces of nonlinear rotation. The geometric scheme for the formation of surfaces of this class includes: an axis of nonlinear rotation, which is a smooth, generally spatial curve, and a forming li...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2024-11-01
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| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2024/%E2%84%964%20(192)%20(%D0%9E%D0%9D%D0%92)/14-21%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C.,%20%D0%9B%D1%8E%D0%B1%D1%87%D0%B8%D0%BD%D0%BE%D0%B2%20%D0%95.%20%D0%92..pdf |
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| Summary: | This work is a continuation of the series of works by the authors devoted to the
issues of shaping surfaces of nonlinear rotation. The geometric scheme for the
formation of surfaces of this class includes: an axis of nonlinear rotation, which is
a smooth, generally spatial curve, and a forming line, also a smooth spatial curve.
When the generating line rotates relative to the curvilinear axis, each point of the
generating line describes a circumferential trajectory in the corresponding normal
plane of the rotation axis. As a result, a surface of nonlinear rotation is formed,
which is a normal cyclic surface. In this work, in order to develop the research
results previously obtained by the authors in the field of shaping surfaces of
nonlinear rotation, the solution to the inverse problem of shaping is considered and
a mathematical justification is given for the possibility of shaping a channel surface
based on solutions to the direct and inverse problems. The work provides numerical
examples of the formation of the surfaces under consideration, accompanied by
mathematical models of surfaces, their computer implementation and visualization.
The research results can be useful in the development of CAD systems that involve
the design of surface forms of products based on cyclic and channel surfaces in
mechanical engineering, construction, architecture and other practical fields |
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| ISSN: | 1813-8225 2541-7541 |