<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.</p>
</abstract>

The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

Kalashnikov Izhevsk State Technical University

Slovak University of Technology in Bratislava

Management Systems in Production Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the...

The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

Published Online: Aug 17, 2020

Page range: 247 - 252

Received: Jan 01, 2020

Accepted: Jun 01, 2020

DOI: https://doi.org/10.2478/mspe-2020-0035

Keywords
analytical method, linear transformations, planar complex curves, symmetries

© 2020 Alexander Lozhkin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

Published Online: Aug 17, 2020

Page range: 247 - 252

Received: Jan 01, 2020

Accepted: Jun 01, 2020

DOI: https://doi.org/10.2478/mspe-2020-0035

Keywordsanalytical method, linear transformations, planar complex curves, symmetries

© 2020 Alexander Lozhkin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
analytical method, linear transformations, planar complex curves, symmetries