Open AccessThe Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves
Author(s) -
Alexander Lozhkin,
Pavol Božek,
Konstantin Maiorov
Publication year - 2020
Publication title -
management systems in production engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.251
H-Index - 6
eISSN - 2450-5781
pISSN - 2299-0461
DOI - 10.2478/mspe-2020-0035
Subject(s) - conic section , transformation (genetics) , trajectory , conical surface , algorithm , permutation (music) , computer science , mathematics , sequence (biology) , mathematical optimization , geometry , biochemistry , chemistry , physics , genetics , astronomy , biology , acoustics , gene
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.