Publication result detail

Dual numbers arithmentic in multiaxis machine error modeling

HRDINA, J.; VAŠÍK, P.; HOLUB, M.

Original Title

Dual numbers arithmentic in multiaxis machine error modeling

English Title

Dual numbers arithmentic in multiaxis machine error modeling

Type

Scopus Article

Original Abstract

When a kinematic chain of a multiaxis machine centre is assembled by means of homogeneous matrices, it is possible to include the error representing matrices within and neglect the error terms which do not affect the prescribed accuracy. Classically, such error terms are identified and neglected according to the system of given identities after the matrix multiplication. In our approach, the matrices itself are designed to form a ring that respects the desired arithmetic of error terms, particularly the ring of matrices over the dual numbers. On the other hand, to make this algebraically possible, several negligible terms remain.

English abstract

When a kinematic chain of a multiaxis machine centre is assembled by means of homogeneous matrices, it is possible to include the error representing matrices within and neglect the error terms which do not affect the prescribed accuracy. Classically, such error terms are identified and neglected according to the system of given identities after the matrix multiplication. In our approach, the matrices itself are designed to form a ring that respects the desired arithmetic of error terms, particularly the ring of matrices over the dual numbers. On the other hand, to make this algebraically possible, several negligible terms remain.

Keywords

dual number, geometric accuracy, volumetric accuracy, CNC machine tools

Key words in English

dual number, geometric accuracy, volumetric accuracy, CNC machine tools

Authors

HRDINA, J.; VAŠÍK, P.; HOLUB, M.

RIV year

2018

Released

08.02.2017

Publisher

MM Science

Location

Praha

ISBN

1803-1269

Periodical

MM Science Journal

Volume

2017

Number

1

State

Czech Republic

Pages from

1769

Pages to

1772

Pages count

4

URL

http://www.mmscience.eu/content/file/archives/MM_Science_2016210.pdf

BibTex

@article{BUT132930,
  author="Jaroslav {Hrdina} and Petr {Vašík} and Michal {Holub}",
  title="Dual numbers arithmentic in multiaxis machine error modeling",
  journal="MM Science Journal",
  year="2017",
  volume="2017",
  number="1",
  pages="1769--1772",
  doi="10.17973/MMSJ.2017\{_}02\{_}2016210",
  issn="1803-1269",
  url="http://www.mmscience.eu/content/file/archives/MM_Science_2016210.pdf"
}