Publication detail

Dual numbers arithmentic in multiaxis machine error modeling

HRDINA, J. VAŠÍK, P. HOLUB, M.

English title

Dual numbers arithmentic in multiaxis machine error modeling

Type

journal article in Scopus

Language

en

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 in English

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

Released

08.02.2017

Publisher

MM Science

Location

Praha

ISSN

1803-1269

Volume

2017

Number

1

Pages from–to

1769–1772

Pages count

4

BIBTEX


@article{BUT132930,
  author="Jaroslav {Hrdina} and Petr {Vašík} and Michal {Holub},
  title="Dual numbers arithmentic in multiaxis machine error modeling",
  year="2017",
  volume="2017",
  number="1",
  month="February",
  pages="1769--1772",
  publisher=" MM Science",
  address="Praha",
  issn="1803-1269"
}