Dual Numbers Approach in Multiaxis Machines Error Modeling

Dual Numbers Approach in Multiaxis Machines Error Modeling

Multiaxis machines error modeling is set in the context of modern differential geometry and linear algebra. We apply special classes of matrices over dual numbers and propose a generalization of such concept by means of general Weil algebras. We show that the classification of the geometric errors f...

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Main Authors: Jaroslav Hrdina, Petr Vašík
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/261759
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spelling doaj-1f94499623e24d1781193e85a877455d2020-11-25T00:25:46ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/261759261759Dual Numbers Approach in Multiaxis Machines Error ModelingJaroslav Hrdina0Petr Vašík1Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, 616 69 Brno, Czech RepublicInstitute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, 616 69 Brno, Czech RepublicMultiaxis machines error modeling is set in the context of modern differential geometry and linear algebra. We apply special classes of matrices over dual numbers and propose a generalization of such concept by means of general Weil algebras. We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multiaxis machines error modeling.http://dx.doi.org/10.1155/2014/261759
collection DOAJ
language English
format Article
sources DOAJ
author Jaroslav Hrdina
Petr Vašík
spellingShingle Jaroslav Hrdina
Petr Vašík
Dual Numbers Approach in Multiaxis Machines Error Modeling
Journal of Applied Mathematics
author_facet Jaroslav Hrdina
Petr Vašík
author_sort Jaroslav Hrdina
title Dual Numbers Approach in Multiaxis Machines Error Modeling
title_short Dual Numbers Approach in Multiaxis Machines Error Modeling
title_full Dual Numbers Approach in Multiaxis Machines Error Modeling
title_fullStr Dual Numbers Approach in Multiaxis Machines Error Modeling
title_full_unstemmed Dual Numbers Approach in Multiaxis Machines Error Modeling
title_sort dual numbers approach in multiaxis machines error modeling
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description Multiaxis machines error modeling is set in the context of modern differential geometry and linear algebra. We apply special classes of matrices over dual numbers and propose a generalization of such concept by means of general Weil algebras. We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multiaxis machines error modeling.
url http://dx.doi.org/10.1155/2014/261759
work_keys_str_mv AT jaroslavhrdina dualnumbersapproachinmultiaxismachineserrormodeling
AT petrvasik dualnumbersapproachinmultiaxismachineserrormodeling
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