@inproceedings{46ddc52081714aa8a6580178e0df420b,

title = "Tolerance-maps applied to the straightness and orientation of an axis",

abstract = "Among the least developed capabilities in well-developed mathematical models for geometric tolerances are the representation of tolerances on form, orientation, and of Rule #1 in the Standards, i.e. the coupling between form and allowable variations for either size or position of a feature. This paper uses Tolerance-Maps{\textregistered}1(T-Maps{\textregistered}1) to describe these aspects of geometric tolerances for the straightness and orientation of an axis within its tolerance-zone on position. A Tolerance-Map is a hypothetical point-space, the size and shape of which reflect all variational possibilities for a target feature; for an axis, it is constructed in four-dimensional space. The Tolerance-Map for straightness is modeled with a geometrically similar, but smaller-sized, four-dimensional shape to the 4D shape for position; it is a subset within the T-Map for position. Another internal subset describes the displacement possibilities for the subset T-Maps that limits form. The T-Map for orientation and position together is formed most reliably by truncating the T-Map for position alone.",

keywords = "Axis, Form tolerance, Position tolerance, Straightness, Tolerance-Map",

author = "S. Bhide and G. Ameta and Davidson, {J. K.} and Shah, {J. J.}",

year = "2007",

doi = "10.1007/1-4020-5438-6_6",

language = "English (US)",

isbn = "1402054378",

series = "Models for Computer Aided Tolerancing in Design and Manufacturing - Selected Conference Papers from the 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005",

publisher = "Kluwer Academic Publishers",

pages = "45--54",

booktitle = "Models for Computer Aided Tolerancing in Design and Manufacturing - Selected Conference Papers from the 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005",

note = "9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005 ; Conference date: 10-04-2005 Through 12-04-2005",

}