### 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®^{1}(T-Maps®^{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.

Original language | English (US) |
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Title of host publication | Models for Computer Aided Tolerancing in Design and Manufacturing - Selected Conference Papers from the 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005 |

Pages | 45-54 |

Number of pages | 10 |

State | Published - 2007 |

Event | 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005 - Tempe, AZ, United States Duration: Apr 10 2005 → Apr 12 2005 |

### Other

Other | 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005 |
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Country | United States |

City | Tempe, AZ |

Period | 4/10/05 → 4/12/05 |

### Fingerprint

### Keywords

- Axis
- Form tolerance
- Position tolerance
- Straightness
- Tolerance-Map

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Modeling and Simulation

### Cite this

*Models for Computer Aided Tolerancing in Design and Manufacturing - Selected Conference Papers from the 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005*(pp. 45-54)

**Tolerance-maps applied to the straightness and orientation of an axis.** / Bhide, S.; Ameta, G.; Davidson, J. K.; Shah, J. J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Models for Computer Aided Tolerancing in Design and Manufacturing - Selected Conference Papers from the 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005.*pp. 45-54, 9th CIRP International Seminar on Computer-Aided Tolerancing, CAT 2005, Tempe, AZ, United States, 4/10/05.

}

TY - GEN

T1 - Tolerance-maps applied to the straightness and orientation of an axis

AU - Bhide, S.

AU - Ameta, G.

AU - Davidson, J. K.

AU - Shah, J. J.

PY - 2007

Y1 - 2007

N2 - 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®1(T-Maps®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.

AB - 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®1(T-Maps®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.

KW - Axis

KW - Form tolerance

KW - Position tolerance

KW - Straightness

KW - Tolerance-Map

UR - http://www.scopus.com/inward/record.url?scp=67349221664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67349221664&partnerID=8YFLogxK

M3 - Conference contribution

SN - 1402054378

SN - 9781402054372

SP - 45

EP - 54

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

ER -