### Abstract

A new mathematical model is introduced for the tolerances of cylindrical surfaces. The model is compatible with the ISO/ANSI/ASME standard for geometric tolerances. Central to the new model is a Tolerance-Map®▲, a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a line (the axis) that can arise from tolerances on size, location and orientation of the cylindrical surface. Each axis in a tolerance zone will be represented with the six Plücker coordinates. Cylindrical surfaces in a tolerance zone for the same hole can then be treated by attaching a size tolerance to each of the lines, thereby forming a screw. Relationships for the content of line solids for a tolerance zone are developed to correspond to the variations of locations. These are then used to obtain a measure for the increment in cost when a more refined tolerance is specified. This model is one part of a bilevel model that is under development for geometric tolerances.

Original language | English (US) |
---|---|

Pages (from-to) | 95-104 |

Number of pages | 10 |

Journal | Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science |

Volume | 216 |

Issue number | 1 |

DOIs | |

State | Published - 2002 |

### Fingerprint

### Keywords

- Geometric tolerances
- Line geometry
- Screws
- Tolerancing

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*,

*216*(1), 95-104. https://doi.org/10.1243/0954406021524837

**Geometric tolerances : A new application for line geometry and screws.** / Davidson, J. K.; Shah, J. J.

Research output: Contribution to journal › Article

*Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*, vol. 216, no. 1, pp. 95-104. https://doi.org/10.1243/0954406021524837

}

TY - JOUR

T1 - Geometric tolerances

T2 - A new application for line geometry and screws

AU - Davidson, J. K.

AU - Shah, J. J.

PY - 2002

Y1 - 2002

N2 - A new mathematical model is introduced for the tolerances of cylindrical surfaces. The model is compatible with the ISO/ANSI/ASME standard for geometric tolerances. Central to the new model is a Tolerance-Map®▲, a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a line (the axis) that can arise from tolerances on size, location and orientation of the cylindrical surface. Each axis in a tolerance zone will be represented with the six Plücker coordinates. Cylindrical surfaces in a tolerance zone for the same hole can then be treated by attaching a size tolerance to each of the lines, thereby forming a screw. Relationships for the content of line solids for a tolerance zone are developed to correspond to the variations of locations. These are then used to obtain a measure for the increment in cost when a more refined tolerance is specified. This model is one part of a bilevel model that is under development for geometric tolerances.

AB - A new mathematical model is introduced for the tolerances of cylindrical surfaces. The model is compatible with the ISO/ANSI/ASME standard for geometric tolerances. Central to the new model is a Tolerance-Map®▲, a hypothetical volume of points that corresponds to all possible locations and variations of a segment of a line (the axis) that can arise from tolerances on size, location and orientation of the cylindrical surface. Each axis in a tolerance zone will be represented with the six Plücker coordinates. Cylindrical surfaces in a tolerance zone for the same hole can then be treated by attaching a size tolerance to each of the lines, thereby forming a screw. Relationships for the content of line solids for a tolerance zone are developed to correspond to the variations of locations. These are then used to obtain a measure for the increment in cost when a more refined tolerance is specified. This model is one part of a bilevel model that is under development for geometric tolerances.

KW - Geometric tolerances

KW - Line geometry

KW - Screws

KW - Tolerancing

UR - http://www.scopus.com/inward/record.url?scp=0036231696&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036231696&partnerID=8YFLogxK

U2 - 10.1243/0954406021524837

DO - 10.1243/0954406021524837

M3 - Article

VL - 216

SP - 95

EP - 104

JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

SN - 0954-4062

IS - 1

ER -