### Abstract

It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve Cd(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve Cd(t); (3) to oscillate the number of control points of offset curve Cd(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.

Original language | English |
---|---|

Pages (from-to) | 471-482 |

Number of pages | 12 |

Journal | Robotics and Computer-Integrated Manufacturing |

Volume | 26 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2010 Oct |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Software
- Mathematics(all)
- Computer Science Applications
- Industrial and Manufacturing Engineering

### Cite this

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*Robotics and Computer-Integrated Manufacturing*, vol. 26, no. 5, pp. 471-482. https://doi.org/10.1016/j.rcim.2010.03.006

**Tool-path generation of planar NURBS curves.** / Lain, Yuan Lung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Tool-path generation of planar NURBS curves

AU - Lain, Yuan Lung

PY - 2010/10

Y1 - 2010/10

N2 - It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve Cd(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve Cd(t); (3) to oscillate the number of control points of offset curve Cd(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.

AB - It has been widely used in CAD field for many years and gradually applied in CAM area with the prevalence of NURBS interpolator equipped in CNC controllers. But few of them provide the tool radius compensation function. In order to achieve the goal of generating tool-path, an algorithm was presented to offset NURBS curves by an optimum process for CAD/CAM systems in this paper. NURBS format is ideal for HSM applications, but not all NURBS outputs are equal and standard. Basically, there are two different ways to generate NURBS tool-paths; one is to fit a NURBS curve to the conventional tool-path output, the other one is to generate a NURBS tool-path from the start. The main targets for the tool-path of this paper are: (1) To keep a constant distance d between progenitor curve C(t) and offset curve Cd(t) on the normal direction of C(t); (2) to alternate the order k of the basis function in offset curve Cd(t); (3) to oscillate the number of control points of offset curve Cd(t) and compare it with progenitor curve C(t). In order to meet the tolerance requirements as specified by the design, this study offsets the NURBS curves by a pre-described distance d. The principle procedure consists of the following steps: (1) construct an evaluating bound error function; (2) sample offset point-sequenced curves based on first derivatives; (3) give the order of NURBS curve and number of control points to compute all initial conditions and (4) optimize the control points by a path searching algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84862973818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862973818&partnerID=8YFLogxK

U2 - 10.1016/j.rcim.2010.03.006

DO - 10.1016/j.rcim.2010.03.006

M3 - Article

AN - SCOPUS:84862973818

VL - 26

SP - 471

EP - 482

JO - Robotics and Computer-Integrated Manufacturing

JF - Robotics and Computer-Integrated Manufacturing

SN - 0736-5845

IS - 5

ER -