Skip to main content
SpringerLink
Log in

On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

A parametric interpolator for the trajectory planning of non-uniform rational basis spline (NURBS) curves is proposed in this study. The input constraints include the chord error, speed limit, acceleration limit and jerk limit. Since there is no unique representation to relate these constraints, appropriate models are developed to determine several feedrates in terms of different kinematic conditions, the minimum one of which is selected as the desired feedrate. A look-ahead stage is developed to plan a series of segment points from the curves, where a segment point represents the change in the acceleration across zero. The segment points, which enable the appropriate design of kinematic profiles, are used in real-time sampling for determining the sampling points. Several examples are presented to demonstrate the feasibility of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bedi S, Ali I, Quan N (1993) Advanced interpolation techniques for NC machines. ASME J Eng Ind 115(3):329–336

    Google Scholar 

  2. Shpitalni M, Koren Y, Lo CC (1994) Realtime curve interpolators. CAD 26(11):832–838

    MATH  Google Scholar 

  3. Yang DCH, Kong T (1994) Parametric interpolator versus linear interpolator for precision CNC machining. CAD 26(3):225–233

    MATH  MathSciNet  Google Scholar 

  4. Tsai M-C, Cheng C-W, Cheng M-Y (2003) A real-time NURBS surface interpolator for precision three-axis CNC machining. Int J Mach Tools Manuf 43(12):1217–1227

    Article  Google Scholar 

  5. Yeh S-S, Hsu P-L (1999) The speed-controlled interpolator for machining parametric curves. CAD 31(5):349–357

    MATH  Google Scholar 

  6. Yeh S-S, Hsu P-L (2002) Adaptive-feedrate interpolation for parametric curves with a confined chord error. CAD 34(3):229–237

    MathSciNet  Google Scholar 

  7. Xu H-Y, Tam H-Y, Zhou Z, Tse PW (2001) Variable feedrate CNC interpolation for planar implicit curves. Int J Adv Manuf Technol 18(11):794–800

    Article  Google Scholar 

  8. Liu A, Ahmad F, Yamazaki K, Mori M (2005) Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics. Int J Mach Tools Manuf 45(4–5):433–444

    Article  Google Scholar 

  9. Yong T, Narayanaswami R (2003) A parametric interpolator with confined chord errors, acceleration and deceleration for NC machining. CAD 35(13):1249–1259

    Google Scholar 

  10. Nam S-H, Yang M-Y (2004) A study on a generalized parametric interpolator with real-time jerk-limited acceleration. CAD 36(1):27–36

    Google Scholar 

  11. Lee K (1999) Principles of CAD/CAM/CAE systems. Addison-Wesley, Reading, Massachusetts

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, National Central University, Taiwan, People’s Republic of China

    Jiing-Yih Lai, Kuan-Yuan Lin & Sheng-Jung Tseng

  2. Mechanical Engineering Department, Tung Nan Institute of Technology, Taiwan, People’s Republic of China

    Wen-Der Ueng

Authors
  1. Jiing-Yih Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kuan-Yuan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sheng-Jung Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wen-Der Ueng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiing-Yih Lai.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lai, JY., Lin, KY., Tseng, SJ. et al. On the development of a parametric interpolator with confined chord error, feedrate, acceleration and jerk. Int J Adv Manuf Technol 37, 104–121 (2008). https://doi.org/10.1007/s00170-007-0954-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-007-0954-7

Keywords

Search

Navigation