Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves

CAD Computer Aided Design

Volumn 30, Issue 8, 1998, Pages 631-640

  Farouki, Rida T ^a,c,d,e,f   Manjunathaiah, Jairam ^a,g,h,i,j   Nicholas, David ^a,k   Yuan, Guo Feng ^a,l   Jee, Sungchul ^a,b,m  

^a UNIVERSITY OF MICHIGAN   (United States)

^b Dankook University   (South Korea)

^c IBM T J WATSON RESEARCH CENTER   (United States)

^d GE GLOBAL RESEARCH   (United States)

^e Department of Obstetrics Gynecology   (United States)

^f UNIVERSITY OF OXFORD   (United Kingdom)

^g NATIONAL INSTITUTE OF TECHNOLOGY KARNATAKA   (India)

^h UNIVERSITY OF MASSACHUSETTS   (United States)

ⁱ SOCIETY OF MANUFACTURING ENGINEERS

^j Pi Tau Sigma   (United States)

^k GENERAL MOTORS CORPORATION   (United States)

^l NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^m Seoul National University   (South Korea)

more..

Author keywords

CNC interpolators; Curvatures; Cutting force; Feedrate; Machining accuracy; Offset curves; Osculating circle; Pythagorean hodographs

Indexed keywords

EID: 0000776279     PISSN: 00104485     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4485(98)00020-7     Document Type: Article

References (30)

1. 2 Pythagorean-hodograph interpolating splines by the homotopy method. Advances in Computational Mathematics, 1996, 5, 417-442.
2. Chou, J.-J. and Yang, D. C. H., Command axis generation for three-axis CNC machining. ASME Journal of Engineering for Industry. 1991, 113. 305-310.
3. Chou, J.-J. and Yang, D. C. H., On the generation of coordinated motion of five-axis CNC/CMM machines. ASME Journal of Engineering for Industry, 1992, 114, 15-22.
4. Farouki, R. T., Pythagorean-hodograph curves in practical use. In Geometry Processing for Design and Manufacturing, ed. R. E. Barnhill. SIAM, Philadelphia, 1992, pp. 3-33.
5. 2 of the hodograph plane. Computer Aided Geometric Design, 1994, 11, 363-390.
6. Farouki, R. T., The elastic bending energy of Pythagorean-hodograph curves. Computer Aided Geometric Design, 1996. 13, 227-241.
7. Farouki. R. T., Pythagorean-hodograph quintic transition curves of monotone curvature. Computer-Aided Design, 1997, 29, 601-606.
8. Farouki, R. T., Manjunathaiah, J. and Jee, S., Design of rational cam profiles with Pythagorean-hodograph curves. Mechanism and Machine Theory, 1998, to appear.
9. Farouki, R. T., Manjunathaiah, J. and Jee, S., Implementation and performance analysis of a real-time CNC interpolator for precision machining of Pythagorean-hodograph curves. ASME Journal of Manufacturing Science and Engineering, 1997, submitted.
10. Farouki, R. T., Manjunathaiah, J. and Yuan, G.-F., G codes for the specification of Pythagorean-hodograph tool paths and associated feedrate functions on open-architecture CNC machines. International Journal of Machine Tools and Manufacture, 1998, to appear.
11. Farouki, R. T. and Neff, C. A., Analytic properties of plane offset curves, Algebraic properties of plane offset curves. Computer Aided Geometric Design, 1990, 7, 83-127.
12. Farouki, R. T. and Neff, C. A., Hermite interpolation by Pythagorean-hodograph quintics. Mathematics of Computation, 1995, 64, 1589-1609.
13. Farouki, R. T. and Rajan, V. T., On the numerical condition of polynomials in Bernstein form. Computer Aided Geometric Design, 1987, 4, 191-216.
14. Farouki. R. T. and Rajan, V. T., Algorithms for polynomials in Bernstein form. Computer Aided Geometric Design. 1988, 5, 1-26.
15. Farouki, R. T. and Sakkalis, T., Pythagorean hodographs. IBM Journal of Research and Development, 1990, 34, 736-752.
16. Farouki, R. T. and Shah, S., Real-time CNC interpolators for Pythagorean-hodograph curves. Computer Aided Geometric Design, 1996, 13, 583-600.
17. Farouki, R. T., Tsai, Y.-F. and Yuan, G.-F., Contour machining of free-form surfaces with real-time PH curve CNC interpolators. Computer Aided Geometric Design, 1998, to appear.
18. Fussel, B. K., Ersoy, C. and Jerard, R. B., Computer generated CNC machining feed rates. In Proceedings of the Japan/USA Symposium on Flexible Automation, Vol. 1, ASME, 1992, pp. 377-383.
19. Henrici, P., Applied and Computational Complex Analysis, Vol. 1. Wiley, New York, 1974.
20. Huang, J.-T. and Yang, D. C. H., A generalized interpolator for command generation of parametric curves in computer-controlled machines. In Proceedings of the Japan/USA Symposium on Flexible Automation. Vol. 1, ASME, 1992, pp. 393-399.
21. Koren, Y., Interpolator for a computer numerical control system. IEEE Transactions on Computers. 1976, C-25, 32-37.
22. Koren, Y., Computer Control of Manufacturing Systems. McGraw-Hill, New York, 1983.
23. Lin, R.-S. and Koren, Y., Real-time interpolators for multi-axis CNC machine tools. Manufacturing Systems. 1996, 25, 145-149.
24. Pottmann, H., Rational curves and surfaces with rational offsets. Computer Aided Geometric Design, 1995, 12, 175-192.
25. Pottmann, H., Curve design with rational Pythagorean-hodograph curves. Advances in Computational Mathematics, 1995, 3, 147-170.
26. Sata, T., Kimura, F., Okada, N. and Hosaka, M., A new method of NC interpolation for machining the sculptured surface. Annals of the CIRP, 1981, 30, 369-372.
27. Shpitalni, M., Koren, Y. and Lo, C. C., Realtime curve interpolators. Computer-Aided Design. 1994, 26, 832-838.
28. Sungurtekin, U. A., Voelcker, H. B., Graphical simulation and automatic verification of NC machining programs. In Proceedings of the IEEE International Conference on Robotics and Automation, Vol. 1, San Francisco, 1986, pp. 156-165.
29. Vann, C. S. and Cutkosky, M. R., Closing the loop in CAD/CAM integration. In Proceedings of the Japan/USA Symposium on Flexible Automation, Vol. 2, ASME, 1988, pp. 915-922.
30. Yang, D. C. H. and Kong, T., Parametric interpolator versus linear interpolator for precision CNC machining. Computer-Aided Design, 1994.26, 225-234.