Analytical envelope surface representation of a conical cutter undergoing rational motion

International Journal of Advanced Manufacturing Technology

Volumn 47, Issue 5-8, 2010, Pages 719-730

  Bi, Qingzhen ^a   Zhu, Limin ^a   Wang, Yuhan ^a   Ding, Han ^a  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Conical cutter; Envelope surface; Flank milling; Line geometry; Rational motion

Indexed keywords

A-PLANE; B-SPLINE; CHARACTERISTIC CURVE; CONE SURFACES; DEGENERATE CASE; DEVELOPABLE SURFACES; ENVELOPE SURFACE; FIVE-AXIS; FLANK MILLING; IN-LINE; LINE GEOMETRY; POINT COORDINATES; RATIONAL MOTIONS; RATIONAL QUADRATIC BEZIER; TOOLPATHS;

CONES; ERROR ANALYSIS; MILLING (MACHINING); SPLINES;

COMPUTATIONAL GEOMETRY;

EID: 77952290407     PISSN: 02683768     EISSN: 14333015     Source Type: Journal    
DOI: 10.1007/s00170-009-2218-1     Document Type: Article

References (32)

1. Abdel-Malek K, Blackmore D, Joy K (2006) Swept volumes: foundation, perspectives, and applications. Int J Shap Model 12 (1):87-127
2. Ketchel J, Larochelle P (2005) Collision detection of cylindrical rigid bodies using line geometry. ASME IDETC, California
3. Eberharter JK, Ravani B (2004) Kinematic registration using line geometry. ASME IDETC, Salt Lake City
4. Pottmann H, Peternell M, Ravani B (1999) An introduction to line geometry with applications. Comput Aided Des 31(1):3-16
5. Peternell M, Pottmann H, Ravani B (1999) On the computational geometry of ruled surfaces. Comput Aided Des 31(1):17-32
6. Chen HY, Pottmann H (1999) Approximation by ruled surfaces. J Comput Appl Math 102(1):143-156
7. Ravani B, Wang JW (1999) Computer aided geometric design of line constructs. ASME J Mech Design 113(4):363-371
8. Pottmann H, Wallner J (2000) Computational line geometry. Springer, Berlin
9. Jüttler B, Wagner MG (1996) Computer-aided design with spatial rational B-spline motions. ASME J Mech Design 118(2):193-201
10. Park FC, Ravani B (1995) Bézier curves on Riemannian manifolds and lie groups with kinematics applications. ASME J Mech Design 117(1):36-40
11. Purwar A, Ge QJ (2005) On the effect of dual weights in computer aided design ofrational motions. ASME J Mech Design 127(5):967-972
12. Zefran M, Kumar V (1998) Interpolation schemes for rigid body motions. Comput Aided Des 30(3):79-189
13. Radzevich SP (2007) Kinematic geometry of surface machining. CRC, New York
14. Sprott K, Ravani B (2002) Kinematic generation of ruled surfaces. Adv Comput Math 17:115-133
15. Roschel O (1998) Rational motion design-a survey. Comput Aided Des 30(3):169-178
16. Jüttler B, Wagner MG (1999) Rational motion-based surface generation. Comput Aided Des 31(3):203-213
17. Xia J, Ge QJ (2001) On the exact representation of the boundary surfaces of the swept volume of a cylinder undergoing rational Bézier and B-spline motions. ASME J Mech Design 123(2):261-265
18. Sprott K, Ravani B (2008) Cylindrical milling of ruled surfaces. Int J Adv Manuf Technol 38(7-8):649-656
19. Senatore J, Monies F, Landon Y, Rubio W (2008) Optimising positioning of the axis of a milling cutter on an offset surface by geometric error minimisation. Int J Adv Manuf Technol 37(9-10):861-871
20. Li C, Bedi S, Mann S (2008) Accuracy improvement method for flank milling surface design. Int J Adv Manuf Technol 38(3-4):218-228
21. Chu CH, Chen JT (2006) Tool path planning for five-axis flank milling with developable surface approximation. Int J Adv Manuf Technol 29(7-8):707-713
22. Lee JJ, Suh SH (1998) Interference-free tool-path planning for flank milling of twisted ruled surfaces. Int J Adv Manuf Technol 14(11):797-805
23. Xia J, Ge QJ (2000) Kinematic approximation of ruled surfaces using NURBS motions of a cylindrical cutter. ASME DAC, Baltimore
24. Zhang W, Zhang YF, Ge QJ (2005) Interference-free tool path generation for 5-axis sculptured surface machining using rational Bézier motions of a flat-end cutter. Int J Prod Res 43(19):4103-4124
25. Monies F, Felicfsj JN, Rubio W, Redonnet JM, Lagarrigue P (2002) Five-axis NC milling of ruled surfaces: optimal geometry of a conical tool. Int J Prod Res 40(12):2901-2922
26. Monies F, Rubio W, Redonnet JM, Lagarrigue P (2001) Comparative study of interference caused by different position settings of a conical milling cutter on a ruled surface. Proc Inst Mech Eng B J Eng Manuf 215(9):1305-1317
27. Monies F, Rubio W, Redonnet JM, Lagarrigue P (2000) Improved positioning of a conical mill for machining ruled surfaces: application to turbine blades. Proc Inst Mech Eng B J Eng Manuf 214(7):625-634
28. Chiou JCJ (2004) Accurate tool position for five-axis ruled surface machining by swept envelope approach. Comput Aided Des 36(10):967-974
29. Li C, Bedi S, Mann S (2006) Flank milling of a ruled surface with conical tools-an optimization approach. Int J Adv Manuf Technol 29(11-12):1115-1124 (Pubitemid 44099789)
30. Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, New York
31. Xia J (2001) Motion based geometric modeling. Dissertation, State University of New York at Stony Brook
32. Murray RM, Li ZX, Sastry SS (1994) A mathematical introduction to robotic manipulation. CRC, Florida