This paper develops methods for the exact analysis and representation of the swept volume of a circular cylinder undergoing rational Be´zier and B-spline motions. Instead of following the traditional approach of analyzing the point trajectory of an object motion for swept volume analysis, this paper develops a new method for swept volume analysis by studying the plane trajectory of a rational motion. It brings together recent work in swept volume analysis, plane representation of developable surfaces, as well as computer aided synthesis of freeform rational motions. The results have applications in design and approximation of freeform surfaces as well as tool path planning for 5-axis machining of freeform surfaces.
Issue Section:
Technical Papers
1.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North Holland.
2.
Bobrow
, J.
, 1985
, “NC Machine Tool Path Generation From CSG Part Representations
,” Computer Aided Design
, 17
, No. 2
, pp. 69
–76
.3.
Ganter, M. A., 1985, “Dynamic Collision Detection Using Kinematics and Solid Modeling Techniques,” Ph.D. Dissertation, University of Wisconsin-Madison.
4.
Oliver, J. H., and Goodman, E. D., 1986, “Color Graphic Verification of NC Milling Programs for Sculptured Surface Parts,” First Symposium on Integrated Intelligent Manufacturing, ASME Winter Annual Meeting, Anaheim, CA.
5.
Wang
, W. P.
, and Wang
, K. K.
, 1986
, “Geometric Modeling for Swept Volumes of Moving Solids
,” IEEE Comput. Graphics Appl.
, 6
, No. 12
, pp. 8
–17
.6.
Choi
, B. K.
, Park
, J. W.
, and Jun
, C. S.
, 1993
, “Cutter-location Data Optimization in 5-axis Surface Machining
,” Computer Aided Design
, 25
, No. 6
, pp. 377
–386
.7.
Sambandan, K., and Wang, K. K., 1989, “Five-axis Swept Volumes for Graphic NC Simulation and Verification,” Proceedings of ASME Design Technical Conferences, DE, 19, No. 1, pp. 143–150.
8.
Jerard
, R. B.
, and Drysdale
, R. L.
, 1988
, “Geometric Simulation of Numerical Control Machinery
,” ASME Computers in Engineering
, 2
, pp. 129
–136
.9.
Weld
, J. D.
, and Leu
, M. C.
, 1990
, “Geometric Representation of Swept Volumes with Applications to Polyhedral Objects
,” Int. J. Robot. Res.
, 5
, pp. 105
–117
.10.
Marciniak, K., 1991, Geometric Modeling for Numerically Controlled Machining, Oxford University Press.
11.
Li
, S. X.
, and Jerard
, R. B.
, 1994
, “5-axis Machining of Sculptured Surfaces With a Flat-end Cutter
,” Computer Aided Design
, 26
, No. 3
, pp. 165
–178
.12.
Ling
, Z. K.
, and Hu
, Z. J.
, 1997
, “Use of Swept Volumes in the Design of Interference Free Spatial Mechanisms
,” Mech. Mach. Theory
, 32
, No. 4
, pp. 459
–476
.13.
Abdel-Malek
, and Yeh
, H.
, 1997
, “Geometric Representation of the Swept Volume Using Jacobian Rank-deficiency Conditions
,” Computer Aided Design
, 29
, pp. 457
–468
.14.
Blackmore
, D.
, Leu
, M. C.
, and Wang
, L. P.
, 1997
, “The Sweep-Envelop Differential Equation Algorithm and its Application to NC Machining
,” Computer Aided Design
, 29
, pp. 629
–637
.15.
Blackmore
, D.
, Samulyak
, R.
, and Leu
, M. C.
, 1999
, “Trimming Swept Volumes
,” Computer Aided Design
, 31
, pp. 215
–223
.16.
Abdel-Malek
, Yeh
, H.
, and Othman
, S.
, 1999
, “Swept Volumes: Void and Boundary Identification
,” Computer Aided Design
, 31
, pp. 1009
–1018
.17.
Ge
, Q. J.
, and Ravani
, B.
, 1994
, “Computer Aided Geometric Design of Motion Interpolants
,” ASME J. Mech. Des.
, 116
, No. 3
, pp. 756
–762
.18.
Ju¨ttler
, B.
, and Wagner
, M. G.
, 1996
, “Computer Aided Design with Spatial Rational B-spline Motions
,” ASME J. Mech. Des.
, 119
, No. 2
, pp. 193
–201
.19.
Srinivasan
, L.
, and Ge
, Q. J.
, 1998
, “Fine Tuning of Rational B-spline Motions
,” ASME J. Mech. Des.
, 120
, No. 1
, pp. 46
–51
.20.
Bodduluri
, R. M. C.
, and Ravani
, B.
, 1993
, “Design of Developable Surfaces Using Duality Between Plane and Point Geometries
,” Computer Aided Design
, 25
, No. 10
, pp. 621
–632
.21.
Pottmann
, H.
, and Farin
, G.
, 1995
, “Developable Rational Be´zier and B-spline Surfaces
,” Computer Aided Geometric Design
, 12
, pp. 513
–531
.22.
Piegl, L., and Tiller, W., 1995, The NURBS Book, Springer, Berlin.
23.
Xia, J., and Ge, Q. J., 1999, “On the Exact Representation of the Boundary Surfaces of the Swept Volume of a Cylinder Undergoing Rational Bezier and B-spline Motions,” Proceedings 1999 ASME Design Automation Conference, Las Vegas, Paper No. DETC99/DAC-8607.
24.
Ge, Q. J., Kang, D., and Sirchia, M., 1998, Kinematically Generated Dual Tensor-product Be´zier Surfaces, Proceedings 1998 ASME Mechanisms Conference, Atlanta, GA, Paper No. DETC98/MECH-5977.
25.
McCarthy, J. M., 1990, Introduction to Theoretical Kinematics, MIT.
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