The present paper describes a unified symbolic model of conjugate geometry. This model can be used to study the geometry of a cutting tool and the surface generated by it on a blank along with the kinematic relationships between the tool and the blank. A symbolic algorithm for modeling a variety of shape generating processes has been developed. It has been shown that using this algorithm one can develop geometric models for conventional machining processes such as milling, turning, etc. as well as unconventional or advanced machining techniques such as Electric Discharge Machining (EDM), Laser Beam Machining (LBM) etc. The proposed symbolic algorithm has been implemented using the symbolic manipulation software, MACSYMA. The algorithm is based on the concepts of envelope theory and conjugate geometry of a pair of mutually enveloping surfaces. A case study on the manufacture of a helicoidal surface and an illustrative example are given at the end of the paper.

Issue Section:
Technical Papers
Topics:
Geometric modeling, Geometry, Manufacturing, Algorithms, Blanks, Electrical discharge machining, Machining, Computer software, Cutting tools, Kinematics, Laser beam machining, Milling, Modeling, Shapes
1.
Acherkan, N., et al., 1973, Machine Tool Design, Vol. 2., MIR Publisher.
2.
Ber
A.
,
Rotberg
J.
, and
Zomback
S.
,
1988
, “
A Method for Evaluation of End Mill Cutting
,”
CIRP Annals
, Vol.
37
, No.
1
, pp.
37
–
40
.
3.
Boltyanskii, V. C., 1964, Envelopes, Macmillan Company.
4.
Chakraborty, J., and Dhande, S. G., 1977, Kinematics and Geometry of Planar and Spatial Cam Mechanisms, Wiley Eastern, New Delhi.
5.
Chang, T. C., and Wysk, R. A., 1985, An Introduction to Automated Process Planning Systems, Prentice Hall, Inc., Englewood, New Jersey.
6.
Faux, I. D., and Pratt, M. J., 1983, Computational Geometry for Design and Manufacture, Ellis Horwood Ltd., Chichester.
7.
Ghosh, P. K., and Mudur, S. P., 1984, “The Brush-Trajectory Approach to Figure Specification: Some Algebraic Solutions,” ACM Transactions on Graphics, Vol. 3, No. 2, April.
8.
Ghosh, A., and Mallik, A. K., 1981, Manufacturing Science, E W P, New Delhi.
9.
Kanumury, M., and Chang, T. C., 1991, “Process Planning in an Automated Manufacturing Environment,” Journal of Manufacturing Systems, Vol. 10, No. 1.
10.
Kaul, A., 1992, “Minkowski Sums: A Simulation Tool for CAD/CAM,” Proceedings of ASME Computers in Engineering Conference, San Francisco, August.
11.
Ma¨ntyla¨, M., 1988, An Introduction to Solid Modeling, Computer Science Press, Inc.
12.
Mortenson, M. E., 1985, Geometric Modeling, John Wiley and Sons, New York.
13.
Perng, D., Chen, Z., and Li, R., 1990, “Automatic 3D Machining Feature Extraction from 3D CSG Solid Input,” Computer Aided Design, Vol. 22, No. 5, June.
14.
Ravani, B., and Wang, J. W., 1990, “Computer Aided Geometric Design of Line Constructs,” Proceedings of ASME Design Automation Conference, Chicago, September.
15.
Shah, J. J., 1991, “An Assessment of Feature Technology,” Computer Aided Design, Vol. 23, No. 5, June.
16.
Srinivasan, R., and Ferreira, P., 1990, “Geometric Models of Machining Processes for Computer Aided Process Planning,” Geometric Modeling for Production Engineering, Wozny, M. J., et al., eds., North-Holland.
17.
Voelcker, H. B., and Requicha, A. A. G., 1977, “Geometrical Modeling of Mechanical Parts and Processes,” Computer Surveys, No. 10, December.
18.
Wang
W. P.
, and
Wang
K. K.
,
1986
, “
Geometric Modeling of Swept Volume of Moving Solids
,”
IEEE C. G.& A.
, Vol.
6
, No.
12
, pp.
8
–
17
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.