Geometric Modeling of Manufacturing Processes Using Symbolic and Computational Conjugate Geometry

[+] Author and Article Information
S. G. Dhande

Mechanical Engineering and Computer Science, Indian Institute of Technology, Kanpur 208 016 India

K. P. Karunakaran

CAD Project, Indian Institute of Technology, Kanpur 208 016 India

B. K. Misra

H. B. T. I., Kanpur, Indian Institute of Technology, Kanpur 208 016 India

J. Eng. Ind 117(3), 288-296 (Aug 01, 1995) (9 pages) doi:10.1115/1.2804333 History: Received July 01, 1992; Revised March 01, 1993; Online January 17, 2008


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.

Copyright © 1995 by The American Society of Mechanical Engineers
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