GEOMETRIC MODELING OF MANUFACTURING PROCESSES USING SYMBOLIC AND COMPUTATIONAL CONJUGATE GEOMETRY

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