The presented work models the geometry of Single Point Cutting Tools (SPCTs) with generic profile. Presently few standard shapes of SPCTs defined in terms of projective geometry are being employed while there is a need to design free-form tools to efficiently machine free-form surfaces with few passes and chosen range of cutting angles. To be able to produce SPCT face and flanks with generic shapes through grinding, a comprehensive geometric model of the tool in terms of the varying grinding angles and the ground depths is required which helps design the tool with arbitrarily chosen tool angles. The surface modeling begins with the creation of a tool blank model followed by transformation of unbounded planes to get the cutting tool surfaces. The intersection of these surfaces with the blank gives the complete model of the tool. Having created the geometric model in two generations of generalization, the paper presents the methodology to obtain the conventional tool angles from the generic model. An illustration of the model has been provided showing variation of tool angles along the cutting edge with changing grinding parameters. When the geometric model is not to be related to the grinding parameters, the SPCT can be modeled as a composite NURBS surface which has been presented towards the end of the work.

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