[personal profile] torquetum
 Ollerton, R.L., Iskov, G.H. & Shannon, A.G. (2002). Three-dimensional profiles using a spherical cutting bit: problem solving in practice. International Journal of Mathematical Education in Science and Technology, 33(5), 763-769.
 
This paper is a very interesting application of vector calculus in a real-life context. Computer Numerical Controlled milling machines often use a spherical bit for the milling of high precision 3d surfaces, such as the gripping surfaces of surgical tissue clamps. If we start with a two dimensional curve approximating the undulating surface, we can find three methods of plotting the path of the centre of the spherical bit: basic calculus, Lagrange multipliers and vector calculus. Extending to the 3d surface, the vector calculus method transfers best. In the process of the calculation the concepts of radius of curvature and cycloids come up.
 
Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

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