• Archives of design research
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• v.13
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• pp.115-120
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• 1996

• Journal for History of Mathematics
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• v.37 no.4
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• pp.93-105
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• 2024

Research on the caustic, the envelope of light rays, began with the geometric optics studies of Huygens and others in the 17th century. One of the most important problems in optics in the 17th century was focusing the sun's rays. This was a problem that had to be solved in order to manufacture various practical optical instruments at the time. Beginning with research on the caustic during this period, the concept of envelope became generalized and expanded to various fields until the 19th century. This paper examines the mathematical history involved in the study of envelope curves. We compare several methods of defining the envelope and provide an example of calculating the envelope accordingly.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1361-1371
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• 1993

The effort of this paper is to develop a methodology of computer aided design and manufacture of spatial cams. The integrated CAD/CAM systems for spatial cams are developed to enable manufacturer to design and machine them readily. The contour of spatial cams can be obtained by applying envelope theory to the cam/follower motion. The mathematical cam contour is evaluated at some increment to generate the numerical data for the CNC programming. Incremental generation of points along a cam contour can be accomplished in consideration with the specified tolerance. The computerized procedure is described in detail with accompanying examples.