Abstract
SOME little time ago Mr. Kempe published in NATURE a theorem of interest in kinematics. I subsequently stated in the same pages that this theorem and all theorems of uniplanar kinematics are most simply and properly proved from the consideration that epicycloidal motion is the basis of all uniplanar motion—and that this is also the proper principle on which to base the theory of planimeters. It may not be out of place to occupy a few lines in NATURE with another curious kinematical theorem allied to Kempe's, which I have just found by this method. If a plane, A, move about in any manner over a fixed plane, B, and return to its original position after any number of revolutions, all those right lines in the plane A which have enveloped glisettes of the same area, are tangents to a conic, and by varying the area of the glisette we obtain a series of confocal conics. I use the term gliseite under protest—“line roulette” would be better, as the former name is more applicable to a curve of another sort.
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MINCHIN, G. A Kinematical Theorem. Nature 24, 557 (1881). https://doi.org/10.1038/024557c0
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DOI: https://doi.org/10.1038/024557c0
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