hypocycloid

“The result is a series of enormous hypocycloid designs which recorded the hidden patterns created by the ride as it turned.”

Boing Boing

“The properties of a hypocycloid were recognized by James White, an”

Kinematics of Mechanisms from the Time of Watt

“Thus in Fig. 39, the diameters of the two pitch circles are to each other as 4 to 5; the hypocycloid has 5 branches, and 4 pins are used.”

Scientific American Supplement, No. 470, January 3, 1885

“The original hypocycloid is shown in dotted line, the working curve being at a constant normal distance from it equal to the radius of the roller; this forms a sort of frame or yoke, which is hung upon cranks as in Figs. 36 and 38.”

Scientific American Supplement, No. 470, January 3, 1885

“Upon examination it will be seen, although we are not aware that attention has previously been called to the fact, that this differs from the ordinary forms of "pin gearing" only in this particular, viz., that the elementary tooth of the driver consists of a complete branch, instead of a comparatively small part of the hypocycloid traced by rolling the smaller pitch-circle within the larger.”

Scientific American Supplement, No. 470, January 3, 1885

“Sj-hypocycloid created December 31, 2008, last edited January 01,”

ArmchairGM Popular Stuff

“It is self-evident that the hypocycloid must return into itself at the point of beginning, without crossing: each branch, then, must subtend an aliquot part of the circumference, and can be traced also by another and a smaller describing circle, whose diameter therefore must be an aliquot part of the diameter of the outer pitch-circle; and since this last must be equal to the sum of the diameters of the two describing circles, it follows that the radii of the pitch circles must be to each other in the ratio of two successive integers; and this is also the ratio of the number of pins to that of the epicycloidal branches.”

Scientific American Supplement, No. 470, January 3, 1885

“Following the analogy, it would seem that the next step should be to employ two branches with only one pin; but the rectilinear hypocycloid of Fig. 38 is a complete diameter, and the second branch is identical with the first; the straight tooth, then, could theoretically drive the pin half way round, but upon its reaching the center of the outer wheel, the driving action would cease: this renders it necessary to employ two pins and two slots, but it is not essential that the latter should be perpendicular to each other.”

Scientific American Supplement, No. 470, January 3, 1885