. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . e radii B 6, B c, B (i . ., describe arcs the intersection of which with theformer gives points in the hypocycloid. The centre of the circle A describes during its revolutiona portion of a circle A A A, concentric with the circle B ; this is the common locus of the centresof all the arcs tangent in the points 6, c, d . . If we wish for greater exactness than that whichwe obtain by considering the elements of the generating circle as straight, we may determi
. Spons' dictionary of engineering, civil, mechanical, military, and naval; with technical terms in French, German, Italian, and Spanish . e radii B 6, B c, B (i . ., describe arcs the intersection of which with theformer gives points in the hypocycloid. The centre of the circle A describes during its revolutiona portion of a circle A A A, concentric with the circle B ; this is the common locus of the centresof all the arcs tangent in the points 6, c, d . . If we wish for greater exactness than that whichwe obtain by considering the elements of the generating circle as straight, we may determine thedevelopment of one of them, and use this length for a 6, 6 c, c d . . This precaution is usefulwhen the radius of the generating circle is very small with respect to the radius of the directingcircle, that is, when the elements, however small they may be, form a decided curve. Elongated Jlypocycloid.—This curve is generated by the point a in the plane of a circle A inva-riably connected with a circle A, which revolves about its own centre along the inner side of athird circle B, called the directing cii-cle, Fig. Construction.—The line of the centres AB determines by its intersection with the circum-ference B the fiist position of the generating point a. Beginning at the intersection o of this lineof the centres with the circumference B, divide the circumference A into a suflacient number ofequal parts 0. 1, 1. 2, ..., each of them having to be considered as a straight line. Mark, inthe same way, beginning at 0, upon the circumference B, an equal number of divisions 0. 1, 1. 2,2. 3 . . representing the development of the preceding. The radii being now produced from thepoints of division 1, 2, 3 ..., give upon the circumference B the corresponding points b, c,d. .;with the radius of the generating circle, describe arcs tangent in these points. Having produced the radii A1, A 2, A 3 ..., and obtained upon the circumference A the pointsof division b, c, d . .
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Keywords: ., bookcentury1800, bookdecade1870, bookidsp, booksubjectengineering
