File:Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for draughtsmen (1897) (14594517890).jpg

Identifier: practicalenginee00will (find matches)
Title: Practical engineering drawing and third angle projection, for students in scientific, technical and manual training schools and for ... draughtsmen ..
Year: 1897 (1890s)
Authors: Willson, Frederick Newton, 1855-1939
Subjects: Mechanical drawing Lettering
Publisher: Princeton, N.J., The author
Contributing Library: The Library of Congress
Digitizing Sponsor: The Library of Congress

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points and a general analysis of the motion. ==■ Locus is the Latin for place; and in father untechnical language, although in the exact sense in which it is used mathe-matically, we may say that the Locus of points or lines is the place where you \n-Ay expect to find them under their conditionsof restriction. For example, the surface of a sphere is the locus of all points equidistant from a fixed point (its centre). Thelocus of a point moving in a plane so as to remain at a constant distance from a given lixed point, is a circle having thelatter point as its centre. 52 THEORETICAL AND PRACTICAL GRAPHICS. 158. We have given, in Fig. 98, two links or bars, MN and S P, fastened at N and P by-pivots to a third link, N P, while their other extremities are pivoted on stationary axes at M andS. The only movement possible to the point N is therefore in a circle about M; while P isequally limited to circular motion about S. The points on the link N^ P, with the exception of its 2 MN _2 MS3
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THE LEMNISCATE AS A LINK-MOTION CURVE ■extremities, have a compound motion, in curves whose form it is not easy to jaredict and whichdiffer most curiously from each other. The figure-of-eight curve shown, otherwise the Lemniscateof Bernoulli, is the point-path of Z, the link NP being supposed prolonged by an amount, P Z,■equal to N P. Since iVP is constant in length, if N were moved along to E the point P wouldhave to be at a distance iV P irom E and also on the circle to which it is confined; therefore itsnew position, /, is at the intersection of the circle P s r by an arc of radius P N, centre F. ThenFf prolonged by an amount equal to itself gives /;, another point of the Lemniscate, and to whichZ has then moved. All other positions are similarly found. If the motion of N is toward D it will soon reach a limit, A, to its fm-ther movement in thatdirection, arriving there at the instant that P reaches a, when NP and PS will be in one straightline, S ^1. In this position any movem

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