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LINK-GEAR MECHANISM FOR TRACING CONCHOIDS OF ELLIPSES

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The lengths of the links comply with the conditions:B͞D=A͞0=a, B͞C=b and F͞B=B͞E=d, where a and b are semiaxes of ellipse p-p. Slider 1 moves along fixed guides t-t, whose axis is parallel to axis Ay and passes through centre 0 of ellipse p-p. Slider 1 is connected by turning pair D to link 4 which, in turn, is connected by turning pairs B and C to link 2 and to slider 5. Slider 5 moves along fixed guides r-r whose axis coincides with axis Ax. Link 2 is connected by a sliding pair to slider 3 which turns about fixed axis A. When slider 1 moves along guides t-t, point B of link 4 describes ellipse p-p, and points F and E of link 2 describe conchoid q-q of ellipse p-p. The equation of the conchoid is (y²+x²)(a²y²+b²x²-2abx²)²=d(a²y²+b²x²)². If d=2a, then points F and E describe a cardioid of ellipse p-p. The equation of the cardioid is (y²+x²)(a²y²+b²x²-2ab²x)²=4a²(a²y²+b²x²)².
$1152$LG,Ge$

Verknüpfte Datensätze
Dokumente: Lever mechanisms  [Streambook]
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