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LINK-GEAR MECHANISM FOR TRACING CURVES OF DISTORTED ELLIPSES

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The lengths of the links comply with the conditions: B͞D=a and B͞C=b, where a and b are the semiaxes of ellipse q-q. Slider 1 moves along fixed guides t-t whose axis coincides with axis 0y. Slider 1 is connected by turning pair D to link 4 which, in turn, is connected by turning pairs B and C to links 2 and slider 5. Slider 5 moves along fixed guides r-r whose axis coincides with axis 0x. Link 2 is connected by a sliding pair to slider 3 which turns about fixed axis 0. When slider 1 moves along guides t-t, point B of link 2 describes ellipse q-q with the equation ρD=0͞B=sqrt((a²b²)/(b²*cos²(ϕ)+a²*sin²(ϕ))) where ϕ is the polar angle between vector ρD and polar axis 0x. Any other point of link 2, lying on its axis, describes a curve which will be the curve of a distorted ellipse with respect to the radius vector having its origin at the centre of the ellipse. Curves l-l, s-s, m-m and n-n are described by points G, E, F and H of link 2. The polar equation for any point K, located along the axis of link 2 at the distance d from point B, is ρK=ρB±d.
$1231$LG,Ge$

Linked items
Documents: Lever mechanisms  [Streambook]
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