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ARTOBOLEVSKY LINK-GEAR MECHANISM FOR TRACING PEDAL CURVES OF HYPERBOLAS

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The lengths of the links comply with the conditions: 0͞C=0͞A=a, 0͞B=c=sqrt(a²+b²) and a<c, where a and b are the transverse and conjugate semiaxes of the hyperbola. Link 1 turns about fixed axis 0 and is connected by turning pair C to slider 3. Slider 3 moves along axis Bm of link 4 which turns about fixed axis B. Cross-piece t-t of slider 3 is connected by a sliding pair to cross-shaped slider 2 which has guides perpendicular to each other. Slider 2 moves along axis An of link 5 which turns about fixed axis A. Centre 0 is placed at the centre of the hyperbola and centre B at one of its foci. Then, when link 1 turns about axis 0, point D of slider 2 describes pedal curve q-q of the hyperbola with respect to one of its vertices. The equation of pedal curve q-q is ρD=0͞D= a*cos(ϕ)+sqrt(a²-c²*sin²(ϕ)) or (x²+y²)²+2(x²+y²)ax=b²y² where ϕ is the polar angle between vector ρD and polar axis Ax.
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Verknüpfte Datensätze
Dokumente: Lever mechanisms  [Streambook]
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