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THREE-LINK TOOTHED PLANETARY MECHANISM FOR TRACING CARDIOIDS

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Gear 1 rolls around identical fixed gear 3. Carrier 2 rotates about fixed axis A. Any random point D of gear 1 lying on its pitch circle describes cardioid q-q with the polar equation p=2r(l+cos(ϕ)) where p is the radius vector of the cardioid, r is the pitch radius of gears 1 and 3, and ϕ is the angle between axis Ox and axis AB of carrier 2. In rectangular coordinates xOy, the equation of cardioid q-q has the form (x²+y²-2rx)²=4r²(x²+y²).
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Documents: Gear mechanisms  [Streambook]
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