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THREE-LINK PLANETARY TOOTHED BEVEL GEARING WITH CIRCULAR PINION AND CROWN GEAR

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Sun crown gear (circular rack) 1 is rigidly attached to the base. Planet bevel pinion 2 rotates about axis OB of carrier 3 which, in turn, rotates about fixed axis OA. Axes OA and OB intersect at point 0. Taking the sign of the angular velocities ω₂ and ω₃ of pinion 2 and carrier 3 into account, the transmission ratio of the mechanism is i₂₃=ω₂/ω₃=1-r₁/r₂=1-z₁/z₂=1-1/sin(δ₂)=1-1/cos(δ) where r₁ and r₂ are the radii of contacting circles on crown gear 1 and on the pitch cone of pinion 2, z₁ and z₂ are the numbers of teeth of gears 1 and 2, δ₂ is the pitch cone angle of pinion 2, and δ is the centre angle (angle between axes OA and OB).
$2336$SG,3L$

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Documents: Gear mechanisms  [Streambook]
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