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THREE-LINK INTERNAL CIRCULAR TOOTHED BEVEL GEARING

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Bevel pinion 1 and internal bevel gear 2 rotate in the same direction about fixed axes OA and OB which intersect at point 0. Taking the signs of the angular velocities ω₁ and ω₂ of gears 1 and 2 into account, the transmission ratio of the mechanism is i₁₂=ω₁/ω₂=r₂/r₁=z₂/z₁=sin(δ₂)/sin(δ₁)=(cos(δ)tan(δ₁)+sin(δ))/tan(δ₁)=tan(δ₂)/(cos(δ)tan(δ₂)-sin(δ)) where r₁ and r₂ are the radii of contacting circles on the pitch cones of gears 1 and 2, z₁ and z₂ are the numbers of teeth of gears 1 and 2, δ₁ and δ₂ are the pitch cone angles of gears 1 and 2, and δ is the centre angle (angle between axes OA and OB).
$2332$SG,3L$

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Documents: Gear mechanisms  [Streambook]
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