Bevel gears 1 and 2 rotate in opposite directions about fixed axes OA and OB which intersect at point 0. Taking the sign 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)=-(sin(δ)-cos(δ)tan(δ₁))/tan(δ₁)=-tan(δ₂)/(sin(δ)-cos(δ)tan(δ₂)) 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). If angle δ=δ₁+δ₂= 90° (mitre gears), then the transmission ratio equals i₁₂=-tan(δ₂)=-cot(δ₁).
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