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THREE-LINK TWO-LOBE LOGARITHMIC-CURVE CENTRODE GEARING

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Wheels 1 and 2 rotate about fixed axes A and B. The outline of each wheel is composed of four identical portions of a logarithmic spiral, arranged symmetrically in pairs. The outlines of the wheels are centrodes in their relative motion. Without taking the sign into account, the transmission ratio in each position of the mechanism is •i₁₂=ω₁/ω₂=B͞P/A͞P where ω₁ and ω₂ are the angular velocities of wheels 1 and 2, and P is the point of contact of the outlines and always lies on line AB. The average transmission ratio in a full cycle of the mechanism is •i₁₂=1. The transmission ratio varies twice each cycle within the limits from i_min=1/(e^(mπ/2)) to i_max=e^(mπ/2) where m=cot(µ) and µ is the constant angle between tangent t-t to the curve and radius vector r. Teeth are to be provided on the outlines of wheels 1 and 2 to obtain the full cycle of positive motion.
$2291$SG,3L$

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Documents: Gear mechanisms  [Streambook]
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