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THREE-LINK FOUR-LOBE OVAL 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 eight identical portions of an oval-type curve, arranged symmetrically in pairs. These portions of the outline are constructed as follows: the radius vector of a point on ellipse a (measured from one of its foci at the angle α from the vertical axis) is equal to the radius vector of the corresponding point on the oval-type curve, measured likewise from the same focus, but at the angle α/4. 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 is •i₁₂=1. The transmission ratio varies four times each cycle within the limits from i_min=(1-k)/(1+k) to i_max=(1+k)/(1-k) where k=c/l, c is the distance between the foci of ellipse a and l is the major axis of ellipse a. Teeth are to be provided on the outlines of wheels 1 and 2 to obtain the full cycle of positive motion.
$2296$SG,3L$

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Documents: Gear mechanisms  [Streambook]
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