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THREE-LINK ELLIPTICAL AND OVAL CENTRODE GEARING

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Wheels 1 and 2 rotate about fixed axes A and B. The outline of wheel 1 is an ellipse with a focus at point A. The outline of wheel 2 is composed of two identical portions of an oval- type curve, arranged symmetrically. 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 horizontal 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/2. The ratio of the lengths of the outlines of wheels 2 and 1 is n=2. The outlines of wheels 1 and 2 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=2. The transmission ratio varies within the limits from i_min=(l₁/l₂)((1-k₁)/(1+k₂)) to i_max=(l₁/l₂)((1+k₁)/(1-k₂)) where k₁=c₁/l₁, k₂=c₂/l₂, c₁ and c₂ are the distances between the foci of ellipse a and between those of elliptic wheel 1, and l₁ and l₂ are the major axes of these ellipses. Teeth are to be provided on the outlines of wheels 1 and 2 to obtain the full cycle of positive motion.
$2298$SG,3L$

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Documents: Gear mechanisms  [Streambook]
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