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THREE-LINK CENTRODE GEARING WITH CIRCULAR AND NONCIRCULAR WHEELS

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Wheels 1 and 2 rotate about fixed axes A and B. The outline of wheel 1 is a circle with its centre at point 0. The outline of wheel 2 is composed of two identical curves, DPC and DEC, arranged symmetrically. The centre-to-centre distance L complies with the conditon •L≅r(l+i)[1-((i-2)e²)/(4i)+(-3i²+2i²+12i+24)ε⁴/(64i³)] where r is the radius of circular wheel 1, ε=e/r is the ratio of the eccentricity e to the radius r and l is the average transmission ratio i=i₁₂=1, 2, 3, 4, ... . Angles ϕ₁ and ϕ₂ of rotation of centrodes 1 and 2 are related as follows: ϕ₂=∫((sqrt(r²-e² sin²(ϕ₁))-e cos(ϕ₁))/(L-sqrt(r²-e² sin²(ϕ₁))+e cos(ϕ₁)))dϕ₁; with limits [ϕ₂,ϕ₁]. 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. Expressed in terms of the parameters of the wheels, the transmission ratio is i₁₂=L/(sqrt(r²-e²sin²(ϕ₁))-ecos(ϕ₁))-1. The transmission ratio varies within the limits from i_min=(1-ε)/(m-(1-ε)) to i_max=(1+ε)/(m-(1+ε)) where m=L/r. The average transmission ratio of the given version is i₁₂=2. The length of each arc, DPC or DEC, equals 2πr. Teeth are to be provided on the outlines of wheels 1 and 2 to obtain the full cycle of positive motion.
$2300$SG,3L$

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Documents: Gear mechanisms  [Streambook]
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