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LINK-GEAR MECHANISM FOR TRACING CRANIOIDS

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The lengths of the links comply with the conditions: A͞D=C͞F=E͞A‘ and C͞F>C͞E. Link 1 turns about fixed axis C. Slotted link 2 turns about fixed axis E. Slider 3, moving along the slot of link 2, is connected by turning pair F to link 1. Link 4 is connected by turning pairs D and A to link 1 and slider 5 which moves along the slot of link 2. When link 1 turns about axis C, points A and A' describe a cranioid consisting of branches a and b with the polar equation ρ=d*cos(ϕ)+b*sqrt(1-m²*sin²(ϕ))+c*sqrt(1-k²*sin²(ϕ)) where ρ=E͞A, d=E͞C, b=C͞D, c=A͞D=C͞F, m=E͞C/F͞C, k=m*(F͞D/A͞D), ϕ = angle between vector ρ and axis Ey. In the indicated position of link AD, point A describes the first branch a of the cranioid. If link 4 is put into position 4' (shown by dash lines), point A' describes the second branch b of the cranioid which is self-intersecting at point E.
$1228$LG,Ge$

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Documents: Lever mechanisms  [Streambook]
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