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ARTOBOLEVSKY LINK-GEAR MECHANISM FOR TRACING CISSOIDS OF DIOCLES

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Link 1, turning about fixed axis 0, is connected by sliding pairs to sliders 2 and 3. Slider 4 moves along fixed guides t-t whose axis is perpendicular to axis 0x. Cross-piece CB of slider 4 is connected by turning pair C to link 5. Link 5 moves in cross-shaped slider 2 which has guides perpendicular to each other. Slider 3 is connected by turning pair B to slider 4. When link 1 turns about axis 0, point D of slider 2 describes cissoid of Diocles s-s with the equation ρD=0͞D=a*sin²(ϕ)/cos(ϕ) or y²=x³/(a-x) where a = diameter of circle p-p, ϕ = polar angle between vector ρD and polar axis 0x. The cissoid of Diocles is a cissoid of circle p-p, of diameter a and passing through point 0, and of straight line q-q tangent to this circle at point G.
$1130$LG,Ge$

Linked items
Documents: Lever mechanisms  [Streambook]
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