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ARTOBOLEVSKY LINK-GEAR MECHANISM FOR TRACING THE COMPANIONS OF CISSOIDS OF DIOCLES

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Link 1, turning about fixed axis 0, is connected by sliding pairs to sliders 3 and 2. Slider 4 moves along fixed guides t-t whose axis is perpendicular to axis Ox. Cross-piece BC 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 companion curve s-s of a cissoid of Diodes, with the equation ρD=0͞D=a/cos(ϕ)+a*cos(ϕ) or y²=x²(2a-x)/(x-a) where a = diameter of circle p-p, ϕ = polar angle between vector ρD and polar axis 0x. Curve s-s is a companion curve of a cissoid of Diocles, i.e. 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.
$1131$LG,Ge$

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Documents: Lever mechanisms  [Streambook]
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