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ARTOBOLEVSKY LINK-GEAR MECHANISM FOR TRACING OBLIQUE PARABOLIC FOLIA

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Link 1 turns about fixed axis 0 and is connected by sliding pairs to slider 3 and to cross-shaped slider 2 which has guides perpendicular to each other. Slider 3 is connected by turning pair A to slider 4 which moves along fixed guides p-p whose axis is perpendicular to axis 0x. Cross-piece Ad of slider 3 is connected by a sliding pair to slider 6. Slider 6 is connected by turning pair B to slider 5 which moves along fixed guides q-q whose axis is perpendicular to axis 0y. Cross-piece Be of slider 6 is connected by a sliding pair to slider 7. Slider 7 is connected by turning pair C to slider 5 which moves along guides p-p. Cross-piece Cf of slider 7 is connected by a sliding pair to slider 2. Since axes 0c, Ad, Be and Cf are perpendicular to each other in this order, figure DABC is always a rectangle. When link 1 turns about axis 0, point D of slider 2 describes oblique parabolic folium s-s with the equation ρD=0͞D=a(1-tan²(ϕ)+b*tan(ϕ))/cos(ϕ) or x³=a(x²-y²)+bxy where ϕ is the polar angle between vector ρD and polar axis 0x.
$1183$LG,Ge$

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