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ARTOBOLEVSKY FOUR-BAR LINK-GEAR MECHANISM FOR TRACING CISSOIDS OF DIOCLES

The length of the links comply with the condition: A͞D=A͞B=a/2. 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 Ox. Cross-piece AB of slide 4 is connected by turning pairs A and B to link 5 and slider 3. Link 5 is connected by turning pair D to slider 2. When link 1 turns about axis 0, point D of slider 2 describes a cissoid of Diocles. This is the cissoid of circle p-p, of radius and passing through point 0 , and of straight line q-q tangent to circle p-p at point G. The equation of the cissoid of Diocles is ρD=0͞D=a/cos(ϕ)-a*cos(ϕ) or y²=x³/(a-x) where ϕ is the polar angle between vector ρD and polar 0x.
$1128$LG,Ge$