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ARTOBOLEVSKY LINK-GEAR MECHANISM FOR TRACING THE CONCOMITANT CURVES OF CISSOIDS OF ELLIPSES

Abstract

The lengths of the links comply with the conditions: D͞K=a and D͞C=b, where a and b are the semiaxes of ellipse p-p. Link 1 turns about fixed axis 0 and is connected by sliding pairs to sliders 7 and 3. Cross-shaped slider 4 moves along fixed guides t-t whose axis is perpendicular to axis Ox. Slider 4 is connected by a sliding pair to slider 5 and by turning pair B to slider 3. Link 6 is connected by turning pairs C, D and K to sliders 5, 7 and 2. Slider 2 is connected by a sliding pair to slider 4. When link 1 turns about axis 0, point D of link 6 describes concomitant curve s-s of the cissoid of ellipse p-p and of straight line q-q which is tangent to the ellipse at point G. The equation of concomitant curve s-s is ρD=0͞D=(4a/cos(ϕ))-((2(b²/a)cos(ϕ))/(sin²( ϕ)+(b²/a²)cos²( ϕ))) or y²=(b²/a²)((x²-2a)/(4a-x)) where ϕ ist he polar angle between vector ρD and polar axis 0x. $1195$LG,Ge$

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