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ARTOBOLEVSKY LINK-GEAR HYPERBOLOGRAPH

Slider 1, moving along fixed guides q-q, has cross-piece CB which is connected by turning pair B to link 3, and cross-piece Cm which moves in slider 5. Link 3 is connected by a sliding pair with slider 2 and moves in slider 4 which turns about fixed axis A. Sliders 2 and 5 are connected together by turning pair D . When slider 1 moves along guides q-q, point D describes hyperbola p-p with the equation ex²+efxy+y²+2gx+2hy=0 where e=tan(α)tan(β), f=-(tan(α)+tan(β ))/2, g=c*tan(α)tan(β)/2, h=((b-c)tan(α)-b*tan(β))/2, b and c = constant dimensions of the mechanism. The axis of guides q-q makes the angle a with the direction CB and axis Ax. The axis of cross-piece Cm of slider 1 makes the angle β with axis Ax and angle 180°-β with the direction CB. If c = 0, α=45° and β=135° , then point D describes an equi lateral hyperbola with the equation x²-y²-2by=0.
$1074$LG,Ge$