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ARTOBOLEVSKY LEVER-GEAR MECHANISM FOR TRACING PEDAL CURVES OF CYCLOIDS OF CIRCLES

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Gear 3 meshes with fixed gear rack 1 and is connected by turning pair L to cross-shaped slider 2 which moves along fixed guides b-b. Slider 2 is connected by turning pair P to slider 5 which moves along axis Md of T-shaped link 4. Link 4 is connected by turning pair M to gear 3 and its crosspiece t-t moves in cross-shaped slider 7 which has guides perpendicular to each other. Slider 7 moves along axis On of link 6 which turns about fixed axis 0. The dimensions of the links comply with the condition: M͞L=L͞P=r, where r is the pitch radius of gear 3. When slider 2 travels with translational motion along guides b-b, gear 3 rolls along rack 1 and point M describes cycloid q of a circle of radius r, with the parametric equations x=rθ-r sin(θ) and y=r-r cos(θ). Point D of slider 7 describes pedal curve s-s of cycloid q with its centre at point 0. The parametric equations of the pedal curve are η=r(1-cos(θ)-(θ/2)sin(θ)) and ξ=r[(θ/2)(1+cos(θ)-sin(θ)] where θ is angle MLP.
$2476$LrG,Ge$

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