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FOUR-BAR SLIDING-LINK MECHANISM FOR TRACING LOGARITHMIC SPIRALS

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Slider 1 turns about fixed axis A. Link 3 moves in slider 1. Roller 2 rotates about axis D-D. When slider 1 turns about axis A, roller 2, cutting into the surface of the drawing with its sharp edge, moves during each instant along a straight line coinciding with the plane of the roller. The envelope of the successive positions of this straight line is a logarithmic spiral with the polar equation, with respect to pole A, ρ=a*e^( ϕ/tan(α)) where ρ=A͞K, ϕ=angle of rotation of radius vector ρ, a=A͞B = initial value of the radius vector, e = base of natural logarithms α = angle between axis AK and the plane of roller 2.
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Documents: Lever mechanisms  [Streambook]
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