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LINK-GEAR CONICOGRAPH MECHANISM WITH A STRAIGHT ENVELOPING LINE

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The lengths of the links comply with the conditions: A͞D=D͞C=C͞B=B͞A. Figure ADCB is a rhombus linkage. Link 1, turning about fixed axis 0, is connected by a sliding pair to slider 2 and by turning pair A to links 3 and 6. Link 7 moves in sliders 8 and 9, and is connected by turning pair D to links 5 and 6. Links 4 and 5 turn about fixed axis C. Slider 8 is connected by turning pair B to links 3 and 4. Sliders 2 and 9 are connected together by turning pair M. When link 1 turns about axis 0 , point M describes a conic section with the equation ρ=p/(1+e*cos(ϕ)) where ρ=0͞M, p=(0͞C²-0͞A²)/20͞A, e=0͞C/0͞A, ϕ = polar angle between vector ρ and the polar axis Ox. Point M describes an ellipse when e<1, a parabola when e=1 and a hyperbola when e>1 . At the same time, straight line Dd envelops the conic section traced by point M.
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Documents: Lever mechanisms  [Streambook]
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