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FOUR-BAR CROSSED-CRANK LINKAGE FOR DRAWING LEMNISCATOIDS

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The lengths of the links comply with the conditions: A͞D=B͞C=2b and A͞B=D͞C= a. Figure ABCD is a crossed-crank linkage. When crank 1 or 2 turns about fixed axis A or D, point K at the middle of connecting rod 3 describes a lemniscatoid with the equation (x²+y²)² =a²(x²-y²)-4b²y². If the lengths of the links comply with the condition a=sqrt(2)b then point K describes a figure-of-eight curve, or Bernoulli lemniscate.
$767$LW,Ge$

Linked items
Mechanisms: Four-bar crossed-crank linkage for drawing lemniscatoids
Documents: Lever mechanisms  [Streambook]
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