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Straight Line Generators
Tchebicheff's Linkage
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Tchebicheff's straight line generator places the point P (the midpoint on the link BC) on a straight line at three points: the two extremes and at the center of travel. Between those points there is a small deviation. The proportions shown here are from Ref[1]. BC = 20, AD = 40, AB = DC = 50. This relationship assures that the link BC lies vertically when it is at the extremes of its travel.
DC = BC + SQRT(AB*AB - AD*AD)
Pafnuty Lvovich Tchebicheff or Chebyshev (b. 1821, d. 1894), the founder of the St. Petersburg Mathematical School, is remembered for his work on prime numbers and probability. He studied theoretical kinematics, particularly rectilinear motion.
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