Inversor from Hart

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Inversor of Hart rods of the same color are of the same length

The Inverter durum (also inversion gear of hard ) is a linear bearing mechanism and a planar coupling mechanism which converts a circular motion into a straight line motion, and vice versa. It is related to the Peaucellier inversor . The way it works is based on the fact that a circle through the center of a geometric inversion is always mapped as a straight line.

The mechanism was found by Harry Hart (1848–1920) in 1874 and published the following year. The Hart inverse has six limbs, the four larger ones form an antiparallelogram . The trajectory of a link point is overall symmetrical. There is also a second form having five members and an A-shaped frame (engl. A-frame ). Sylvester and Kempe found a generalization to Hart's Inversor, the so-called Quadruplanar Inversor .

  • Hart's A-Frame - the short rods are half as long as the long rods, the central rod is connected to the long rod for a quarter of its length

  • Dimensions:
    AB = 4
    AC = BD = 4
    CE = ED = 2
    Af = Bg = 3
    fC = gD = 1
    fg = 2

  • Dimensions:
    AB = Bg = 2
    AC = AE = 3
    CD = EF = 12
    EC = FD = 6
    Cp = pD = 6
    Eg = 6

literature

  • Hart: On Certain Conversions of Motion. In: Messenger of Mathematics. NS vol. 4 (1875), pp. 82-88, 97-100, Hathi Trust (accessed March 25, 2016)
  • Hart: A parallel motion. In: Proceedings of the London Mathematical Society . vol. 6 (1874–1875), pp. 137–139, Hathi Trust (accessed March 25, 2016)
  • Norbert Treitz: Physical conversations: The antiparallelogram (II). In: Spectrum of Science. May 2006, Spektrum.de (accessed on March 25, 2016)

Individual evidence

  1. ↑ Evert A. Dijksman: On the History of Focal Mechanisms and Their Derivatives. In: International Symposium on History of Machines and Mechanisms. Proceedings HMM2004, pp. 303-314, Google Book (accessed March 25, 2016)
  2. ↑ Evert A. Dijksman: True Straight-line Linkages Having a Rectilinear Translating bar. In: Advances in Robot Kinematics and Computational Geometry. 4th Workshop, 1994, pp. 411–420, TU Eindhoven (accessed on March 25, 2016)
  3. ↑ Inversor (according to Hart), description of the mechanism in the DMGLIB (accessed on March 25, 2016)
  4. ^ Sylvester-Kempe Inversor, Kinematic Model by Martin Schilling, Smithsonian (accessed March 25, 2016)

Web links

Commons : Inversor von Hart  - collection of images, videos and audio files