Reversible cube

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Breaking down the cube into a central, reversible part ("cube chain") and two outer remains (identical "bolt bodies")
Inverted cube chain :
parts of the outer surfaces of the cube are now inside; the hollow cube is indicated by six edges (three of the six remaining edges would be the extensions of the three joints on the outside)

The reversible cube (belt) is an invention by Paul Schatz , who developed a theory of motion from it, which he called inversion kinematics.

A third of the volume can be removed from a cube from two diagonal corners in such a way that the remainder lying between them and hinged to form a chain at the edges can be turned inside out, i.e. reversed from the inside out.

The chain consists of six identical, irregular tetrahedra . Their articulated connections are at their joints that they had in the cube. The chain links can be rotated together around themselves (each around its own longitudinal axis). Reversible cube means that there is a position in which the links partially enclose a cube, now a hollow cube.

Three of the pairs of opposite corner points of the original cube are located in opposite joints of the chain. In this, they have the same distance in every position as in the cube, namely the length of its spatial diagonal. Schatz observed the path that such a diagonal takes when the chain was turned inside out and discovered the oloid . If one fixes one of the six tetrahedra and observes the path of the diagonal opposite it, one recognizes that the area swept over by it is the surface ( ruled surface ) of a geometric body. Schatz called this body Oloid.

Schatz described the everting movement of the chain of cube in an endless, rhythmically pulsating sequence as an inversion movement and assumed that it had found a form of movement that was just as original as translation and rotation . Schatz also considered all platonic solids to be invertible. But only the inversion of the cube became known. The inversion kinematics established by Schatz has so far been limited to this special case.

Schatz developed a number of technical applications, all of which are based on the invertible cube or the oloid. One example is a mixer made up of three links in the cube chain. Such a mixer, in which two of the three links are driven and the middle link carries the mixing container, was produced by Schatz during his lifetime . The moving oloid is used to circulate and stir liquids.

The television broadcaster WDR used an animation of the cube chain as a transmitter logo in the 1970s.

The project SmartInversion the company Festo created a filled with helium flying object which travels within the meaning of inversion kinematics.

The oloid has become a popular item for artists and for crafting and playing.

Individual evidence

  1. ↑ A current product is the Turbula mixer ( [1] )
  2. ↑ Oloid stirrer
  3. ↑ SmartInversion - floating link chain with inversion drive. Retrieved March 29, 2018 .

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