Schatz Linkage, Evertible Cube, Oloid

Schatz Linkage, Evertible Cube

The Schatz Linkage is illustrated in great details by Schatz in his book (2013/1975). It looks simple but is full of wonderful mathematical ideas, which can be hard to imagine without a physical model. It is, in essence, based on an evertible (invertible) cube and is the foundational structure of the oloid. The linkages bars are 80mm center to center, measuring 98mm from end to end. They can be printed in vertical position; a raft, with or without support, will help with bed adhesion. Once assembled, you can turn the either one of the axles to twist the linked pieces. Please also try to rock the middle bar and see what happens. Have fun!

References

1. Schatz, P. (2013/1975). The study of rhythms and technology: The evertible cube | polysomatic form-finding (P. Carline, Trans.). Sugen: Niggli Verlag (Original work published 1975 in German).
2. Bu, L. (2023). The oloid and the evertible cube: 3D design and printing. In J. Holdener, E. Torrence, C. Fong & K. Seaton (Eds.), Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture (pp. 417-420). Halifax, NS: Tessellations Publishing. https://archive.bridgesmathart.org/2023/bridges2023-417.html#gsc.tab=0