Orthogonally Constrained 3D Schatz Linkage Bar, Evertible Cube

Orthogonally Constrained 3D Schatz Linkage Bar

Could we name the linkage system “Orthopython”?

I came up with this design while playing with Schatz’s Evertible (or invertible) Cube (https://www.thingiverse.com/thing:5089176), in search of a robust version for classroom use. For each bar, the two linkage axes are orthogonal to each other at all times, and any pair has an angle between -90 and +90 degrees. So the system is orthogonally constrained when all joints are fully extended.

In this particular design, a six-bar-ring does not evert (or invert) itself because of the constraints. However, one can build a cube belt ring of the central edges of a cube (when it is held vertically with respect to a main diagonal). One might just as well leave the two endpoints free for a flexible python-like system. When more pieces are added, the system becomes really interesting, esp. for young students, as illustrated in the figures.

For printing, please keep the bar(s) vertical to avoid using support. A raft is recommended for bed adhesion. The axis-to-axis distance is 50mm. The tight version is 0.2mm less than the regular loose version along the hole diameter.

References

1. Schatz, Paul (2013). The study of rhythms and technology : the evertible cube : polysomatic form-finding (4th Ed., P. Carline, Trans.). Niggli Verlag.
2. https://www.thingiverse.com/thing:5089176