topo gear

This page contains supporting movies for the paper Topological design of geared metamaterials by Anne S. Meeussen, Jayson Paulose, and Vincenzo Vitelli at the Instituut-Lorentz for theoretical physics, Leiden University.

Video summary

Movie link



Supplementary movie 1
A gear lattice with a flexible edge

The rigidity of a prototype geared metamaterial is probed manually. The top and bottom edges are pinned down but the rest of the lattice is free. It is rigid everywhere except at one edge, picked out over the other by a nontrivial topological characterization, called the polarization RT, of the underlying spectrum of mechanical excitations.

Supplementary movie 2
Weyl points with nontrivial winding

The animation shows the numerically-obtained determinant of the compatibility matrix C(k) over the hexagonal Brillouin zone for a series of hexachiral unit cells. The polarization is RT=0 for the first lattice in the series and RT=-a1 for the last lattice in the series. The change in polarization is effected by zeroes of det C(k) (white dots) with nontrivial topological windings sweeping through the Brillouin zone.

Supplementary movie 3
Stable and unstable geared metamaterials

The video is a composite of experiments on two prototypes with free boundaries, one of which pushes back against external compression while the other collapses completely. The difference is due to the real-space topology of the link network, which has odd-sided plaquettes for the lattice on the left and even-sided plaquettes for the lattice on the right. Odd-sided plaquettes frustrate global rotation of gears, which counterintuitively provide stability to the lattice on the right.