It was established by Professor O'Rourke and others that a 3-D, open polygonal chain of five links can be "locked" -- there is no way to reconfigure it without passing one link through another. All links are rigid, and all joints universal. It is however an unsolved problem to determine if a chain whose links are the same length can lock.
Motivated by protein folding, we have been examining chains of cylinders (rather than segments). We believe we have constructed an example of five equal-length cylinders that are locked. The axes of the cylinders are shown in the figure below. This configuration has the property that the first and last links are equidistant from three other links. We found this configuration via gradient descent search in a four-dimensional configuration space.
I will continue working on this topic for my honors thesis.
Advisor: Joseph O'Rourke
This work was supported by the Schultz Foundation.