More detailed slo-mo --- https://www.youtube.com/watch?v=H7ZIBb8kSVk Some references following Chen, Guest, Fowler, Feng "Symmetry Adapted Analysis of the Hoberman Switch-Pitch Ball" http://www2.eng.cam.ac.uk/~sdg/preprint/IASSSwitchPitch.pdf << The Hoberman Switch-Pitch ball is used as the inspiration for a symmetry analysis of a novel type of deployable structure. The underlying structure of the Switch-Pitch is essentially cubic, consisting of eight nodes that are connected via revolute joints to twelve linking bars, each of which is connected to two nodes. A simple mobility count suggests that the structure is over-constrained, but a symmetry mobility analysis shows that the structure is in fact mobile, and retains tetrahedral symmetry as it folds. >> WFL On 7/17/17, James Propp <jamespropp@gmail.com> wrote:
I made a slo-motion video of a Hoberman Flip-Out wobbling between blue-in and blue-out states:
https://m.youtube.com/watch?v=VC_KKTGWIOY
Has anyone tried to analyze this phenomenon?
Qualitatively it seems clear what's going on: centrifugal force (or whatever we're supposed to call it since it's not "really" a force) causes the thingies to spin out, and they overshoot, so then centrifugal force spins them the other way, and so on. But that's only a crude sketch of the dynamics. The Flip-Out has only one configurational degree of freedom, so it might be possible to solve it analytically and figure out the period of the oscillation (as a function of the position of the axis and the angular velocity), at least if it's rotating about some axis of symmetry.
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun