Robotics Science

YouTuber 36AM3B has lots of cool deployable-structure models in his channel, including an expanding frame (visible to the rear in this video) made from 5 of the 6-bar linkages shown here. I got interested in Bricard linkages because of this recent model from Thingiverse user raju, which purports also to be a 6-bar Bricard linkage but looks, to me, an awful like what I’ve always called a kaleidocycle or flexahedron. And I don’t really know enough about any of them to understand the fine distinctions. Can somebody help me out?

5 thoughts on “Paper model of expanding 6-bar Bricard linkage

  1. The thing at thingiverse is a kaleidocycle, as described in a called _M. C. Escher Kaleidocycles_ by mathematician Doris Schattschneider and designer Wallace Walker (originally published in 1977, but still available). Kaleidocycles are linked rings of tetrahedra that can be turned “inside out” endlessly.

    The best theoretical explanation of kaleidocycles is at

    If you want to make a kaleidocycle we have a website that lets you upload 4 photos and maps them onto a kaleidocycle pattern.

    Flexagons are flat models, some of which can be turned inside out endlessly. Others can be folded and unfolded to reveal hidden faces, but have backwards-forwards motion. Martin Gardner wrote about them, and I think I saw the square one on the back of a cereal box a while ago.

  2. Thank you very much! I spent a lot of time yesterday trying to read about Bricard linkages on the web but couldn’t find much information, and I thought maybe the kaleidocycle was somehow a special case of the Bricard linkage, but the model in the video doesn’t “endlessly” rotate. It’s got clear endpoint configurations.

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I am descended from 5,000 generations of tool-using primates. Also, I went to college and stuff. I am a long-time contributor to MAKE magazine and My work has also appeared in ReadyMade, c't – Magazin für Computertechnik, and The Wall Street Journal.

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