I have worked on the geometry of shape-changing polyhedra (SCP) since 1969. An introduction the logic of this geometry can be seen in a paper I delivered to the Bridges Conference this August, 2016: http://archive.bridgesmathart.org/2016/bridges2016-225.pdf. Examples of four SCP cores and shells can be seen below in the short movie clips and animations below.
New technologies have created new possibilities for SCPs. Certain polymers can be heated to expand or contract according to currents controlled by a micro-processor – functioning as code controlled hinges. Servos of various types and sizes as well as hydraulics can similarly be controlled. Various other technologies under development will eventually lead to a wide variety of practical shape shifting objects. Potential applications are endless and include things like packages that expand or contract to fit their contents; super tools that change their shape based on the needed function; robots and solar panels that fold up from a single sheet; shape changing aircraft, see shape transforming furniture, and transforming architectural forms. My work on shape changers is featured in my new book “3D Thinking,” to be published by Thames and Hudson Spring 2017. There is a logic to developing and extending shape-changers. Examples of SCPs follow where any module shown can repeat infinitely in space and can be macro, micro, or nano sized.
Core 1 – Extended Shell 1
Core 1 – Extended Shell 1 – Two Combined – Shows “Equilibrium” Positions. Equilibrium Positions are various stable positions / positions of balance for the shape changing polyhedra.
Core 1 – Extended Shell 1 – Multiple Combined – Shows Various Equilibrium Positions
Core 2 – Extended Shell 2
Core 2 – Extended Shell – Multiple Combined
Core 3 – Extended Shell 3
Core 12 – Shell 12
MIT: Fold Up Robot