Bitriangular Lattice Actuation Truss

These animations go together with the paper Energy-Efficient Actuation in Infinite Lattice Structures, which you can download as a PDF or a figureless PostScript. The animations can be accessed from the PDF file by using a browser with Acrobat, but they are given here in case you want to view them separately in another browser. They are animated GIFs, so Netscape or Internet Explorer (or Konqueror, or most other browsers) should display them fine. If you need these animations in another format (AVI, MPEG, etc.) and don't know how to do the conversion yourself, contact Aleksandar at

    Each of the arc lengths in the bitriangular lattice can be changed periodically without changing the lengths of the other bars. The next three figures show this for the three active (green) arcs per unit cell. It should be clear from the illustrations that changing the length of each of the three active arcs does not require changing the length of the other arcs (to first order) and also induces a global strain (lattice deformation) in the infinite network:

  1. Figure 1
    First activation mode
  2. Figure 2
    Second activation mode
  3. Figure 3
    Third activation mode
  4. By combining actuations in the three active arcs, one can induce any global strain. The next two illustrations show how to contract (strain=-identity) or expand (strain=+identity) the infinite network using the three active arcs per unit cell:

  5. Figure 4
    Contracting the structure
  6. Figure 5
    Expanding the structure
  7. The previous animations were only for small deformations (though for visualization purposes the actual deformations were large). However, since isostaticity is a generic property, it is actually possible to achieve (almost) any large global deformation without changing the length of the inactive arcs. This however requires solving a system of ODEs to determine how to adapt the actuation (i.e. how to change the lengths of the active bars) in time.

    The following two animations illustrate this for the bitriangular lattice network. The first one shows the large deformation that we are trying to achive: It consists of shrinking the unit cell by 25% and also making it into a square (from the original rhomboid with 60-degree angle). Although this may not be possible to see with naked eye, the lengths of the red bars are unchanged to several decimal places during this actuation!

  8. Figure 6
    A large deformation: Lattice
  9. Figure 7
    A large deformation: Actuation