@article{13188,
  abstract     = {The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length.
We also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics.},
  author       = {Hafner, Christian and Bickel, Bernd},
  issn         = {1557-7368},
  journal      = {ACM Transactions on Graphics},
  keywords     = {Computer Graphics, Computational Design, Computational Geometry, Shape Modeling},
  number       = {5},
  publisher    = {Association for Computing Machinery},
  title        = {{The design space of Kirchhoff rods}},
  doi          = {10.1145/3606033},
  volume       = {42},
  year         = {2023},
}

@article{9376,
  abstract     = {This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes.},
  author       = {Zhang, Ran and Auzinger, Thomas and Bickel, Bernd},
  issn         = {1557-7368},
  journal      = {ACM Transactions on Graphics},
  keywords     = {multistability, mechanism, computational design, rigidity},
  number       = {5},
  publisher    = {Association for Computing Machinery},
  title        = {{Computational design of planar multistable compliant structures}},
  doi          = {10.1145/3453477},
  volume       = {40},
  year         = {2021},
}