Uploaded July 2024 | Updated September 2026, 2 days ago
Supplemental video for the paper:
Kinematic Modeling of a Flat-foldable Auxetic Metamaterial
Huijuan Feng, Wujie Shi, Pino Trogu, and Jian S. Dai, Fellow, IEEE
Presented at ReMAR 2024 -- The 6th IEEE/IFToMM International Conference on Reconfigurable Mechanisms and Robots
Music by Mauro Panzeri: "Looping 2006 07"
The first part of the video shows a 3D-printed replica of a transformable, flat-foldable shape designed in 1996 by the Italian topology researcher Giorgio Scarpa, consisting of a prismatic tetrahedron with additional hinges which bisect the walls of the extruded prisms. The shape is shown in the transition from the unfolded state to the flat-folded state, with outward flat-folding induced by the deformation of the creases. The reverse motion is then shown, along a different folding path, back to the original configuration.
The second part of the video shows a similar model, modified to include additional bisecting hinges along the diagonal of eight of the twenty-four square plates in the extruded tetrahedral unit cell. This modified shape is also shown in the transition from the unfolded state to the flat-folded state and back. Two transitions are shown: (1) Inward rigid flat-folding enabled by the additional creases with return to the unfolded state; and (2) Outward rigid flat-folding of the altered model similar to the original one, also with return to the initial unfolded state.
Authors:
Huijuan Feng, Wujie Shi and Jian S. Dai are with Shenzhen Key Laboratory of Intelligent Robotics and Flexible Manufacturing Systems, Southern University of Science and Technology, Shenzhen 518055, China
Pino Trogu is with the School of Design, San Francisco State University, San Francisco CA 94132 USA -- Corresponding author e-mail: trogu@sfsu.edu
Article abstract:
Although many metamaterials can change shape, this flexibility often comes at the expense of the structural integrity which is difficult to preserve in their reconfigured mode. In this work, we introduce a transformable, flat-foldable shape designed in 1996 by the Italian topology researcher Giorgio Scarpa, consisting of a prismatic tetrahedron with additional hinges which bisect the walls of the extruded prisms. The shape is rigid when unfolded, and when scaled into a periodic, space-filling honeycomb, it yields a flat-foldable, prismatic metamaterial that preserves its developed, structurally sound unfolded state in the absence of external stimuli or mechanical loads. However, this new metamaterial is still kinematically rigid when only revolute hinges are admitted. To overcome the limitation that this improved design still relies on bending of the plates and torsional hinges, we introduce additional bisecting hinges along the diagonal of eight of the twenty-four square plates in the extruded tetrahedral unit cell. This modified design, now with only rigid plates and revolute hinges throughout the material, preserves both the rigidity and the flat-foldability, while also introducing the rigid foldability due to the presence of the additional diagonal hinges. A kinematic analysis of the folding motion of the tetrahedral unit cell is presented, showing how this bisecting technique can be generalized to yield auxetic metamaterials with both rigid foldability and negative Poisson’s ratio. The straightforward bisecting of rigid plates connected by standard revolute hinges offers great opportunity for the design of reconfigurable metamaterials, mechanisms, and robots that combine flat-foldability and self-supported structural integrity when unfolded.
Link to article: static.trogu.com/documents/conference/2024_remar/feng_shi_trogu_dai_REMAR2024.pdf
Supplemental video for the paper:
Kinematic Modeling of a Flat-foldable Auxetic Metamaterial
Huijuan Feng, Wujie Shi, Pino Trogu, and Jian S. Dai, Fellow, IEEE
Presented at ReMAR 2024 -- The 6th IEEE/IFToMM International Conference on Reconfigurable Mechanisms and Robots
Music by Mauro Panzeri: "Looping 2006 07"
The first part of the video shows a 3D-printed replica of a transformable, flat-foldable shape designed in 1996 by the Italian topology researcher Giorgio Scarpa, consisting of a prismatic tetrahedron with additional hinges which bisect the walls of the extruded prisms. The shape is shown in the transition from the unfolded state to the flat-folded state, with outward flat-folding induced by the deformation of the creases. The reverse motion is then shown, along a different folding path, back to the original configuration.
The second part of the video shows a similar model, modified to include additional bisecting hinges along the diagonal of eight of the twenty-four square plates in the extruded tetrahedral unit cell. This modified shape is also shown in the transition from the unfolded state to the flat-folded state and back. Two transitions are shown: (1) Inward rigid flat-folding enabled by the additional creases with return to the unfolded state; and (2) Outward rigid flat-folding of the altered model similar to the original one, also with return to the initial unfolded state.
Authors:
Huijuan Feng, Wujie Shi and Jian S. Dai are with Shenzhen Key Laboratory of Intelligent Robotics and Flexible Manufacturing Systems, Southern University of Science and Technology, Shenzhen 518055, China
Pino Trogu is with the School of Design, San Francisco State University, San Francisco CA 94132 USA -- Corresponding author e-mail: trogu@sfsu.edu
Article abstract:
Although many metamaterials can change shape, this flexibility often comes at the expense of the structural integrity which is difficult to preserve in their reconfigured mode. In this work, we introduce a transformable, flat-foldable shape designed in 1996 by the Italian topology researcher Giorgio Scarpa, consisting of a prismatic tetrahedron with additional hinges which bisect the walls of the extruded prisms. The shape is rigid when unfolded, and when scaled into a periodic, space-filling honeycomb, it yields a flat-foldable, prismatic metamaterial that preserves its developed, structurally sound unfolded state in the absence of external stimuli or mechanical loads. However, this new metamaterial is still kinematically rigid when only revolute hinges are admitted. To overcome the limitation that this improved design still relies on bending of the plates and torsional hinges, we introduce additional bisecting hinges along the diagonal of eight of the twenty-four square plates in the extruded tetrahedral unit cell. This modified design, now with only rigid plates and revolute hinges throughout the material, preserves both the rigidity and the flat-foldability, while also introducing the rigid foldability due to the presence of the additional diagonal hinges. A kinematic analysis of the folding motion of the tetrahedral unit cell is presented, showing how this bisecting technique can be generalized to yield auxetic metamaterials with both rigid foldability and negative Poisson’s ratio. The straightforward bisecting of rigid plates connected by standard revolute hinges offers great opportunity for the design of reconfigurable metamaterials, mechanisms, and robots that combine flat-foldability and self-supported structural integrity when unfolded.
Link to article: static.trogu.com/documents/conference/2024_remar/feng_shi_trogu_dai_REMAR2024.pdf
