A Multi-Stable Curved Line Shape Display

Wing-Sum Law, Sofia Wyetzner, Raymond Zhen, and Sean Follmer
  Paper  | ICRA 2024

From left to right: 1. the curved line display with the bias, extrude, and translate motions indicated, 2. a person using their hand to explore the curved line display, and 3. a multi-segment simulation of the curved line display making the shape of a Talbot

In this work, we present a multi-stable curved line shape display, with which we are able to display high curvature, smooth shapes by bending the ends of a flexible rod. We used a discrete elastic rods simulation to inform our actuation strategy, and demonstrated the display's ability to display a variety of shapes consistent with simulation results.

Curved lines are present in many designs, but are difficult to represent on shape-changing displays. One way to overcome this limitation is by bending smooth, flexible materials. Due to system multi-stability, we model the system and determine the actuation method using separate initializations for a discrete elastic rods model (M. Bergou et al. 2008).

Top left image indicates the node mechanical hardware for biasing and extruding. Bottom left image indicates the node mechanical hardware for translating. Right column shows the steps of actuation, described below in the caption.

Shape generation occurs by (1) extruding enough material to allow biasing, (2) biasing toward the central control point (the pink circle), (3) extruding until the interior rod is the desired arc length, (4) biasing to match desired boundary conditions, and (5) translating to desired height difference. Actuation steps pictured are annotated still frames pulled from a video of the device being operated.

 

Animation of the steps listed in the caption above.

Animation of the actuation steps.

 

Over a total of 16 different shapes, the overall mean standard deviation within N = 3 trials over all 16 shapes of 0.75 mm (0.47% of the display’s maximum vertical range). These results show that our curved line display can consistently generate the same shape given the same actuation instructions over a variety of different shapes. For nearly all of the shapes, there is good agreement between the simulation and the physical display. Excluding the two shapes marked with **, the mean RMSE between the height physical display and our model was 6.68 mm (3.85% of the display’s maximum vertical range).

 

Eight graphs showing the results of the physical display compared to those of the discrete elastic rods simulation.

We were unable to match the physical display for the two shapes marked with **. Both of these shapes had a stable “peak” shape on the physical display, but when we simulated the display using those boundary conditions, the final shape collapsed into the other stable configuration. If the rightmost boundary condition is allowed to be more horizontal, we can simulate a shape with better agreement with the physical system (curves marked with * in the rightmost column of the figure below). We hypothesize that the discrepancy between the physical display and the simulation is due to some unintended compliance in the system.

The poster we presented at ICRA 2024:

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