Stanford Seminar - Cartography to shape morphing at many length scales

Key Concepts

• Soft Robotics
• Shape Memory Polymers (SMPs)
• Mechanical Bistability
• Targeted Shape Morphing
• Autonomous Deployment
• Conformal Mapping
• Auxetic Materials
• Lithography and Etching
• Glass Transition Temperature
• Stereographic Projection
• Kinematic Mechanisms
• Visco thermal elasticity

I. Introduction to Soft Robotics and Motivation

• The presenter clarifies that they are not a roboticist but study solder mechanics, design, and computation.
• Soft robotics involves designing and constructing robots with flexible bodies and electronics.
• Softness in robots implies bodies with stiffness much higher than the manipulated objects, where elasticity is negligible. Rigid robots have a finite number of controlled degrees of freedom.
• Soft robots present a continuum problem where every material bit deforms, making control complex.
• Examples of soft robots include the Vine Robot (Allison) and robots using kirigami patterns with magnetic discs (Renee J). These designs make it difficult to define the number of degrees of freedom.
• The goal is to simplify the control of continuously deforming elastic bodies by leveraging nonlinearity in mechanics.
• The presenter introduces two key mechanical systems exhibiting nonlinearity: light switches (bistability) and steady putty (visco thermal elasticity).
• The presentation aims to show how these ingredients can be applied to engineering systems to achieve interesting behaviors.

II. Autonomously Deploying Solar Panel Array

• This project demonstrates an autonomously deploying solar panel array that is entirely 3D printed.
• The actuation mechanism is distributed throughout the system, enabling 100% of the material to contribute to the deployment.
• The system achieves a targeted 10-fold aerial expansion.
• Shape memory polymers (SMPs) are used, which are thermal set presence that exhibit phase transformation at different temperatures.
• SMP Mechanism:
  1. Heating: Heat the SMP above its glass transition temperature ($T_g$), transitioning from a glassy to a rubbery phase.
  2. Deformation: Apply a mechanical deformation to change the shape from A to B.
  3. Cooling: Cool the SMP while maintaining the deformed shape to lock in the new shape in the glassy phase.
  4. Autonomous Recovery: Reheat the SMP above $T_g$ to autonomously recover the original shape.
• The solar panel array utilizes a compliant sheet affixed with solar PV cells and a structural frame.
• The design incorporates a ring inspired by the Hoberman sphere, simplified to scissor mechanisms.
• The rotational hubs in the scissor mechanisms are replaced with SMP hubs to inject elasticity, creating a preferred state.
• A flasher origami is used in the middle of the solar panel. The mechanics of folding is studied to control the folding pattern. Two possible fold patterns are identified, each with different energy minimums along the folding path.
• The entire structure, including the ring and origami, is 3D printed using SMPs with different transition temperatures.
• Submerging the structure in water at 45°C causes the SMPs to expand autonomously, deploying the solar panel.
• The system is robust because the actuation comes from the distributed string energy of the material, making it less dependent on a single point of actuation.

III. Targeted Shape Morphing Using Bistable Auxetic Metamaterials

• The objective is to morph a flat shape into a user-specified 3D shape and maintain that shape indefinitely without external forces.
• Bistability is used to achieve this.
• The presentation shows examples of conventional and bistable auxetic materials. Key features are opening and staying open, and isotropic expansion.
• The presenter discusses the potential to combine auxetic metamaterials with wafer fabrication to create flexible electronics that can be deployed into 3D shapes.
• A cornea shape is used as an example, and the amount of expansion needed to deploy a disc into this shape is calculated.
• The goal is to embed approximately 2,000 unit cells onto the cornea.
• Unit Cell Design:
  • The unit cell consists of four squares connected by slits.
  • Rotating the squares by a fixed angle results in an expansion.
  • This transformation is bistable.
  • The amount of opening ($\lambda$) can be controlled by changing the initial inclination angle ($\theta$) and the length of the inner square.
• Fabrication Process:
  1. Deposit two layers of polyimide.
  2. Apply a photoresist.
  3. Pattern the geometry using a digital masking system.
  4. Etch down the grooves.
  5. Peel off the structure.
  6. Perform a secondary etching.
• The mechanics of the unit cells are characterized. The force required to pull on the sheet is measured. The tension stiffness at the second equilibrium is controlled.
• The presenter explains how different $\lambda$ values across the sheet can lead to different expansion forces in different areas.

IV. 3D Shaping through Conformal Mapping and Deployment

• 3D shapes are achieved from 2D patterns through conformal mapping and by controlling $\lambda$. Conformal mapping flattens a 3D surface into a 2D plane while minimizing angular distortion.
• Stereographic projection is used to calculate the aerial change required to transform a disc into a hemisphere.
• For arbitrary meshes, an algorithm minimizes angular distortion while preserving isotropy.
• A grid is laid out on the flattened 2D mesh, and unit cells are assigned based on the $\lambda$ value at each location.
• The structure is deployed by pushing past its second equilibrium with an indentor and then releasing. Finite element analysis (FEA) confirms the process and shows that the deployed shape is at a strain energy minimum.
• The deployed structure can withstand mechanical loading, and different shapes can be created.
• As a demonstration, a parabolic surface is created to converge collimated light rays into a single point. The experimental results match the predictions from geometrical optics.
• The same behavior can be achieved on a larger scale using a laser cutter and natural rubber.
• The future work with NASA involves deploying structures with simple inflation-based mechanisms.

V. Material-Based Local Motion

• The goal is to combine bistability with shape memory polymers to achieve locomotion.
• A shape memory polymer is connected to a bistable mechanism. When the SMP extends autonomously, it pushes the bistable mechanism to the other state.
• Ores are connected to the bistable mechanism through a pivot, causing the system to swim backward.
• The time it takes to transition can be tuned using the thickness of the material.
• The 3D printer is used to manufacture materials with different glass transition temperatures, allowing for sequential motion.
• An example is shown where a robot swims forward, delivers a payload, and then swims back.

VI. Conclusion

• The presentation showed three projects that leverage shape memory polymers and mechanical bistability to achieve autonomous deployment, targeted shape morphing, and material-based locomotion.
• 3D printing is an essential tool for prototyping and demonstrating these concepts.

VII. Q&A Highlights

• In response to a question about folding the origami pattern, the presenter explains that the structure tends to fold into the second row of motion due to its lower energy requirement.
• The design of these mechanisms combines creativity, mathematical formulation, and computational optimization. The presenter expresses uncertainty about the role of AI in this process due to the difficulty of defining the problem and obtaining training data.
• The accuracy of simulations for these materials is high, but the computational cost is a limitation.
• There is a vocabulary of popular tessellations of patterns that tend to have desired geometric features.
• The morphing between shapes can be repeated many times, especially on larger scales.