cs.ROApr 3, 2026

Elastomeric Strain Limitation for Design of Soft Pneumatic Actuators

Authors: Gregory M. Campbell

Organizations: Mechanical Engineering and Applied Mechanics Presented to the Faculties of the University of Pennsylvania

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

Modern robots embody power and precision control. Yet, as robots undertake tasks that apply forces on humans, this power brings risk of injury. Soft robotic actuators use deformation to produce smooth, continuous motions and conform to delicate objects while imparting forces capable of safely pushing humans. This thesis presents strategies for the design, modeling, and strain-based control of human-safe elastomeric soft pneumatic actuators (SPA) for force generation, focusing on embodied mechanical response to simple pressure inputs. We investigate electroadhesive (EA) strain limiters for variable shape generation, rapid force application, and targeted inflation trajectories. We attach EA clutches to a concentrically strain-limited elastomeric membrane to alter the inflation trajectory and rapidly reorient the inflated shape. We expand the capabilities of EA for soft robots by encasing them in elastomeric sheaths and varying their activation in real time, demonstrating applications in variable trajectory inflation under identical pressure sweeps. We then address the problem of trajectory control in the presence of external forces by modeling the pressure-trajectory relationship for a concentrically strain-limited class of silicone actuators. We validate theoretical models based on material properties and energy minimization using active learning and automated testing. We apply our ensemble of neural networks for inverse membrane design, specifying quasi-static mass lift trajectories from a simple pressure sweep. Finally, we demonstrate the power of multiple pressure-linked actuators in a proof-of-concept mannequin leg lift.

Figures & tables

DescriptionExamplesDegrees of FreedomNumber of MaterialsExtensible/ Inextensible 1 1 1 We will consider extension and extensible materials in the same way Baines describes shape change [ 9 ] : ”there is a valid non-identity stretch tensor U in the polar decomposition of the deformation gradient F .” Simply put, if the relative distance of two points on a body changes then there has been material stretch and that body has extended. The difference between an inextensible pressure chamber and an extensible pressure chamber is the difference between an air mattress and a balloon. An air mattress goes from an uninflated state to an inflated state: the membrane unfolds but does not undergo substantial stretch. The membrane of the balloon, on the other hand, stretches, extended from an unfolded shape to a new, larger shape.
Single Response
Pneunet[ 4 , 10 ]Bend1 +E
Limited Tube[ 11 , 12 , 13 ]Extend/Bend/Twist2E
FREE / PAM[ 14 , 15 , 16 , 17 ]Contract/Extend/Twist1-2I 2 2 2 Though these are often made with extensible materials, they are characterized by their enclosure in inextensible fibers. This fundamentally differentiates them from limited tube/surfaces, which have additional opportunity for unrestricted expansion.
Limited Surface[ 18 , 19 , 20 , 21 ]Extend/Complex2E
Bellows[ 22 , 23 ]Extend/Bend1I
Table 1.1: Soft pneumatic actuators with embedded trajectory response to pneumatic input.
Figure 2.1: A. Actuator expansion formed into three different shapes; shape chosen by clutch activation. Top-view presented over side-view. B. Expansion of soft, elastomeric actuator to 3.1 kPa under three different clutch activation configurations. C. Soft actuator manipulation of 3.7 g ball. D. Manipulation of 820 g textbook.
Figure 2.2: System Overview. A. Overview of actuator test system with labels. B. Model of silicone membrane with clutch locations superimposed. Model includes stiff silicone reinforced with fabric, soft unsupported silicone, four outboard clutches, and one inboard clutch. C. Clutch is highlighted with yellow. i) Outboard clutch is activated and restricts membrane expansion. ii) Outboard clutch is deactivated and membrane is free to expand.
Figure 2.3: Circuit Diagram. Clutch circuit diagram, building upon Diller et al.’s [ 51 ] .
Figure 2.4: Depth camera data (left), simulation (center), and experimental system (right) for actuator shape comparison at 3.1 kPa. A. Plateau shape. B. Round shape. C. Pyramidal shape.
Figure 2.5: Mode 1 Actuator Characterization. A. Plot of actuator workspace along 4 DoF, looking at the actuator from a top-down view. Each DoF is accessed by activating a different set of clutches. Photos of corresponding positioning of 40 mm diameter ball. B. Plot that tracks position of ball once it has been placed on the actuator. The actuator lifts it to the specified direction and then releases the inboard clutch to rapidly apply force to the ball in the desired direction. Photos of corresponding projectile motion for 40 mm diameter ball. C. Labeled photo of actuator with directions and DoFs.
DoFDirectionForce (N)Std (N)
DoF 1Back-Right1.20.21
Front-Left1.40.28
DoF 2Front-Right1.10.41
Back-Left1.40.19
DoF 3Front2.40.35
Back2.70.72
Table 2.1: Forces and Standard Deviations for Each DoF and Direction.
Figure 2.6: Mode 2 Manipulation. A. Textbook lifted and tilted by pneumatic inflation to 3.1 kPa during right clutch activation. B. Textbook returned from tilt by clutch deactivation. C. Vicon data for textbook roll angle response to inflation under clutch activation and to clutch deactivation.
Figure 3.1: (left) Silicone-sheathed electrostatic clutch. On-state properties are controlled electronically via pulse-width modulation of high voltage square-wave. System consists of a variable silicone layer connected with Sil-Poxy adhesive to a 50 μm\mu m electrode layer of AL-sputtered BOPET with a 25 μm\mu m layer of Luxprint dielectric. (right) Antagonistic clutch system attached to the left side of a SPA to provide position control during inflation. Inflation with fully activated clutch superimposed over inflation with deactivated clutch.
Figure 3.2: Clutch fabrication process: A. Masking and abrading the aluminum-sputtered BOPET. B. Resulting clutch sheet ready to be cut (back of sheet). C. Cut clutch plates on silicone sheathing with holes for adhesive contact. D. Assembled sheathed clutch.
Figure 3.3: Clutch Control: Block diagram of electrical control for simultaneous high-voltage PWM and tensile testing
Figure 3.4: (left) Experimental setup for clutch force characterization. (right) Clutch force response during loading and unloading at various PWM duty cycles (duty cycle indicated by color).
Figure 3.5: Empirical relation between clutch force multiplier from Eq. 3.3 ( ζ\zeta ) and PWM duty cycle. (inset) Example waveform for PWM output at 50% and 100% duty cycle.
Figure 3.6: (left) Experimental setup for dynamic energy dissipation with sheathed clutch. (right) Maximum stage vertical displacement as a function of clutch activation force as modeled via energy methods (Eq. 3.4 , lines) and seen in experimental results (points). The blue line estimates dynamic response based on modeling of the clutch and sheath, while the orange line adds the work done by a constant force stage friction.
Figure 3.7: (top) SPA inflated to approximately 25 kPa with different clutch duty cycles. (left) Diagram of SPA expansion with fully activated clutch. (right) PWM effect on bending angle and horizontal displacement.
Figure 4.1: Theoretical layout used in mass-spring methods for inflated membranes. Points represent masses, lines represent springs, and empty regions (such as the shaded regions) represent pressure areas
Figure 4.2: left: measurements used to solve for surface area of inflated membrane for stretch calculations, right: plot of pressure-stretch relation described in eqn. 4.3 compared to experimental data from inflation of an unrestricted silicone membrane
Figure 4.3: Schematic of the membrane (gray) with strain limiter (black) in the A. undeformed state, and B. deformed state while in contact with external force (blue).
Figure 4.4: A. Design parameters for example membrane. B. Compressive Testing (top) Testing procedure for each membrane: expansion from a flat plane into a set height load-cell. Procedure is repeated for different heights. (bottom) Example of physical test measuring force for varying pressure at a set height. C. (left) Pressure, height, and six design parameters predict force output for a given membrane. (middle) Model (blue) overlaid with force-pressure training data at varying heights (0-70mm from purple to yellow). (right) 3-D visualization of 6-D design space. Example training set points in black, model from C in blue, model from D in green. D. Optimization for lifting task. (left) Physical testing to verify lift trajectories at a given mass. (right) Model planes for (blue) training parameters and (green) design parameters optimized to hit target trajectories (trajectories in black).
Figure 4.5: Model Architecture. (Top) Characterization data, pressure and height, and design inputs, ring radius and width, membrane thickness, and contact radius, are inputs to the actuator model. (Bottom) The model solves for force output relative to pressure.
Figure 4.6: Model RMSE [N] of best performing model hyperparameters tracked to the corresponding parameters: output force polynomial degree relative to pressure, multi-layer perceptron depth and width, and ring encoder MLP width.
Figure 4.7: Experimental trajectories: (left) Pressure-height-force data from lifts at three different masses for each of five membranes (lines) with target points for each trajectory (circles). (right) RMSE between experimental trajectories and target way-points for each pairing of membrane and target.
Table 4.1: Perturbation Study - Key
Figure 4.8: Mass lift results for ablation study across contact strain limitation, lubrication, and contact plate shape. (Top) Ringed membranes. (Bottom) Unringed membranes.
Figure 4.9: Shank lift experiment using two co-designed membranes. (Top) Modeled trajectory (red) compared with characterization data (green) and lift trajectory (black) for Membranes A and B. (Middle) Modeled trajectory (circles) compared with experimental results (xs) for height (left) and force (right) versus pressure. (Bottom) Low pressure (left) and high pressure (right) states for Membranes A and B (relative left and right) connected to a single pressure source to lift shank.
MembraneThicknessContact RadiusRing_1 RadiusRing_1 WidthRing_2 RadiusRing_2 Width
A3.038.146.1559.15
B2.025.449.0562.05
Table 4.2: Shank lift membrane parameters
Figure 4.10: Equilibrium experiment for multiple membranes connected to a single pressure source each lifting 2 kg in parallel. (Top) Effect of external perturbations on internal pressure (green) and equilibrium position of membranes (blue and orange). (Bottom) Membranes used in equilibrium experiment, shown in unladen, inflated configuration at shared internal pressure. (Inset) Membranes performing lift experiment - prior to perturbation.
Figure A.1: One-factor-at-a-time analysis of gear efficiency for (top) number of teeth and (bottom) profile shift coefficient
Table 29
Figure A.2: (left) CAD for 3D-printed Wolfrom gear. Parts include planet gears (red), sun gear (blue), stage 1 ring (grey), stage 2 ring (green), and two carriers (one shown, gold). (right) CAD for 3D-printed valve mold in ‘section view’ to show negative space for domed valve and hole for injection molding.
Figure A.3: Experimental test setup for (top) gear spin and (bottom) valve pressurization.
Figure A.4: Reward function score (Eqn. A.16 ) for gear design iterations among the two design strategies.
MaterialLubricantzshz_{\text{sh}}zr2z_{r2}xsx_{s}xr2x_{r2}Gear Ratio
PLALI676-0.5872-0.076463.6
PLANone680-0.800.54456.9
PLALI6760.75130.1686107.7
Table 33
Figure A.5: Valve pressure error values for Taguchi (circle and triangle) designs and Bayesian Optimization (triangle initialization, star generated) designs. Logarithmic scale accentuates the Pareto front.
DesignMaterialtt [mm]hdomeh_{dome} [mm]lcutl_{cut} [mm]cut
2DS200.201.00.75X
5E00300.751.01.00triple
6E00300.202.21.50slit
7E00300.501.52.00X
BO 9DS200.21.160.75X
Table 35
Figure A.6: Model uncertainty, quantified by standard deviation, versus number of iterations included in the training set for a Gaussian Process Regression (GPR) model trained on BO (blue) or Taguchi (red) data. (top) Uncertainty for gear predictions. (bottom) Uncertainty for valve crack pressure predictions.
Figure B.1: Various pressure-vessel designs. From left to right: laser-cut rectangular chamber (arcylic), burst 3D-printed cylindrical chamber (VeroBlue), 3D-printed and laser-cut mount and port (PLA and acrylic), laser-cut mount and port (acrylic).
Figure B.2: Diagram of surface chosen for use in Gauss’s Law calculation of electric field between electrodes with charge Q
Figure B.3: left: testing system electromechanical setup, right: image of testing system
More in this topic

Soft Pneumatic Actuators

See all 25 papers

Explore similar work

CardsList
May 24, 2026

Soft Pneumatic Actuators for Soft Robotics: A Motion-Based Review of Actuation Mechanisms and Performance Trade-offs

Soft pneumatic actuators are widely used in soft robotics because they can produce large motions while remaining compliant enough to interact safely with objects, environments, and the human body. However, their performance is not solely determined by pressure. Instead, the response depends on the way the actuator is built, including the shape of its chambers, the placement of reinforcements, the use of folds, material stiffness, and the constraints that guide its deformation. As the literature has expanded, it has become more difficult to determine which mechanism is most suitable for a given application and which reported results can be compared across studies. This review examines soft pneumatic actuators according to the design strategies used to generate four motion classes: linear, bending, twisting, and omnidirectional actuation. For each class, it analyzes the structural features that define the deformation path, including braid angle, fold geometry, fiber orientation, chamber arrangement, structural asymmetry, and internal constraint layers. It then discusses how the design choice affect motion output, force generation, air demand, repeatability, durability, fabrication difficulty, and robotic integration. The review further identifies key conditions that must be considered when selecting or comparing actuators, including pressure, loading condition, actuator size, pneumatic supply, and hysteresis This approach helps explain why actuators with similar motion outputs may differ substantially in design requirements, pneumatic demand, and practical suitability. It also highlights the design priorities needed for compact, efficient, repeatable, and deployable soft pneumatic systems in wearable, biomedical, and mobile robotic applications.

Mohammed Abboodi

Soft Pneumatic ActuatorsSoft RoboticsPneumatic Actuation
AskPDF
May 19, 2026

Topology-Optimized Pneumatic Soft Actuator: Design and Experimental Validation

This paper demonstrates the computational design of soft elastomeric pneumatic actuators using nonlinear topology optimization. An existing density- and porohyperelasticity-based topology optimization framework was extended from 2D to 3D and used to generate two manufacturable actuator designs, which were then studied numerically and experimentally. For both designs, the objective was to maximize the bending response for a prescribed actuation pressure under two different allowable strain limits. A key advantage of the employed topology optimization framework is that it can consistently, during the optimization, account for the very large deformations induced upon pressurization. The two optimized 3D designs were fabricated using stereolithography and experimentally tested to validate their performance.

Sumit Mehta, Konstantinos Poulios

Department of Civil and Mechanical Engineering Technical University of Denmark, Denmark

Topology OptimizationSoft Pneumatic ActuatorsSoft RoboticsPneumatic Actuation
AskPDF
Feb 27, 2026

Geometry-based pneumatic actuators for soft robotics

Soft pneumatic actuators enable safe human-machine interaction with lightweight and powerful applied parts. On the other side, they suffer design limitations as regards complex actuation patterns, including minimum bending radii, multi-states capabilities and structural stability. We present geometry-based pneumatic actuators (GPAs), a design and implementation approach that introduces constraint layers with configurable CNC heat-sealed chambers. The approach achieves predictable deformation, near-zero bending radii, multi-states actuation, and enables customizable and repeatable complex actuated geometries. Mathematical modeling reveals predictable linear angle transformations and validates nonlinear torque-angle relationships across diverse configurations. We demonstrate versatility of the GPAs approach through three applications: a 49 g wrist exoskeleton reducing muscle activity by up to 51%, a 30.8 g haptic interface delivering 8 N force feedback with fast response, and a 208 g bipedal robot achieving multi-gait locomotion. GPAs establish a configurable platform for next-generation wearable robotics, haptic systems, and soft locomotion devices.

Rui Chen, Daniele Leonardis, Domenico Chiaradia +1

Institute of Mechanical Intelligence, School of Advanced Studies Sant’Anna (SSSA), 56127 Pisa, Italy.

Soft Pneumatic ActuatorsPneumatic ActuationRoboticsSoft Robotics
AskPDF