Modeling and Design Tool for Soft Pneumatic Actuators

Soft actuators are an integral component of soft robotic systems. Although the scalability, customizability, and diversity of soft pneumatic actuators (SPA) are widely recognized, comprehensive techniques for modeling and designing soft actuators are lacking. Characterizing and predicting the behavior of soft actuators is challenging due to the nonlinear nature of the materials used and the large range of motions they produce. In this work, mathematical tools and new design concepts are employed to improve the performance of these actuators compared to existing designs. A comprehensive, cohesive, and open-source simulation and design tool for soft actuators using the finite element method (FEM) has been developed, readily compatible with and extensible to a diverse range of soft materials and design parameters. This design tool can enable the generation of improved predictive models that will help us to rapidly converge on new and innovative applications of these soft actuators. 

Table showing SPA applications in assistive wearable devices for biomedical assistance along with corresponding design requirements, achievable using the modeling and design tool presented. 

Thorough characterization of the hyperelastic and viscoelastic behavior is illustrated using a sample soft material (Ecoflex 00_30), and an appropriate material constitutive law. SPA performance (displacement and blocked-force) are simulated for two types of SPA and validated with experimental testing. Real-world case studies are also presented in which SPA designs are iteratively optimized through simulation to meet specified performance criteria and geometric constraints.

Numerical simulation results using Finite Element Analysis (FEA) for soft actuators in bending and linear motion. Simulations predict motion-force profiles obtained with the actuators, enabling the design of more efficient systems.

The videos below show simulations developed using the FEM for soft pneumatic actuators in linear and bending motion. In these simulations, the soft actuator core is covered with a stiffer shell structure that has a pre-specified pattern on it to guide the motion of the actuator along a prescribed trajectory. 

Design

Two types of designs for soft pneumatic actuators are discussed here. The scripts and models available on the design tool enable customized variations in geometry, material properties and performance for these two designs depending on the desired application of study. 

1. Single-Chamber Shell-Reinforced Actuators

The classical unconstrained multi-chamber actuator undergoes excessive inflation at high values of input pressure which can eventually lead to mechanical failure at the stress concentration regions such as the narrow connecting corridors or at the chamber wall peripheries. As a design improvement over the unconstrained actuators, novel shell-reinforced actuators have been developed. These actuators comprise two materials, one for the highly stretchable actuator core and the other for the unstretchable shell. The shell constrains excessive inflation of the actuator and guides it along the desired trajectory. 

Two types of single-chamber actuators are studied - bending actuators and linear actuators. The shell patterns for these two different types of actuators are shown below. The slit number and slit width on the shell surface influence the motion and stress profile obtained. The design parameters include the chamber dimensions, wall thickness, shell dimensions and pattern, and material properties for both the shell and the chamber. 

Furthermore, to remove the stress concentration regions at the chamber connection regions, only a single air chamber is created in this design.  The images for these actuators in motion are shown below. 

2. Classical Multi-Chamber Unconstrained Actuators

In this type of soft actuator, the actuator is comprised of multiple air corridors connected by narrow connecting passages for pressurization. The actuator is fabricated by attaching two identical halves with an adhesive. The entire unit is made of a single material. The material used in the present work is a highly stretchable silicone rubber material. The actuator is not constrained radially in this case. The design parameters include the individual chamber dimensions, air passage dimensions, wall thickness and material properties. 

Two types of multi-chamber actuators are studied - bending actuators and linear actuators. The images for these actuators in motion are shown below. 

1. Shell-reinforced SPA

Despite the established potential of SPAs and their diverse implementation towards robotic systems for meeting desired functional requirements in crucial applications such as the ones described above, the lack of repeatability in currently existing SPA design and fabrication procedures greatly limits their potential and performance in such systems. 

In an effort to circumvent some of these fabrication and repeatability issues, a new actuator design has been developed where the actuators are made in a single molding step. The presented two-part, shell-reinforced, SPA design shown below allows “fool-proof” prototyping of both bending and linear actuators and produces results in the desired performance range. 

The presented numerical models using FEA accurately predict the complex mechanical response and the performance obtained with the designed actuators while allowing rapid design iterations to optimize the design parameters. The following images show the simulation results obtained for bending and linear shell-reinforced actuators using the design tool along with the corresponding experimental images. The design and modeling procedures for these actuators are listed step-by-step and illustrated in detail in the Model Demo Section

The design tool and a complete set of models used in the current study are also available open-source on the Reconfigurable Robotic Laboratory website (http://rrl.epfl.ch) where it is possible to use the models developed in the present work as a starting point to modify and create different geometries and materials for any robotic application. 

2. Multi-Chamber SPA

The open-source downloadable scripts available with the design tool enable automation of the design and modeling procedure for the classical multi-chamber SPAs. The following design capabilities are supported by the tool:

1. Creation of desired geometry for the actuator. Currently, linear and bending motion profiles are supported by the tool. The user can specify the number of air chambers desired, dimensions of chambers, connecting passage dimensions, wall thickness etc. as input parameters and a ready to use Abaqus INP file with the specified geometry is generated. 

2. Characterization of hyperelastic and viscoelastic soft material effects. These effects are demonstrated here with a typically used silicone elastomer material to fabricate SPAs - Ecoex 00-30, which exhibits desirable mechanical behavior for soft robotic components. The tool fits experimentally gathered stress-strain data on the elastomer collected through multiple mechanical tests to a hyperelastic stress-strain constitutive law. Multiple commonly used hyperelastic stress-strain constitutive laws are supported. Time dependent effects can also be included by fitting experimental stress-relaxation data collected through prescribed tests to a viscoelastic Prony series describing stress relaxation effects within the material.

3. Finite element procedures for modeling SPAs. The scripts automate procedures such as generation of INP file, meshing the actuators, desired pressure load application, specifying the necessary boundary conditions depending on the application and testing conditions for the actuator and generating the mesh desired. The model results are plotted using another script and the results can be simulataneously validated against experimental prototype results, for linear and bending actuators. Optimization of actuator parameters to meet targeted metrics is also possible. 

These procedures are illustrated step-by-step in the Model Demo SectionThe following images show the simulation results obtained for bending and linear shell-reinforced actuators using the design tool. 

Modeling

Soft pneumatic actuators are designed to handle large deformations and large mechanical strains. At these high values of strain, the actuator behavior is highly unpredictable. The materials employed to fabricate these actuators exhibit complex hyperelastic, viscoelastic non-linear behavior. Furthermore, fabricating soft pneumatic actuators is time consuming and it is helpful to know the performance characteristics obtainable a priori. Thus, numerical models using the finite element method (FEM) are developed to predict actuator behavior at large deformation values so as to design more efficient actuators and soft robotic components. 

A set of four demos is presented in this section to guide the user step-by-step through the process of creating and testing a numerical model for the actuators using the commercial FEM software AbaqusTM . The software interfaces with the python scripts provided in the design tool and enables the automation of the design procedure by providing capabilities for geometry and material variation as input design parameters. 

The following demos are provided:

Demo 1: Modeling Multi-Chamber Linear Actuators

Demo 2: Modeling Multi-Chamber Bending Actuators

Demo 3: Modeling Single-Chamber Shell-Reinforced Linear Actuators

Demo 4: Modeling Single-Chamber Shell-Reinforced Bending Actuators

Demo 1: Multi-Chamber Bending SPA

1. ACTUATOR GEOMETRY

The script create_geom.py is used to create both linear as well as bending actuators. In this case, the script is run to create a 4-chambered bending actuator as shown below. The bending actuator achieves bending motion due to a thin un-stretchable layer attached at the bottom of the structure. Due to the symmetry of the structure, only half the portion of the entire actuator is created and modeled.

The geometric parameters of the actuator, such as the height, width and the length of a chamber, and the height and width of the inlet tunnel, the wall thickness, along with the number of chambers can be customized using the script. Further details on the input parameters are described in the script.

As an example, the following geometry is generated in Abaqus CAE when the script is run using the parameters shown below:

Example: create_geom.py actuator bnd U ogden3.mat outfile.cae 0.05 200 4 --mesh_size 2.0 --chamber 8 8 2 --wall 7


2. MATERIAL CONSTITUTIVE MODEL

The elastomers typically used to create soft actuators exhibit hyperelastic behavior. The design tool provides the ability to model this behavior using several well-established constitutive laws (for a complete list, please see the scripts section). In addition, the user has the option to include viscoelastic behavior as well to capture any time dependent effects. For this example, the chambers are made in Exoflex-30 material while the thin un-stretchable layer is made of silk. The material Ecoflex-30 is modeled using a hyperelastic model while silk is modeled using a linear elastic model, as shown in image below. A matfile containing the material parameters is provided as an input to the script. A 3-term Ogden model is used for Ecoflex-30 in this example, with the following coefficients:

mu1 = 0.001887; alpha 1 = -3.848; mu2 = 0.02225; alpha2 = 0.663; mu3= 0.003574; alpha 3 = 4.225; D1 = 2.93; D2 = 0; D3 = 0



3. PRESSURE LOADS

The input loads are also specified as one of the parameters in the script above. In this example, an input pressure of 50 kPa was specified on the chamber and passage walls.  The following figure shows the corresponding load application in the Abaqus CAE file generated using the script.



4. BOUNDARY CONDITIONS

The boundary conditions include half symmetry, as mentioned previously, and no translation for the inlet portion. These are also applied by default in the CAE file generated using the script. The corresponding images are shown below.



5. MESH GENERATION

The input and CAE files generated are ready to run for obtaining output and post-processing as they also include a mesh definition. In this case, due to the hyperelastic behavior of the materials used to create the actuators,  standard quadratic elements are used with hybrid formulation and reduced integration. This ensures that any issues associated with shear or volumetric locking are avoided and that large deformations are permitted, as is expected in the case of the materials implemented for these actuators. The following image shows the mesh generated using the script, using a default element size of 2.0. The mesh size can be controlled as an input parameter through the script.



6. OUTPUT ANALYSIS

A variety of analysis can be performed using the design tool, including evaluation of the actuator performance under free and blocked loading conditions. This is specified in the script using the 'test' input parameter. Either 'U' or 'F' can be specified, signifying a free displacement test or a blocked force test, respectively.

Abaqus ODB result plots for bending motion generated are shown below for the free displacement condition, in which actuator images before and after pressurization are superposed. Plots for bending angle obtained vs. input pressure can also be generated using the script, as shown below.

Further, the actuators can also be tested under blocked end conditions using the scripts provided. For this the 'test' parameter in the script would be modified to the value 'F' instead of 'U' for the example shown above.

Demo 2: Multi-Chamber Linear SPA

The following demo shows how to use the scripts to create and model a 4-chambered linear SPA using the design tool. 

1. ACTUATOR GEOMETRY

The script create_geom.py is used to create both linear as well as bending actuators. In this case, the script is run to create a 4-chambered linear actuator as shown below. Due to the symmetry of the structure, only a quarter portion of the entire actuator is created and modeled.

The geometric parameters of the actuator, such as the height, width and the length of a chamber, and the height and width of the inlet tunnel, the wall thickness, along with the number of chambers can be customized using the script. Further details on the input parameters are described in the script. 

As an example, the following geometry is generated in Abaqus CAE when the script is run using the parameters shown below:

Example: create_geom.py actuator lin U ogden3.mat outfile.cae 0.05 200 4 --mesh_size 2.0 --chamber 8 8 2 --wall 7

 

2. MATERIAL CONSTITUTIVE MODEL

The elastomers typically used to create soft actuators exhibit hyperelastic behavior. The design tool provides the ability to model this behavior using several well-established constitutive laws (for a complete list, please see the scripts section). In addition, the user has the option to include viscoelastic behavior as well to capture any time dependent effects. For this example, the material Ecoflex-30 is modeled. A matfile containing the material parameters is provided as an input to the script. A 3-term Ogden model is used in this example, with the following coefficients:

mu1 = 0.001887; alpha 1 = -3.848; mu2 = 0.02225; alpha2 = 0.663; mu3= 0.003574; alpha 3 = 4.225; D1 = 2.93; D2 = 0; D3 = 0

3. PRESSURE LOADS

The input loads are also specified as one of the parameters in the script above. In this example, an input pressure of 50 kPa was specified on the chamber and passage walls.  The following figure shows the corresponding load application in the Abaqus CAE file generated using the script. 

4. BOUNDARY CONDITIONS

The boundary conditions include quarter symmetry, as mentioned previously, and no translation for the inlet tunnel. These are also applied by default in the CAE file generated using the script. The corresponding images are shown below. 

5. MESH GENERATION

The input and CAE files generated are ready to run for obtaining output and post-processing as they also include a mesh definition. In this case, due to the hyperelastic behavior of the materials used to create the actuators,  standard quadratic elements are used with hybrid formulation and reduced integration. This ensures that any issues associated with shear or volumetric locking are avoided and that large deformations are permitted, as is expected in the case of the materials implemented for these actuators. The following image shows the mesh generated using the script, using a default element size of 2.0. The mesh size can be controlled as an input parameter through the script. 

6. OUTPUT ANALYSIS

A variety of analysis can be performed using the design tool, including evaluation of the actuator performance under free and blocked loading conditions. This is specified in the script using the 'test' input parameter. Either 'U' or 'F' can be specified, signifying a free displacement test or a blocked force test, respectively.

Abaqus ODB result plots for displacement and Von Mises stress are showed below for the free displacement condition, from which plots for displacement vs. input pressure can be generated. 

The stress plots are helpful in identifying the stress concentration regions within the actuator, such as in the narrow passage walls between chambers in the image above. The actuator can then be better designed given a specific application. 

Displacement plots as a function of input air pressure, such as the one shown below, can be easily generated using the script run_tests, and used to evaluate the actuator motion profile. 

Similarly, the actuator can be simulated under blocked conditions to generate plots as shown below. 

 

Demo 3: Shell-Reinforced Bending SPA

1. ACTUATOR GEOMETRY

The models for bending shell-reinforced actuators are available open-source here

In these actuators, a single air chamber is modeled for providing enhanced mechanical reliability of the actuator by eliminating stress concentrations at narrow passage walls. Furthermore, the cross-section of the air chamber is circular in this case as compared to the square cross-section for multi-chamber actuators described in other demos. The bending actuator achieves bending motion due to a thin un-stretchable layer attached at the bottom of the structure. Due to the symmetry of the structure, only half the portion of the entire actuator is created and modeled.

The geometric parameters of the actuator, such as the length and diameter of the chamber, the wall thickness, and the cut spacing on shell surface can be customized using the models provided.

As an example, the following geometry is generated in Abaqus CAE for a bending actuator with an outer diameter of 4 mm, wall thickness of 2 mm and total length of 40 mm. The number of cuts on shell surface is 7, at a cut spacing of 1 mm.



2. MATERIAL CONSTITUTIVE MODEL

The elastomers typically used to create soft actuators exhibit hyperelastic behavior. The design tool provides the ability to model this behavior using several well-established constitutive laws (for a complete list, please see the scripts section). In addition, the user has the option to include viscoelastic behavior as well to capture any time dependent effects. For this example, the chamber is made in Exoflex-30 material while the thin un-stretchable shell layer is made of a plastic material such as PET. The material Ecoflex-30 is modeled using a hyperelastic model while the shell is modeled using a linear elastic model (due to stresses in shell not exceeding elastic range). A 3-term Ogden model is used for Ecoflex-30 in this example, with the following coefficients:

mu1 = 0.001887; alpha 1 = -3.848; mu2 = 0.02225; alpha2 = 0.663; mu3= 0.003574; alpha 3 = 4.225; D1 = 2.93; D2 = 0; D3 = 0

3. PRESSURE LOADS

In this example, an input pressure of 50 kPa was specified on the chamber walls.  The following figure shows the corresponding load application in the Abaqus CAE file generated.



4. BOUNDARY CONDITIONS

The boundary conditions include half symmetry, as mentioned previously, and no translation or rotation for the inlet portion. The corresponding images are shown below.

5. INTERACTION

To achieve bending motion profile, a thin strip portion at the bottom of the shell is attached to the core surface using an adhesive. The shell is permitted to slide over the surface of the actuator and guide its trajectory in the remaining portions. To implement this condition in Abaqus, a tie constraint is imposed at the thin unstretchable portion while a contact property is defined to include finite sliding in tangential orientation with a specified coefficient of friction in the remaining portions, as shown below.



6. MESH GENERATION

In this case, due to the hyperelastic behavior of the material used to create the actuator core,  standard linear 3-D stress elements are used with hybrid formulation and reduced integration. This ensures that any issues associated with shear or volumetric locking are avoided and that large deformations are permitted, as is expected in the case of the materials implemented for these actuators. For the shell structure, standard linear shell elements with reduced integration are used. The following image shows the mesh generated for the shell, as an example.

7. OUTPUT ANALYSIS

A variety of analysis can be performed using the design tool, including evaluation of the actuator performance under free and blocked loading conditions. Abaqus ODB result plots for linear extension motion generated are shown below for the free displacement condition.

 

Demo 4: Shell-Reinforced Linear SPA

1. ACTUATOR GEOMETRY

The models for linear shell-reinforced actuators are available open-source here.

In these actuators, a single air chamber is modeled for providing enhanced mechanical reliability of the actuator by eliminating stress concentrations at narrow passage walls. Furthermore, the cross-section of the air chamber is circular in this case as compared to the square cross-section for multi-chamber actuators described in other demos. The linear actuator achieves linear motion due to the corresponding shell pattern discussed earlier in the design section. Due to the symmetry of the structure, only half the portion of the entire actuator is created and modeled.

The geometric parameters of the actuator, such as the length and diameter of the chamber, the wall thickness, and the cut spacing on shell surface can be customized using the models provided.

As an example, the following geometry is generated in Abaqus CAE for a linear actuator with outer diameter of 4 mm, wall thickness of 2 mm and total length of 40 mm. The number of cuts on shell surface is 13, at a cut spacing of 0.5 mm.



2. MATERIAL CONSTITUTIVE MODEL

The elastomers typically used to create soft actuators exhibit hyperelastic behavior. The design tool provides the ability to model this behavior using several well-established constitutive laws (for a complete list, please see the scripts section). In addition, the user has the option to include viscoelastic behavior as well to capture any time dependent effects. For this example, the chamber is made in Exoflex-30 material while the thin un-stretchable shell layer is made of a plastic material such as PET. The material Ecoflex-30 is modeled using a hyperelastic model while the shell is modeled using a linear elastic model (due to stresses in shell not exceeding elastic range), as shown in images below. A 3-term Ogden model is used for Ecoflex-30 in this example, with the following coefficients:

mu1 = 0.001887; alpha 1 = -3.848; mu2 = 0.02225; alpha2 = 0.663; mu3= 0.003574; alpha 3 = 4.225; D1 = 2.93; D2 = 0; D3 = 0


3. PRESSURE LOADS

In this example, an input pressure of 50 kPa was specified on the chamber walls.  The following figure shows the corresponding load application in the Abaqus CAE file generated.



4. BOUNDARY CONDITIONS

The boundary conditions include half symmetry, as mentioned previously, and no translation or rotation for the inlet portion. The corresponding images are shown below.

5. INTERACTION

In this design, the shell is permitted to slide over the surface of the actuator and guide its trajectory. To implement this condition in Abaqus, a contact property is defined to include finite sliding in tangential orientation with a specified coefficient of friction, as shown below. 

Surface-to-surface contact is then defined between the shell and the actuator surface using the contact property defined above, as shown in the image below.



6. MESH GENERATION

In this case, due to the hyperelastic behavior of the material used to create the actuator core,  standard linear 3-D stress elements are used with hybrid formulation and reduced integration. This ensures that any issues associated with shear or volumetric locking are avoided and that large deformations are permitted, as is expected in the case of the materials implemented for these actuators. For the shell structure, standard linear shell elements with reduced integration are used. The following image shows the mesh generated for the shell, as an example.



7. OUTPUT ANALYSIS

A variety of analysis can be performed using the design tool, including evaluation of the actuator performance under free and blocked loading conditions. Abaqus ODB result plots for linear extension motion generated are shown below for the free displacement condition.

It is seen that the stress concentration occurs at the notches in the shell structure. This stress can be reduced by increasing the number of cuts on the shell surface. The following image shows reduction in stress obtained for the case of an actuator with 21 cuts on shell surface, as an example.

Fabrication

The fabrication procedure for the single-chamber shell-reinforced actuators and the multi-chamber unconstrained actuators is discussed in detail in this section. 

1. Shell-Reinforced SPA Fabrication

The technique used to fabricate the soft pneumatic actuators presented ensures robustness and repeatability in manufacturing, since it leaves minimal manual intervention and margin for error.

The actuators are composed of two main parts: 1) the actuator body and 2) the un-stretchable shell. The actuator body is made out of highly elastomeric siloxane material (EcoflexTM 00-30, Smooth-on-Inc., PA, USA). The un-stretchable shell is made from a much stiffer plastic material (polyethylene terephthalate (PET), Q-ConnectTM). Images of two types of fabricated actuators, in bending and linear motion are shown below. 

1. FABRICATING ACTUATOR BODY

  • SINGLE STEP MOLDING: The actuator comprises of a single air chamber, created in a single-step molding process. This is done to avoid the traditionally used two-step molding process for creating soft pneumatic actuators in which two separate halves need to be glued to form the air chambers, thereby reducing fabrication errors and possibility of delamination at the interface.
  • GRIPPING AT CHAMBER ENDS: At each end of the chamber, an additional length of rubber material is provided to facilitate attachment of fixtures for gripping the actuator during testing, since gripping on the active chamber portion can potentially constrict the air flow passage and alter the performance of the actuator. 
  • END CAPS: To grip the actuator for testing, end-caps are attached at the actuator at the border of its air chamber, thus ensuring maximum force/torque delivery.

2. FABRICATING UN-STRETCHABLE SHELL 

  • SHELL PATTERN: The un-stretchable shell mounted on top of the actuator body surface constrains the actuator body to inflate in only the desired configuration. The pattern created on the shell surface governs the displacement obtained. Bending and linear actuators were fabricated using the sequence shown below. 
  • LASER CUTTING: To construct the shells, 2D patterns are cut out of universal inkjet transparency films made from PET (Q-ConnectTM) using a laser cutter. Multiple slits are cut out on the shell surface in well-defined patterns. These slits permit the appropriate level of inflation of the contained rubbery material in the desired direction while the remaining uncut portion provides circumferential reinforcement to avoid excessive radial expansion of the actuator body.
  • ROLLING UP SHELLS AND GLUING: The cut patterns are then rolled up and glued into a cylindrical shape, to conform to the shape of the encased actuator body. Unlike the shell for bending actuators, which requires only one laser-cut pattern per shell, the shell for linear actuators consists of a glued assembly of two symmetric patterns (see Figure below). For these actuators, having two symmetrically layered glue-zone bands ensures the expansion of the actuator in the linear motion desired. 
  • ATTACHING SHELL TO BODY: To prevent the shell from slipping out over the actuator body at high pressures, the shell and the body are maintained in place by screws drilled through the end caps and the actuator wall thickness. To track the position of the actuator with a high speed camera, tracking points are also glued onto each end-cap.

3. INFLATION COMPENSATION AT CHAMBER ENDS

From experimental testing, it was observed that at the border of the air chambers, the ballooning rate is approximately double than that at other portions along the the rest of the laces. This is due to the fact that the air flow at the edge of the chamber undergoes a dramatic change in cross-sectional area from a very small inlet diameter to a much larger diameter for the air chamber, thereby introducing vortices and turbulent flow in that region, leading to larger instabilities and inflation of the actuator body in that region. To compensate for this added inflation effect at the end of the chamber, slits that are half the width of the slits in all other portions on the shell surface are created at the extremities of the shell pattern. This design improvement is found to help substantially in achieving a uniform pattern of inflation with the actuators.

2. Multi-Chamber SPA Fabrication

These classical type of SPAs comprise multiple air chambers connected by narrow passages. The SPAs are fabricated using a conventional soft lithography process. The fabrication steps are listed below:

STEP 1. A 3D-printed mold defining the locations of the SPA chambers and their inter-connecting air channels is created.

STEP 2. Next, an elastomer in liquid form (EcoflexTM 00-30 from Smooth-on Inc.) is mixed using a centrifugal mixer then de-gassed in a vacuum chamber at 1.10−4 kPa.

STEP 3. This liquid is poured into the molds, de-gassed again, then cured for 45 min at 70 ◦C.

STEP 4. (1) For linear actuators two of the cured elastomer blocks are joined using a thin layer of uncured, de-gassed silicone applied by a procedure similar to sandwich micro-contact printing. (2) Using the same procedure, bending actuators are assembled by bonding the cured silicone block to a thin inextensible layer, fabricated by embedding a layer of silk fabric in a 0.75 mm-thick layer of de-gassed silicone cured at room temperature (image sequence for bending actuators at end of page).

STEP 5. The assembly is then cured at room temperature for two hours to guarantee proper bonding.

STEP 6. Finally, the assembly process is completed by inserting the air tubing (for all the SPAs in this work the tube length is 300 mm) and applying a flexible epoxy around it to ensure a proper seal.

The following images show step-by-step fabrication sequence for bending SPAs by including the additional un-stretchable layer. 

Case Studies

In this section the spa_optimize_geometric_parameters design tool is used to select design parameters based on the two different applications. Researchers may follow the same procedure using this tool to answer their own design questions.

First, we define the application in terms of quantifiable design criteria constraints. Next, given an initial selection of geometric parameters, the design tool simulates the SPA to determine the selected performance characteristics. Based on the results, the design tool iterates over the parameter space using a COBYLA optimization loop. As there may be several “optimal” solutions, this optimization loop is again embedded within a global-optimization basin-hopping algorithm, which searches for new optimal solutions by permutating the parameters to find new starting points for the COBYLA loop.

In this way multiple unique designs meeting the design criteria can be discovered with only one single starting point from the user. A design is then selected, implemented, and tested experimentally in order to validate the approach. The two case studies presented here show application of the design tool for a multi-test single-optimization of a linear SPA for soft rodent exoskeletons, and a constrained single-test multi-optimization for a bending SPA for soft hand-rehabilitation gloves.

 

 

 

 

Case Study 1: Linear SPA Design for Soft Exoskeleton

A SPA-driven exoskeleton designed for locomotor rehabilitation of mammals with neurological disorders is modeled using the SPA design tool. The soft exoskeleton is designed to guide the limbs of a rodent subject through a controlled, predefined trajectory defining a step, with motion occurring solely in the saggital plane. SPAs were chosen over electrical motors to maximize the agility of the subject during the spastic motion of the limbs. The mechanism is composed of two linear SPAs attached to a two-link chain, as shown in Figure below. 

The required displacement and blocked-force are summarized in Table 1. A maximum strain constraint is also included in the optimization in order to avoid the high-strain regimes where failure occurs in the real-world. This constraint is applied as an optimization penalty for strains above the upper limit.

Table 1. Design requirements for Case Studies 1 and 2. The constraints and performance criteria are defined based on the application requirements. In Case Study 2, the actuator is allowed free displacement up to 150, beyond which the actuator is blocked in order to measure blocked-force. 

The initial design parameters of the linear SPA were based on intuition and are shown in Table 1. These values serve as the optimization starting values. The geometric parameters to be optimized are the number of chambers, chamber height × width ×depth, wall thickness, and inter-chamber air passage height ×width. These seven parameters are reduced to five by constraining the chambers and passages to remain square (height equals width). With these five geometric parameters and the criteria and constraints in Table 1, the spa_optimize_geometric_parameters tool is able to converge toward an optimal SPA design. A plot of the performance of various designs during the optimization loop is shown below.

The plot shows three design-groupings (blue, red, and blue-green) generally provide the best displacement and force performance. The best result from each of these design groups is marked in the figure and the corresponding design parameters are given in Table 2. It is clear that the starting point, noted as “CS1 Initial” in Table 2, formed the basis for the red group of results. The optimization process was able to improve on this initial design by thickening the walls, decreasing the size of the inter-chamber tube, and reducing the depth of the chambers to improve performance. The other two designs in Table 2 are significantly different from the initial design, based on longer, thinner actuator designs determined by the basin-hopping algorithm.

Table 2. Design parameters for Case Studies 1 and 2. The initial SPA designs were built using intuition, all other designs are generated by the FEA optimization tool. Lengths in mm, masses measured experimentally on fabricated actuators.  

These three actuators were then fabricated and tested. Values from experimental testing of the initial and final designs are shown in Table 3. The rapid exploration of the solution space shown here represents a major improvement in the design procedure. We can rapidly explore non-evident SPA configurations, rather than simply iterating experimentally one factor at a time based on intuition design decisions.  
 
Table 3: Performance results for Case Studies 1 and 2 on the initial and final designs, showing both experimental (EXP) and simulation (FEM) values determined using optimization.
 

Case Study 2: Bending SPA Design for Hand Rehabilitation Glove

The compliant and light-weight SPAs have applications in actuated gloves for rehabilitation and assistance of patients suffering from reduced mobility and strength. Currently, these gloves use bending SPAs. The actuators can apply force during flexion or extension, allowing the glove to support a wide range of functional rehabilitation tasks.

Our goal for the rehabilitative glove focuses on the repetitive training of isolated movements for functional activities of daily living (ADL). A number of hand studies in the literature provide measurements of required range of motion of the joints in the hand (i.e., grip angle of finger) and pinching forces required for a large range of functional tasks in ADL, and the requirements considered here are summarized in Table 1. The initial and optimized design parameters from the simulation are summarized in Table 2. The other four initial designs are not tested, as the simulation results already indicated that those designs were too far from meeting the requirements.

Results from the experimental testing of the initial and final design parameters are shown in Table 3 and in Figure below. The initial design bursts at 32 kPa before reaching the desired force at the grip angle of 150°. The sample based on the optimized parameters achieved goal force and stayed close to the simulation results.

Open-Source Downloads

A set of zipped Abaqus CAE and INP files for modeling shell-reinforced actuators are available for free download below:

1. Bending Shell Actuators - Free Displacement Testing (One end of actuator clamped before pressurization; Other end free during pressurization)

2. Bending Shell Actuators - Blocked Force Testing (One end of actuator clamped before pressurization; Other end clamped at a specified position following initial pressurization up to a specified limit)

3. Linear Shell Actuators - Free Displacement Testing (One end of actuator clamped before pressurization; Other end free during pressurization)

4. Linear Shell Actuators - Blocked Force Testing (Both ends of actuator clamped before pressurization; Pressure increased up to a specified level afterwards)

The complete spa_guided_design_tool for modeling classical multi-chamber actuators is available to the public under the open-source MIT license. Included here is a brief description of the tools and capabilities available. The modules are all written in Python, and some modules interface with the commercial FEM software Abaqus in order to create meshes and run simulations. In order to access the complete set of scripts needed to simulate the actuators, please contact the authors with your name, affiliation and a brief description of your intended application with the aid of the SPA design tool.

spa_run_tests Used to initiate AbaqusTM and run a simulation or series of simulations. It also supports submitting jobs to high-performance compute clusters which use the SLURM queuing system.

spa_create_geom Interfaces with AbaqusTM in order to automate the process of creating a geometry, meshing it, and applying boundary conditions. Given actuator type (linear or bending), desired test (displacement or blocked force), and a set of geometric parameters such as wall thickness, chamber size, and mesh refinement, this tool will output a complete, ready-to-run AbaqusTM input file. This input file can then be run using spa_run_tests or further modified by the user using the AbaqusTM CAE interface.

spa_optimize_geometric_parameters Facilitates SPA design optimization through automated iterative design simulations, as discussed in the case studies presented here. AbaqusTM is required.

spa_calc_hyperelastic_parameters Fits experimental stress-strain data, collected through tests as described in the first Appendix, to a hyperelastic stress-strain constitutive law. AbaqusTM is not required. The following hyperelastic models are available to the user (others may be easily added):

spa_optimize_hyperelastic_parameters Performs an additional fitting step for the hyperelastic material laws in order to extrapolate missing data or optimize SPA behavior given some actuator testing data, as discussed in the section on material characterization. AbaqusTM is required.

spa_calc_viscoelastic_parameters Fits experimental stress-relaxation data, collected through tests. to a viscoelastic Prony series. AbaqusTM is not required.

spa_plot_results This module provides several useful scripts for visualizing experimental and/or simulation results, used to create the plots in this work. AbaqusTM is not required. The following scripts are included within this module:

create_experimental_plots.py - Plot raw experimental data versus time.

create_hyperelastic_plots.py - Plot stress versus strain for hyperelastic testing data with fits from spa_calc_hyperelastic_parameters.

create_principalcomponentanalysis_plots.py - Plot optimization iteration results from spa_optimize_geometric_parameters in scatterplot form.

create_result_plots.py - Plot displacement or blockedforce versus pressure from FEM simulations and/or experiments.

create_viscoelastic_plots.py - Plot stress versus strain for viscoelastic testing data with fits from
spa_calc_viscoelastic_parameters. 

Corresponding Author

Contact Gunjan Agarwal about this project