Paediatric ankle rehabilitation system based on twisted and coiled polymer actuators

Rehabilitation is crucial for children with physical disabilities arising from various conditions. Traditional exoskeletons, reliant on electric motors and rigid components, making them cumbersome, heavy, and unsuitable for use outside clinical facilities. To overcome these, researchers are turning to soft wearable rehabilitation robots (SWRRs) with artificial muscles based on smart materials like twisted and coiled polymer actuators (TCPs). TCPs offer enhanced compliance, adaptability, comfort, safety, and reduced weight—critical for paediatric use. Despite facing challenges like low operating frequencies and high temperatures, TCPs are explored as potential artificial muscles for SWRRs, due to their advantages on the force they can generate, the strain and a linear behaviour. This study details a proof of concept for a paediatric rehabilitation system for ankles based on TCPs, including the actuator characterization, mechanical design, control strategy, and human-computer-interface (HCI). The resulting device achieved a 1.4 Nm torque, a 10° range of motion in dorsiflexion within 5 s, and integrated electromyographic HCI. This research marks a promising step towards innovative, soft wearable rehabilitation solutions for children with physical disabilities.


Introduction
Ongoing paediatric physical disabilities can result from various causes, including neurological conditions like Cerebral Palsy [1], strokes [2], acquired brain injuries [3], neuromuscular diseases such as Duchenne muscular dystrophy [4] and Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.spinal muscular atrophy [5], as well as traumatic injuries.Children with physical disabilities often face limitations in performing daily activities independently, which can impede their typical development.Mobility and exploration are crucial aspects of a child's development, contributing to cognitive, physical, social, and emotional growth [6].
Rehabilitation plays a vital role in assisting these children in recovering or maintaining functionality, enabling them to interact with their environment, and ultimately improving their quality of life and autonomy [7].Rehabilitation exoskeletons have gained significant attention for their potential to address mobility challenges in individuals with physical disabilities.They offer advantages such as enabling extensive practice for children with substantial disabilities, reducing the effort required from therapists during exercises, and providing a quantitative assessment of the patient's motor function [8].
However, most existing rehabilitation exoskeletons rely on electric motors and rigid components for their functionality.Unfortunately, these designs are often cumbersome, heavy, and unsuitable for use outside clinical facilities [9].To overcome these limitations, researchers are now focusing on developing soft wearable rehabilitation robots (SWRRs) that incorporate artificial muscles based on smart materials (AMSMs).AMSM provides increased compliance, adaptability, comfort, safety, and reduced weight [10].
Due to this advantages they are interesting to be used in paediatric devices as the main characteristics that differentiate them from the adults version are safety, operability, weight and motivation [11].Safety can be improved thanks to the compliance of the materials [12].And the weight can be reduce drastically preventing abnormal movements pattern and increase energy consumption [13,14].Due to this advantages they are interesting to be used in paediatric devices as the main characteristics that differentiate them from the adults version are safety, operability, weight and motivation [11].Safety can be improved thanks to the compliance of the materials [12].And the weight can be reduce drastically preventing abnormal movements pattern and increase energy consumption [13,14].
AMSMs are soft actuators composed primarily of material with a low Young's modulus like that of soft biological materials (10 4 -10 9 Pa) that can sense and directly convert physical stimulus (e.g.light, electrical, heat) into physical displacement [15][16][17].
Shape memory alloys (SMAs) [18] and dielectric elastomer actuators (DEAs) [19] are indeed promising AMSM solutions for SWRR.However, they each have limitations that hinder their widespread use in this context.
DEAS present desirable characteristics with strain reaching 200%, a high bandwidth up to the range of kHz and high efficiency [20][21][22].However, DEAs need high voltage, in the order of hundreds of volts, requires bulky and expensive electronics.Moreover, DEAs are challenging to produce in a compact size to generate appropriate amounts of power and force [23,24].
SMAs present the advantages of power density and stress, these being as high as 50 W g −1 and 200 MPa, respectively [22,25].These advantages have made them the most popular option on SWRR prototypes [10].However, they have limitations to be used on SWRR, as they have low efficiency, a small strain range (up to 8%) and high thermal hysteresis making them difficult to control [20,22,23].SMAs present the advantages of power density and stress, these being as high as 50 W g −1 and 200 MPa, respectively [22,25].These advantages have made them the most popular option on SWRR prototypes [10].However, they have limitations to be used on SWRR, as they have low efficiency, a small strain range (up to 8%) and high thermal hysteresis making them difficult to control [20,22,23].
Another noteworthy type of AMSM is the twisted and coiled polymer actuator (TCP).TCPs are created by twisting precursor polymer fibres and applying heat treatment [26].To activate TCPs, an external heat source, such as metallic wires, is employed to induce joule heating, thereby enabling precise electrical control.TCPs offer several advantages, including high power density (27 W g −1 ), stress (10 MPa), strain capacity (21%), and linear behaviour with minimal hysteresis.However, they do face certain limitations, such as low operating frequencies (<1 Hz), low power efficiency (<1.32%) and high operating temperatures (>80 • C) [20,22,27].Due to their advantages three promising examples of wearable devices based on TCPs were founded: Sutton et al [28] developed an assistive wrist orthosis with a single degree of freedom.This device employed 16 TCP) actuators made of silver-coated Nylon 6.6 sewing thread.It generated a torque of 0.3 Nm to the wrist joint in the flexion direction within 3.9 s.They implemented a proportional-integralderivative (PID) controller to accurately follow a 0.1 Hz sinusoidal signal with a 10 N amplitude.The prototype was able to track the movement during activation but encountered challenges with slow response times during the relaxation phase.
IGrab [27], an ergonomic orthotic device to assist in finger flexion and extension movements, was designed by Saharan et al.The device featured a combination of 3D-printed components and sewn parts, including artificial tendons routed from the fingers to the wrist.The finger tendons were linked to TCP actuators, which were mounted on a forearm bracelet.Frictionless pulleys optimised TCP actuation, and rubber strips enhanced energy efficiency.When applying a 0.6 A step signal, the fingers reached their maximum displacements within 25 s (i.e. the index finger was able to move 40 • for the metacarpophalangeal joint, 21 • for the proximal interphalangeal joint, and 11 • in the case of the distal interphalangeal joint), with further improvements observed when using pulsed signals, reducing actuation time to under 5 s.
Patiño et al [29] developed a wearable orthotic device for hand rehabilitation featuring individual TCP actuators for each finger.The orthosis consisted of two main components: one fitted to the dorsum of the hand and another for the fingers.Each finger incorporated a silicone tube housing a TCP and a filament strain sensor.The TCP actuators within the finger structure could generate forces of approximately 3 N when a 0.3 A step input was applied.
The orthotic devices mentioned demonstrate the application of TCPs in hand and wrist rehabilitation.However, there is a notable absence of studies exploring the feasibility of TCP utilization in the lower limb or paediatric systems.Moreover, previous literature has extensively investigated TCP as an actuation type and its mechanical design (inherent to the explored joint).Nevertheless, other critical components remain insufficiently explored in these works.These unexplored parameters may include considerations related to control strategy and human-computer interface (HCI), which are crucial for successfully developing and implementing paediatric SWRR systems [11,30] (figure 1).
This paper explores the feasibility of TCPs as artificial muscles to drive SWRRs for children with physical disabilities.It highlights the advantages and the current limitations of TCPs on SWRR.The paper presents the design process of a prototype for paediatric ankle SWRRs based on TCPs covering the main parameters of SWRRs being the actuator characterization, the mechanical design based on the biomechanical requirements for paediatric ankle dorsiflexion, the implementation of a control strategy that is merged with an HCI, with this covering the essential parameters that require a paediatric SWRR.

Design of the device and methods
This section presents a description of the TCP manufacturing process and its behaviour.Then, the biomechanical structure of the ankle and a dummy based on it are given as they are required to design and test the SWRR.Later, the design process of the SWRR is presented.Finally, the behaviour of the prototype and a mathematical model are shown.

TCPs manufacturing
The TCP actuators were fabricated using the process similar to Chossat et al [31].A 1.5 m Nylon fishing line as the precursor fibre (EDGE Mono trace 80 LB) with a diameter of 840 µm.The nylon fibres were twisted and coiled alongside a 36 AWG (127 µm) Nickel-Chromium 80 (NiCr) wire (Fogslord).One end of the nylon fibre was firmly attached to the output shaft of a NEMA17 motor, while the other end was connected to a slider carrying a 1000 g weight (17.68 MPa, value according with: Force (1 Kg * 9.8 m s −2 )/ Fibre Cross Sectional Area (π * (420 × 10 −4 m) 2 )).The NiCr wire was also suspended from the motor shaft but was only weighted with 1.6 g (1.2 MPa) to maintain it in a straightened state.The nylon fibres were twisted and coiled at a slow rotation speed of 250 RPM.The twisting and coiling process was stopped manually once the precursor fibre was fully coiled.For the annealing process, the embedded NiCr wire was employed to produce Joule heating.This annealing process consisted of five consecutive five-minute periods, each applying an annealing current of 240 mA.A 1 min cooling phase was inserted between each annealing period.After this treatment, TCPs with an average length of 44 cm and a diameter of 1.97 ± 0.04 mm were produced, the measurement were taken with a digital calliper (Duratool).The resulting actuators were trimmed to 39.5 cm and clamped with insulated male spade electric terminals.Each electrical terminal required 5 mm for crimping, which led to a 10 mm reduction in the functional area.Table 1 depict the main manufacturing parameters of the fabricated TCPs.
To test the fabricated samples, a custom-made experimental test bench was utilised to measure force and displacement (figure 2(a)).In both cases, an Arduino NANO served as the data acquisition system.A transistor (Vishay Siliconix IRF540) regulated the voltage from the power supply, while an NTC thermistor (TE Connectivity, 5K3A1) was employed to monitor the temperature of the TCP.
In the force test (figure 2(b)), one end of the actuator was fastened to a fixed hook, and the other end was connected to a 10 Kg load cell (TAL220).This load cell was interfaced with the Arduino through an analogue-to-digital converter (Avia semiconductor, HX711).For the displacement test (figure 2(c)), the actuator was suspended with a weight above a laser displacement sensor (Sick OD mini OD1-B100C50I14), which was connected to a current sensor (Texas Instruments INA269) interfacing with the Arduino.The calibration process for the sensor can be found in the supplementary information (Calibration Procedures).
Both force and displacement tests applied a square signal of 2400 s on and 240 s off to observe the strain and power relationship.The 240 s duration was chosen to allow the system to reach a stable condition.Experiments were repeated at different power levels ranging from 160 mA to 240 mA with the applied current incrementing by 20 mA.
Throughout the experiments, data on TCA temperatures, power consumption, and the weight distance from the sensor were continuously recorded using an Arduino NANO with a sampling time of 50 ms.In the case of the displacement test, various weight values ranging from 600 g to 1000 g were employed to assess the actuator's performance.Each test (force and strain) was performed using 5 different actuators, each one used 4 times, for 20 trials per test.

TCP behaviour
Characterising the performance of the manufactured actuators is essential to determine their suitability for the SWRR requirements.In these tests using TCPs as linear actuators, two primary parameters of interest are force and strain, which will later be converted into torque and range of motion (ROM).The mean of the last 50 samples before turning off the applied power was averaged to calculate the maximum in both tests.This average represents the system's steady state after the step signal was applied.Then, from the 20 maximum values, the mean and standard deviation of the maximum force, temperature, displacement, and strain were obtained.
Figure 3 displays the results obtained from the force test.The TCP actuator's maximum force output is 7.9 ± 0.5 N (807.9 ± 57.6 g) when a current of 240 mA is applied.However, it is important to note that when considering the prestress of the fibre (0.7 ± 0.2 N or 76.8 ± 21.2 g), the maximum change in force is 7.1 ± 0.4 N (730.0 ± 46.3 g) (figure 3(a)).To assess the response times for heating (τ h ) and cooling (τ c ), the analysis focused on the average time required for the actuator to reach 63% of a steady-state value after a step input.The analysis results indicate that the average τ h is 31.42 ± 1.02 s, and τ c is 28.2 ± 0.4 s.At the highest applied power level, the generated temperature reached 78.35 In contrast, the results from the displacement test highlight the noticeable impact of pre-strain (generated by the weights) on the actuator's length, causing it to contract from 386.0 ± 3.7 mm to 380.2 ± 3.7 mm, 373.88 ± 4.08 mm, 365.3 ± 4.8 mm, 357.9 ± 5.3 mm.This pre-strain has a direct effect on the actuator's contraction.When a current of 240 mA was applied with different loads, the maximum displacements were as follows 38.7 ± 1.9 mm, 39.8 ± 0.8 mm, 40.4 ± 2.1 mm, 43.5 ± 2.4 mm, 44.5 ± 1.1 mm for weights of 1000 g, 900 g, 800 g, 700 g, and 600 g, respectively (figure 4(a)).Nevertheless, when the final elongation is considered, the strain can be obtained using the following formula: Here, strain (S) represents the relationship between the initial length (L) of the actuator and the resulting stroke (∆L) when activated, expressed as a percentage.Analysing the strain data, the results were as follows: 10.02% ± 0.45%, 10.4% ± 0.1%, 10.9% ± 0.6%, 11.7% ± 0.7%, 12.3% ± 0.3% for weights of 1000 g, 900 g, 800 g, 700 g, and 600 g, respectively (figure 4(b)).It is noteworthy that these strain values align with the findings from the maximum force analysis, where the maximum generated force was observed at 7.1 N (730.0 ± 46.3 g).After this point is possible to see a fall in the displacement and strain.The average response times (τ h ) and (τ c ) are measured at 39.2 ± 1.3 s and 20.6 ± 0.5 s, respectively.

Ankle biomechanics
The ankle, characterised by its intricate anatomy, comprises the tibiotalar joint and the transverse tarsal joint, collectively affording a broad spectrum of multidirectional motion.Critical motions within the ankle joint complex encompass plantar-and dorsiflexion, occurring predominantly in the sagittal plane, as well as ab-/adduction in the transverse plane and inversion-eversion in the frontal plane.Combinations of rotations across the subtalar and tibiotalar joints generate three-dimensional motions called supination and pronation [32,33].
However, it is worth mentioning that the majority of ankle movement primarily occurs within the sagittal plane, with plantar and dorsiflexion being predominantly governed by the The plantar-dorsiflexion movement within a 66 • range is commonly observed during daily activities such as walking, climbing stairs, etc.These activities typically occur at a frequency of around 1.75 Hz.However, it is important to note that during rehabilitation sessions, these movements are often executed at much lower frequencies, usually falling below 0.2 Hz [10,36,37].

Dummy testing platform
For conducting trials on the paediatric ankle SWRR, a mannequin designed to replicate the lower limb proportions of an average 10 year-old child was employed.Accurate measurements for the leg were derived from the World Health Organization's (WHO) child growth standards [38] and the anthropometric data provided by Winters [39].These references guided the determination of limb dimensions, resulting in a crus length (knee to ankle) of 40 cm, foot length and width of 22 cm and 7 cm respectively.Thet total foot weight 300 g.The used dummy is shown in figure 5.
To assess the exoskeleton's response to various torques, diverse weights were added to the foot, situated 10 cm from the ankle's centre of rotation.The weights ranged from 500 g to 3000 g, incremented in 500 g intervals.This weight variation corresponded to a torque spectrum from 3 Nm to 0.5 Nm.

Paediatric ankle SWRR design
The SWRR consisted of two 3D-printed braces that wrapped around the top part of the crus brace (CB) and the second one on top of the foot instep brace (FIB), figure 5.The FIB was positioned 5 cm away from the centre of rotation of the ankle.Both braces use Velcro to maintain the position over the mannequin.Furthermore, the braces are divided into two different parts: the brace and the lid.This design allowed the connection of the TCPs in series using copper tape between both parts as the electrical connection.The computer-aided design (CAD) model of both braces is displayed in figure 5.The entire device weight was 300 g (without a power supply or battery), making each brace weight 150 g.
On figure 6 an ankle model is showed.P1 is the point at where the TCPs are connected to FIB, P2 is the point where the TCP is connected to CB and P0 the point at the centre of rotation with coordinate (0,0).The coordinate of P1 (X p1 , Y p1 ) is: Then L Tcp can be written as: And θ 2 : where r is the radius between the centre of rotation and P1, θ 1 is the angle of the foot during dorsiflexion, θ 2 is the angle between the TCPS and the braces, L V is the distance between P1 and P2 when θ 1 = 0, L H is the distance between the centre of rotation and the connection of the TCP on CB (x axis).Finally, L Tcp is the length of the TCPs.In the case of the generated Torque (T), the system can be evaluated as follows: where F W is the force generated by the weight used on the experiments, r W the distance of the weight to the centre of rotation, F f is the force generated by the weight of the foot and r f is the foot centre of gravity, F FIB is the force generated by the weight of the FIB and r FIB the distance of the weight to the centre of rotation, F TCP is the force generated by the TCPs.
With the mechanical model of the SWRR, the behaviour of the TCP and the requirements given in section 2.3.Then The SWRR was designed to provide dorsiflexion movement of children with the following characteristics: (i) being able to provide an angular displacement of 10 • in the plantarflexion direction, (ii) providing a torque of 1.5 Nm.Hence, five TCPs of 30 cm, when unloaded, were used for this.The number of fibres was constrained to five as the biggest challenge for TCPs is the speed.Keeping in mind that the width of the leg was 7 cm, a gap of 12 mm was left to prevent heat crosstalk and improve the cooling time [40].Furthermore, this study is centred on reaching frequencies that can be used in a rehabilitation set-up of 0.2 Hz.Hence, a PID controller was developed to achieve the desired angular displacement in 5 s (section 3).

SWRR test
The performance assessment of the paediatric ankle SWRR was carried out using the testing setup described in section 2.4.The electronic components used were nearly identical to those employed in the force and displacement tests for the unit TCP.These components included an Arduino, a MOSFET, and a thermistor.However, a key distinction lies in the sensor utilised to record angular displacement (figure 2).To fulfil this purpose, a 9-degree-of-freedom Inertial Measurement Unit (IMU), was employed (LSM9DS1, STMicroelectronics).
Both testing procedures followed the application of a square signal, consisting of 180 s on and 180 s off, to establish the strain-power relationship.The selection of the 180 s duration allowed sufficient time for the system to reach a stable equilibrium.The experiments were conducted across various current levels, spanning from 160 mA to 240 mA (incrementally adjusted by increasing the current in 20 mA steps), encompassing all the different TCP actuators.Throughout the test, data about TCA (Thermally Activated Contractile) temperatures, power consumption, and the angular displacement of the foot were recorded and stored on a computer, with the data acquisition performed using an Arduino NANO at a sampling rate of 50 ms.The testing protocol encompassed a range of torque conditions, spanning from 0.5 Nm to 3.0 Nm in 0.5 Nm increments.In addition to the torque generated by the load, it is essential to account for the total negative torque produced by the combined weight of the foot and the FIB (300 g from the dummy and 150 g from FIB), which amounts to approximately 0.4 Nm.Each test was conducted four times utilizing the identical set of actuators.The mean of the last 50 samples before deactivating the applied power was computed to determine the maximum in both tests.This average reflects the system's steady state following the application of the step signal.Subsequently, from the 4 maximum values obtained, the mean and standard deviation of the maximum angular displacement, and temperature were calculated.
The results depicted in figure 7(a) sows the effect of the load on the TCPs fibres, stretching the fibres decreasing the initial starting point to −15, −27 • , −33 • , −37.5 • , −40 • and −42.5 • respectively to the applied torque of 0.5 Nm, 1 Nm, 1.5 Nm, 2 Nm, 2.5 Nm, and 3 Nm.After removing this offset figure 7(b) illustrate that the maximum ROM was attained under a 1.0 Nm load.These findings align with the design objectives, as they are closest to the specified 1.5 Nm torque requirement, registering at around 1.4 Nm.The resulting angular displacement was of 25.1 • ± 0.3 • .The observed behaviour resembled that of the linear displacement of the TCP; as the load increased, displacement decreased, and elongation increased (indicated by a shift to a higher negative angle in the starting position).Conversely, when the load was too low (e.g.0.5 Nm), the device experienced saturation.The relation between the input power and displacement can be seen as a linear relation.For example, the linear equation for the 1.0 Nm load will be equal to: where α is the angular displacement in degrees, furthermore the R 2 if the linear equation is 0.9896 and a RMSE of 0.556.The values for τ h and τ c ranged between 19 and 30 s (figure 7(c)).Additionally, the relationship between input power and temperature resembled that of the single fibre configuration, having its maximum temperature at 83.7 • C ± 0.2 • C when the 240 mA was applied (figure 7(d)).

SWRR model
After acquiring experimental data from the SWRR prototype, a computer model was developed by establishing a connection between ROM and input power.For this purpose, the 1.0 Nm load scenario was selected, as it closely approximated to the required torque of 1.5 Nm when the weight of the foot is taken into account and offered the most significant ROM (25 • , sufficient for full dorsiflexion).The input signal comprised the applied power, while the output signal represented the resulting angular displacement.This dataset was then processed using the System Identification Toolbox in MATLAB.The Toolbox produced a power-angular displacement transfer function denoted as TFPD(s).The best model was as follows: The model provides an accuracy of 92.83%.

Control strategy and results
Utilising the transfer function TFDP (s), a PID controller was tuned with the aid of the Control System Toolbox in MATLAB.Subsequently, a closed-loop system with the PID controller was simulated in MATLAB/Simulink.The simulation was focused on minimising potential issues such as overshoot, controller settling error, and power requirements, as any such errors could lead to the incorrect application of force to the user, potentially causing harm.To attain the desired maximum ROM of 10 • , it took 5 s, corresponding to an inverse After the closed-loop controller was tuned, it was implemented on an Arduino NANO microcontroller.A maximum power limit of 148 W was imposed, as determined by the capacity of the available power supply (60 V, 2.46 A).A pulse-width modulation strategy was employed to apply the requisite power.Three distinct tests were conducted: a step input test to evaluate the controller's performance, followed by a chirp test to assess the actuator's bandwidth.Lastly, an HRI was established using an electromyography (EMG) sensor MyoWare 1.0 (MyoWare) to capture muscle signals from the calf, demonstrating its potential as a control mechanism for the SWRR.Ag/AgCl electrodes were used, with bipolar electrodes situated on the belly of the tibialis anterior muscle and a reference electrode placed on the tibia.The EMG signal acquisition was performed with a 33 year-old male subject, using the same test bench employed for SWRR characterisation, now including the EMG sensor for the HRI test (as show in video S1).

Step signal
The reference signal for the step response was set at 10 • , representing the ROM commonly observed during walking activities.In figure 8(a), the plot illustrates the position reference and the system's output when subjected to a step signal in the SWRR.The output closely tracks the reference signal; however, the system exhibits an overshoot response.It takes approximately 5 s to move from 0 • to 10 • .The power graph reveals that the controller initially requires the maximum available power of 148 W, which decreases to an average of 17 W (figure 8(b)).

Chirp signal
A chirp test was used to benchmark the working frequency of the whole system to understand its capabilities.A chirp signal consists of a sinusoidal sweep signal that varies its frequency over time, which can be expressed as follows: Here f 0 is the final frequency, A is the amplitude of the sinewave, t is the time, and c is the chirp rate, described by: where f e is the final frequency, and T s is the time it takes to sweep from f 0 to f e .The sinewave had an amplitude of 10 • , aligning with the required displacement, covering from a baseline of 0 • to 10 • .The frequency range was from 0.001 Hz to 0.1 Hz (figure 9(a)).The cutoff frequency was identified when the magnitude decreased to −3 dB.During the test, the actuator reached the −3 dB threshold at a frequency of 0.025 Hz (figure 9(b)).Regarding temperature, the actuator maintained an average temperature of 53 • C, indicating that the TCP struggled to track the chirp signal precisely (figure 9(c)).The power response was distinct, as the system attempted to operate at that frequency by oscillating between maximum power and zero (figure 9(d)).To enhance response time without requiring an external cooling system, an offset of 10 • was introduced on the ROM, operating within the 10 • -20 • range.With this adjustment, the working frequency improved to 0.034 Hz, which was 1.36 times faster.Nevertheless, it still fell short of the target of 0.2 Hz.

EMG HRI
The EMG signal was sampled at a frequency of 20 Hz, corresponding to the speed of the serial communication.Using the MyoWare 1.0 sensor, two types of signals were obtained: the EMG raw signal and the EMG envelope (EMGe) signal.The latter serves as an amplitude-modulated representation of the raw signal.To identify muscle activation, a threshold of 150 mV was set for the EMGe signal, preventing errors coming from movement artefacts.The activation pattern remained active for 8 s to achieve the 10 • movement, followed by 90 s to allow the system to cool down and return to the starting position, following a similar approach to Pittaccio et al [36].
From the graphical representations, it is evident that the system is triggered when the EMG envelope surpasses the 150 mV threshold (figures 10(a) and (c)).This activation prompts the utilisation of the entire power output, which relaxes over 90 s (figure 10(b)).These observations confirm that the SWRR device responds effectively to the EMG signal.

Discussion and conclusion
This study explored the proof of concept for a SWRR system using TCP AMSM.The research included an actuator characterisation and the design process to meet biomechanical requirements.The resulting device is lightweight, flexible, and compact, meeting the minimum biomechanical needs of children with physical disabilities.This includes achieving a 10 • ROM within 5 s, a torque of 1.5 Nm and an HRI.However, several improvements are needed before this technology can be applied in rehabilitation settings.
The study's results indicate that the behaviour of single fibres is similar to the multifibre approach integrated in the SWRR.With differences in displacement and force as they translate into angular displacement and Torque.These differences are due to the mechanical design, and there's a tradeoff between torque and displacement, as they are inversely proportional.
Despite the challenges, the technology appears highly adaptable, and many approaches can be taken to improve the performance.To enhance torque, incorporating additional fibres, as seen in previous TCP studies, is a viable direction [40,41].In this study, that approach was followed to get the required torque, as a single fibre would be insufficient to generate the necessary force.
Using longer actuators can significantly improve ROM, as this study shows.While the initial design requirement was a 10 • ROM, the longer actuators enabled an impressive 25.18 • ROM, effectively covering the full dorsiflexion range.This approach offers an additional advantage, as previously emphasised by Gonzalez et al [42], which is the reduction in temperature.This temperature control is vital for ensuring the device's safety during use.It is worth noting that the pain threshold for human skin at the dermal/epidermal layer is approximately 44 • C [27].In this context, when considering the 10 • ROM, the temperature was 65 • C lower compared to the temperatures reached when the actuator operated at its maximum stroke, which often exceeded 90 • C. Nonetheless, if the device is intended for use with children, the incorporation of an insulation layer, such as Polytetrafluoroethylene, is advisable to ensure optimal comfort and safety [43].
Nevertheless, coming from equations ( 2) and ( 5), the variation of r affect the linear displacement need to generate an angular displacement and the toque in an inverse manner.Is possible to improve this factor by tunning these distances, in the case of the study the r was chosen to be as small as possible because is the technology is envisioned to be used as a fabric that will be incorporated in clothes like socks.
The primary challenge associated with this technology pertains to its reaction time.However, this initial disadvantage could be solved by dividing this problem into two distinct aspects due to the actuator's unidirectional nature, where applying power triggers contraction but cannot control elongation.
On one side, accelerating the contraction time necessitates increased applied power, leading to higher temperatures more quickly.The critical constraint lies in the need to carefully regulate this applied power to prevent heat-induced damage to the actuator.The research demonstrated that implementing the suggested control strategy allowed faster speeds without harming the actuator, preventing the fibre from overheating and burning [29].Nevertheless, this approach demands substantial power levels to achieve rapid responses, often exceeding 100 Watts.This power requirement poses a challenge given the limitations of current battery technology.Nonetheless, advancements in energy storage and transmission are ongoing, promising improvements in energy density and battery miniaturisation [44][45][46].
On the other hand, addressing the relaxation phase poses a more complex challenge.This research sought to optimise the device's cooling process without external systems, relying on convective airflow.These optimisations involved creating sufficient spacing between each actuator to prevent heat transfer between individual fibres [40].Regrettably, this consideration is counterproductive in the design as it limits the number of fibres used in the SWRR to produce higher torques.
Additionally, it was experimented with operating within an optimal temperature range, introducing an offset from the initial working point (from 0 • to 10 • ) to achieve a faster movement previously investigated by Gonzalez et al [42].This approach increased the frequency by 1.36 times.However, it did not significantly improve due to the actuator's considerably slower natural frequency than the required frequencies (0.02 Hz in TCP versus 1 Hz in walking activity).
Two potential alternatives come to light to address this issue.The first is incorporating a cooling system, as seen in numerous TCP research studies [47,48].The second option involves adopting agonist-antagonist muscle systems [43,49].However, it is important to note that these approaches entail increased system complexity, requiring additional components that expand the system's size and weight.Furthermore, it necessitates more sophisticated control strategies to activate each component as needed.
Finally, another crucial facet of SWRR technology is the HCI.To demonstrate the device's feasibility, a straightforward EMG HCI was implemented, showcasing the technology's capabilities.This approach allowed system activation to be controlled based on the user's intent through muscle activation, a pivotal component of rehabilitation therapy that enhances user engagement.Looking ahead, it would be compelling to explore the incorporation of various wearable sensor technologies in conjunction with TCP technology to create SWRR devices that can seamlessly integrate into the daily lives of children.This advancement holds the promise of substantially improving their overall quality of life.
This study presents innovative components to design paediatric ankle SWRRs.These elements provide solutions to specific issues of traditional exoskeletons (weight and compliance) and can be translated to develop SWRR for different purposes.Nevertheless, as discussed, the technology still needs to be improved for its widespread adoption in rehabilitation settings.Additionally, it is essential to collaborate closely with human users to understand better and address any technology shortcomings.

0Figure 3 .
Figure 3. Force power relationship (a) and temperature power relationship during the isotonic force test.Confident intervals (CI) included.

Figure 5 .
Figure 5. Paediatric leg dummy and CAD design of the SWRR braces.

Figure 6 .
Figure 6.Free body diagram for (a) displacement and (b) forces acting on the dummy.

Figure 7 .
Figure 7. TCPs relations dummy test characteristics.(a) Angular displacement-torque relation when the maximum current of 240 mA is applied.(b) Angular displacement-power relation and (c) temperature-power relation when a torque of 1 Nm is applied.Confident intervals (CI) included.

Figure 8 .
Figure 8.(a) Angular displacement and temperature of the SWRR after applying a step signal of 10 • using a PID controller.(b) Power was applied to generate the 10 • displacement.

Figure 9 .
Figure 9. Chirp test results.(a) angular displacement of the SWRR following the chirp signal.(b) Magnitude decay in dB through frequency.(c) TCP temperature.(d) Power used by the SWRR.

Figure 10 .
Figure 10.(a) Angular displacement generated after the EMG threshold was surpassed.(b) Power consumption of the SWRR during the EMG activation.(c) An EMG signal is used to trigger the SWRR.