Soft,Wearable,and Pleated Pneumatic Interference Actuator Provides Knee Extension Torque for Sit-to-Stand

Abstract

Soft wearable actuators can help connect machines and humans, providing a personalized, ergonomic, and cooperative physical interface between people and their world. Until now, the torque of these interfaces has been limited, restricting their ability to assist the completely paralyzed. This article presents a method for realizing a soft structure that stably and comfortably applies a knee extension torque to the body that is sufficient for sit-to-stand (STS). The structure, the pleated pneumatic interference actuator (PPIA), is based on pleated inflatables; is lightweight, collapsible, and clothing integratable; and generates torque from buckling of a constrained fabric-reinforced rubber tube. Multiple PPIAs were integrated into a soft orthosis, the soft lift assister for the knee (SLAK). The SLAK was inflated to a pressure of 320 kPa, and it produced a maximum 324 Nm torque at a flexion angle of 82°. This exceeds the peak 180 Nm torque required for STS and torques required for other everyday tasks. The SLAK met the torque requirement for STS, which is more than 93% of the STS motion when worn by a test leg. Worn by a human, it shows potential for complete support, which is more than 100% of the motion. The PPIA's theoretical model overestimated torque at low to moderate flexion angles and underestimated PPIA torque at high flexion angles. Further development of the PPIA will focus on testing the SLAK with human subjects; increasing the PPIA's speed and flexibility; reducing the PPIA's bulk; and improving the PPIA's model accuracy.

Introduction

From the wheel to the computer, machines have played an important role in enhancing humans' interaction with the world. The role of machines that cooperatively work with humans can be further enhanced through the development of soft, wearable, and high torque actuators. These actuators act as the physical interface that exchanges forces and motion between body-worn machines, their wearers, and the surrounding environment. They have the potential to improve human productivity in, for example, search and rescue tasks,¹ assistive devices for rehabilitation from injury or sickness,^2,3 restoration of independence in people with disabilities,^4–6 augmentation of human performance,⁷ and ergonomic support in industrial applications.⁸ Specific soft devices include the wearable suits made for rehabilitating the hands and feet of stroke patients by Polygerinos et al.³ and Awad et al.,⁹ respectively. However, these actuators only produce low torques. They cannot generate the high torques required to completely assist the completely paralyzed. Simultaneously realizing soft, wearable, and high torque actuators is challenging. Actuator softness requires the use of materials that cannot effectively transmit high torques. These materials' low compressive and torsional stiffness means they are significantly displaced when loaded with a high torque, limiting actuator stroke, or possibly resulting in actuator failure. Soft and high torque are relative terms. Wearability gives them context, defining actuator softness properties and torque capabilities as comparable to human joints. Although nature has soft and “wearable” actuators (muscles) that can produce large joint torques, manmade actuators with these three properties have not yet been made. Developing such actuators is our aim.

Actuator softness is important, because it contributes to a natural, safe, and robust interaction.¹⁰ In this work, soft means that the actuator, in the directions in which it interacts with its wearer and environment, has a similar or lesser impedance (stiffness, damping, and inertia properties) relative to that of its wearer and environment in those directions. This recognizes that human joints significantly change impedance depending on their loading condition. For example, the ankle's stiffness during standing increases when perturbations are applied¹¹ and the leg's stiffness increases during running as the ground surface stiffness increases.¹² In general, joint impedance increases to transmit high torques, meaning that unactivated muscles have a lower impedance, and hence different softness than activated muscles.^11,13,14

High torque in soft, wearable actuators enables them to replicate the high force density of human muscles. It gives them the strength to do tasks that humans can do, and it potentially enables their completely paralyzed wearers to again engage in everyday tasks. Here, high torque is the ability to generate the highest torques required for activities of daily living (ADLs) in humans. In the upper limbs, Rosen et al.¹⁵ found this to be 10 Nm at the shoulder, but in the lower limbs it is 180 Nm per leg for extension of the knee during sit-to-stand (STS).¹⁶ Given the knee extension, torque during STS is the highest torque demanded of human joints during ADLs, and it is taken as the torque requirement to meet in the actuator presented in this work. This magnitude torque is also significantly larger than that generated by soft actuators in the literature (of a suitable size to be worn on the body). Outside of our research, these include Yap et al.'s¹⁷ bending bellows made of 3D-printed Ninjaflex (thermoplastic polyurethane [TPU]) with a maximum torque of 10 Nm; Fang et al.'s¹⁸ nylon fabric-TPU knee extension bellows with a torque of 25.7 Nm; Thalman et al.'s¹⁹ nylon fabric-TPU elbow flexion bellows with a torque of 27.6 Nm; and the nylon fabric-reinforced-TPU pneumatic interference actuator (PIA) in Chung et al.'s²⁰ ExoBoot with a torque of 39 Nm. We have also reported initial data on the predecessor to this work's actuator in Veale et al..²¹ A maximum torque of 150 Nm at 200 kPa and a flexion angle of 70° were presented.

Further, wearability is the extent that the actuator is ergonomically suited to be worn on the human body. Noteworthy ergonomic factors are the actuator's comfort and compatibility with the natural body movements and everyday living scenarios of its wearer.²²

Given the current lack of soft, wearable, and high torque actuators, this work aims at filling this gap. It does so by presenting a method for realizing a lightweight, backdrivable, collapsible, and clothing-integratable soft structure. The structure is based on the principle of other inflatable pleated actuators,^23–25 and it is unique in that it applies a high torque to the human body while remaining in place over its range of motion (ROM). We name this the soft lift assister for the knee (SLAK). The high torque capability of the SLAK's actuator was validated by its ability to generate sufficient knee extension torque for STS over nearly all of the STS movement.

Knee Orthoses' Requirements for Full STS Support

Ideally, a knee extension orthosis for full support of STS should fulfill the requirements in Table 1. More specifically, the actuator should provide, for a given flexion angle, at least the extension torque indicated by the requirement envelope in Figure 1. This ensures that the actuator can provide sufficient knee extension torque for STS^16,26,27 of an 80 kg user (the maximum weight of an average-sized adult male, taken as one standard deviation above the mean body weight of a mid-sized adult male from Ref.²⁸). Orthoses that actively support other movements may have other requirements, particularly those regarding orthosis performance.

FIG. 1.

The torque-angle relationship for knee extension torque of an 80 kg person for STS. The required torque is indicated by the upper boundary of the blue area, where the maximum torque corresponds to 2.25 Nm/kg when normalized by user body weight. The state-of-the-art in the torque performance of soft wearable actuation is the ExoBoot,²⁰ represented by the red line. Note that this device was for the ankle and hence does not feature in State-of-the-art in Knee Exoskeletons and Exosuits section. STS, sit-to-stand. Color images are available online.

Table 1.

Key Performance and Ergonomic Requirements for a Sit-to-Stand Knee Extension Orthosis That Can Provide Full Support of an 80 kg User

Category	Requirement	Max value	Source
Performance	ROM (°)	93	¹⁶
	Speed (°/s)	175	¹⁶
	Torque (Nm)	180	¹⁶
	Power (W)	325	¹⁶
Ergonomic	Weight on knee (kg)	1–2	^{4, 29, 30}
	Generated sound level [dB(A)]	50–60	^{31, 32}
	Don/doff time (s)	300	³³

ROM, range of motion.

In addition to performance requirements, the ergonomic requirements of a knee orthosis are also important. They are, however, more difficult to quantify due to their user specific nature. Hence, not all are listed in Table 1. Key ergonomic requirements include minimal knee orthosis weight, generated sound level, and temperature; and ease of donning (putting on the orthosis) and doffing (removing the orthosis). Normal compression and shear interaction forces³⁴ and breathability³⁵ are to be optimized for comfort. Also important, orthosis size, as quantified by an orthosis' profile, or maximum distance from the body surface over its ROM, should be minimized to minimize restriction of the user's movements when no support is needed^22,36 and to prevent stigmatization.^37–39

State-of-the-art in knee exoskeletons and exosuits

Table 2 summarizes the key features, torque, ROM, maximum profile over ROM, and weight of a number of active knee orthoses in the literature. Maximum continuous torques range from 4.4 to 140 Nm, ROM from 50° to 360°, weight from 0.09 to 5.8 kg, and profile from 0.0375 to 0.3 m. Only Pratt et al.³⁰ reported a don/doff time (600 s).

Table 2.

Key Actuation and Ergonomic Properties of the State-of-the-Art in Active Knee Orthoses

Device	Type	Torque generation	Max continuous torque (Nm)	ROM (°)	Max profile (m)	Weight (kg)
Active Knee Exosuit (Slade et al.⁴²)	SK-A-B	Geared servomotor extends the knee with a Bowden cable pulling on a four-bar linkage	9	120	0.085^a	1.2^b,c
AssistOn-Knee⁴⁴	SK-N-U	Geared servomotor drives a self-aligning knee-mounted pulley and series elastic element via a Bowden cable	35.5	180	0.05^a	1.4^d
iT-Knee⁴⁰	SK-N-U	Geared servomotor drives knee via a torsional series elastic element and 3D self-aligning mechanism	140	130	0.1^a	3.57^e
Knee Exoskeleton (Shepherd and Rouse⁴⁵)	SK-A-U	Servomotor and 2:1 belt transmission drives knee joint via a ballscrew and leaf spring series elastic element	40	120	0.0375	3.9^c
Knee Exosuit (Fang et al.¹⁸)	SU-N-U	Soft inflatable bellows extends knee on inflation	25.7	360	0.12	0.09^f,g
Knee Exosuit (Sridar et al. ⁴³)	SU-N-U	Soft I-beam cross-section inflatable tube extends knee on inflation	4.4	$\geq 60$	0.045^a	0.16^f
Knee Exoskeleton (Witte et al. ⁴¹)	SK-N-U	Geared servomotors drive knee flexion/extension Bowden cables	120/75^h	120	0.25^a	0.76^d
KNEXO⁴⁶	SK-N-U	Antagonistic pleated pneumatic artificial muscles drive the knee with a four-bar linkage	75^a	$\geq 50$	0.07^a	5.8^f
Myosuit⁴	SU-A-B	Servomotor with a 4:1 pulley transmission drives a knee extending Bowden cable coupled between the ankle and hip	43.5	$\geq 80$	0.06^a	2^a–c
RoboKnee³⁰	SK-A-U	Servomotor driven ballscrew with series elastic element mounted between thigh and calf shells	125^a	110	0.3^a	2^a,c
SERKA⁴⁷	SK-N-U	Geared servomotor drives knee-mounted pulley and torsional series elastic element via a Bowden cable	41	$\geq 80$	0.05^a	1.2^d

Under the category “Type” the following codes are used: exoskeleton (SK), exosuit (SU), autonomous (A), nonautonomous (N), unilateral (U, meaning one leg actuated), and bilateral (B, meaning both legs actuated).

Values were estimated from photos, text, and data.

Estimated weight of unilateral version of device.

Not including body mounted battery weight.

Not including grounded geared motor or power supply weight.

Not including grounded power supply weight.

Not including grounded pressure source weight.

Not including body mounted electronics and valve weight.

Extension/Flexion torque.

None of the orthoses has a maximum continuous knee extension torque of the required 180 Nm in Table 2. Only three^30,40,41 of the 10 orthoses surveyed could provide a maximum torque higher than the lowest STS requirement (represented by the data in Fig. 1 of Roebroeck et al.²⁷) of 65 Nm. Of the devices in Table 2 that explicitly stated their maximum ROM, all could provide the required 93°, and around half had a maximum profile of 0.06 m or less.

Comparing orthoses' weights shows that the lightest autonomous device was 1.2 kg,⁴² within the weight requirement of 1–2 kg, and the lightest nonautonomous device was 0.09 kg,¹⁸ well under the weight requirement. The exosuit devices^4,18,43 were at or under the upper 2 kg weight requirement.

These devices, which can be considered as soft wearables in terms of their primary use of nonrigid and clothing-like materials, cannot provide even Roebroeck et al.'s²⁷ STS torque of 65 Nm. This shows there is not yet a non-rigid (highly soft and wearable) active knee orthosis that can provide the torque for STS.

Actuator Concept

A variety of fundamental soft actuation principles exist.⁵² These include electronic electroactive polymers (EAP), ionic EAP, thermally activated smart materials, pressurized fluid actuators, photoresponsive actuators,⁵³ pH-activated actuators,⁵⁴ and magnetic field sensitive actuators.⁵⁵ The first four of these have been manufactured on a scale that is relevant to providing meaningful assistance in an active orthosis. These are summarized in Table 3.

Table 3.

Example Mechanisms, Pros, and Cons of the Four Types of Soft Actuators Manufactured in a Scale Relevant to Active Orthoses

Type	Example mechanism	Pros	Cons
Electronic EAP	PVC gel actuator: An electric field generated Maxwell force deforms a PVC gel⁴⁸	Moderate force, long lifetime	Low power output, rigid electrode structure
Ionic EAP	PVA-PAA polymer gel: Submersing the gel into a solvent causes it to swell reversibly^49,50	High ROM	Low force, controlled operating environment
Pressurized fluid	McKibben PAM: Inflation of a rubber tube constrained by a braided sleeve causes the assembly to shorten²²	High force, moderate ROM	Force decreases rapidly with shortening, vulnerable to leakage
Thermally activated smart material	Super-coiled polymer muscle: Heating of a coiled polymer fiber with a high negative temperature coefficient results in its contraction⁵¹	Ease of manufacture	Slow, inefficient

EAP, electroactive polymers.

The focus of this article is improvement of the torque of current soft actuators, the most promising of which is the pressurized fluid type in Table 3. One of the most simple possible pressurized fluid actuators is a flexible inflated tube. When it buckles, it generates a torque that tries to straighten it (Fig. 2A). A comparable extending actuator is found in the joints of spiders and other exoskeletal creatures.^56–58 Nesler et al.⁵⁹ have modeled and characterized the buckling tube actuator, the PIA used by Chung et al.²⁰ in the ExoBoot. Functionally, it generates the torque required to extend the knee. However, only a small fraction of the PIA's length, the region that buckles, is used to generate torque. Hence, as done by others,^23–25 we increased the number of buckling regions to increase its torque for a given flexion angle and pressure. We added a pleat in the PIA, that is, two valley folds and a mountain fold (Fig. 2B). Such a structure we call a pleated PIA (PPIA). The pleat is held in place by a pleat constraint (Fig. 2C) that cancels the counter-torque generated by the mountain fold. The pleat can be placed on the top or the bottom of the PPIA's tube. Adding this pleat to the PIA enables a PPIA to generate torque in one direction over more than 180° and, depending on its geometry and the required flexion angle, this torque is greater than that produced by an equivalent diameter PIA. Also important is prevention of kinking (severe folding of the tube that prevents fluid from flowing past the fold¹⁸) of the tube, which can be prevented with an anti-kink cord (Fig. 2E). Compared with the PIA, the pleat gives the PPIA a theoretical ROM of $18 0^{\circ} + 2 α$ .

FIG. 2.

The PIA (A) and PPIA (B) are made of a flexible tube, diameter D, that produces a torque $τ$ when inflated to a pressure P at an angle $θ$ . When the actuator is attached to a limb or other articulated body, the distance between the body's joint center and the line projected parallel from the PPIA's mountain fold is the pleat misalignment $p_{a}$ (C). In this work, an anti-kink cord running through the PPIA's tube prevents choking of air flow in the PPIA. The pleat constraint is implemented by a flexible, inextensible layer attached to the underside of the PPIA's tube. The PPIA's pleat angle $α$ is the angle of the pleat when the actuator is in the straight position. The width of the pleat width is $p_{w}$ (D). The geometry of a PPIA bent to the angle $θ_{P P I A}$ , assuming it is made of two symmetrically flexed PIAs bent to $θ_{P I A}$ (E). PIA, pneumatic interference actuator; PPIA, pleated pneumatic interference actuator; SLAK, soft lift assister for the knee. Color images are available online.

Actuator modeling

As shown by Nesler et al.,⁵⁹ the theoretical model of the PIA can be derived from the virtual work principle for bending pressurized fluid actuators: $τ (θ, P) = - P \frac{Δ V (θ)}{Δ θ},$ (1)

where (referring to Fig. 2) $τ$ is the actuator extension torque, $θ$ the flexion angle, P the gauge pressure, and V the volume. Assuming a cylindrical tube with diameter D and no losses yields the volume and torque of a PIA as $V_{P I A} (θ_{P I A}) = \frac{π D^{3} tan (θ_{P I A} ∕ 2)}{4},$ (2)

and $τ (θ_{P I A}, P) = \frac{π D^{3}}{8} \frac{P}{{cos}^{2} (θ_{P I A} ∕ 2)} .$ (3)

The two buckling points of a PPIA can be modeled by two PIAs. It is assumed the PIAs are equally deflected and generate the same amount of torque. As the PIAs are mechanically in series, the torque of one PIA is the torque of the PPIA. Figure 2E, and the assumption that the pleat constraint keeps the distance between the base of the valley folds constant, shows that the flexion angle $θ_{P P I A}$ of the PPIA is related to its PIAs' buckling angles by $θ_{P I A} = θ_{P P I A} ∕ 2 + α$ . This is derived from the geometry shown in Figure 2E: $360 = β + 2 θ_{P I A} + 180 - 2 α$ and $180 = β + θ_{P P I A}$ . The pleat angle of the straight PPIA is $α$ (Fig. 2D). Thus, for the PPIA, the volume is an adaptation of Equation (2): $V_{P P I A} (θ_{P P I A}) = \frac{π D^{3} tan ((θ_{P P I A} ∕ 2 + α) ∕ 2)}{4},$ (4)

and using this with Equation (1) gives $τ (θ_{P P I A}, P) = \frac{π D^{3}}{8} \frac{P}{{cos}^{2} ((θ_{P P I A} ∕ 2 + α) ∕ 2)} .$ (5)

Figure 3 shows that in theory and practice a PPIA with the same dimensions and pressure as a PIA produces more torque over the desired range of flexion angles, as well as a positive torque when θ = 0° ( $θ$ will be assumed to refer to $θ_{P P I A}$ for the remainder of the text). In the data, the PIA and PPIA produced significantly lower torques than predicted when their buckling points were nearly straight, because the tubes tended to bend rather than buckle. The PIA's torque plateaued at around $\pm 2$ Nm, because further volume reduction due to an increasing positive or negative flexion angle was compensated by the sides of the buckling point bulging outward (such that the actuator cross-section became elliptical). This occurred in the PPIA, but to a lesser extent, which is why the PPIA's measured torques approached (but remained less than, due to other loss factors) the modeled torque for higher flexion angles.

FIG. 3.

A comparison of the theoretical torque versus angle curves of the PIA and PPIA along with experimental data points (three measurements at each test angle). The asymptote in the PIA model's line at $θ = 0^{\circ}$ indicates this initial torque is the torque required to buckle the actuator. These results were created with Equations (3) and (5) and the parameters: $D = 0.043 m$ , $P = 100 k P a$ , and $α = 5 0^{\circ}$ . Color images are available online.

Equation (5) is a good starting point for understanding the impact that the PPIA's physical parameters have on its behavior. It may be also useful for sizing a PPIA given desired torque requirements. However, Nesler et al.⁵⁹ showed that significant hysteresis losses were present in a PIA. These may be present in a PPIA. This means that to produce a required torque at a given angle, a real PPIA will likely need to be operated at a higher pressure or have a larger diameter than Equation (5) would suggest. Other factors affecting the accuracy of the PPIA's model include unmodeled hysteresis, deformation of the actuator tubes and pleat, and change in $α$ as a function of $θ$ . Incorporating some of these factors into the theoretical model, using an empirical model, or a combined theoretical–empirical model are possible ways to improve model accuracy, as has been done with other pressurized fluid actuators.^60–62

Actuator Fabrication

The PPIA is a simple actuator, but ensuring it can effectively transmit large torques to the knee is a challenge. The design of the PPIA is closely coupled to the design of the flexible fabric sleeve and webbing that connect it to the thigh and calf. Figure 4 shows how the SLAK consists of three PPIAs that are positioned behind the leg. The side PPIAs add extra bulk and mass compared with Veale et al.'s²¹ single PPIA orthosis (the SLAK's volume is 5 L and its mass is 1.95 kg). However, they potentially have the benefit of increasing the SLAK's ROM and torque output, because they eliminate the torque counteracting lateral support cords of the single PPIA orthosis.

FIG. 4.

The SLAK in the flexed (A) and extended (B) positions. The SLAK is shown worn by an instrumented test leg used to measure its torque. SLAK, soft lift assister for the knee. Color images are available online.

An exploded view of the SLAK is shown in Figure 5A with accompanying component descriptions in Table 4. Simply explained, the SLAK is made of three fabric layers connected by stitching: the sleeve layer (1–7, 18), the constraint layer (8–10), and the base layer (11–17, 19–26). The sleeve layer provides a means to attach the PPIAs' inflatable tubes to the SLAK without sewing through them—the tubes are inserted into this layer. The constraint layer introduces the folds in the sleeve layer and, hence, tubes, thus forming PPIAs. The outer constraints also hold the PPIAs away from the base layer so that when they are inflated they do not squeeze the wearer's leg. Last, the base layer enables the PPIAs to be coupled to the leg with velcro (hook-and-loop fastener) and buckles. A more detailed explanation of how the SLAK was constructed, along with scale drawings of all the custom components, can be found in the Supplementary Data.

FIG. 5.

An exploded view of the SLAK showing how all its parts fit together (A). Note that the anti-kink cords (18) cannot be seen as they are contained in the sealed tubes (6). The SLAK is worn as shown in (B). Color images are available online.

Table 4.

Bill of Materials of the Components Used in the Soft Lift Assister for the Knee, as Labeled in Figure 5A

Number	Component description	Quantity
1	Sleeve top	1
2	Inlet nut (thread of 7.7 mm outer diameter × 32 threads per inch)	3
3	Inlet washer (20 mm outer diameter × 8 mm inner diameter)	3
4	Inlet (stem and rubber base of a Dunlop bicycle valve)	3
5	Inlet patch	3
6	Sealed tube	3
7	Sleeve bottom	1
8	Central pleat constraint	1
9	Outer pleat constraints	2
10	Outer pleat constraint reinforcement	4
11	Lower base layer	1
12	Loop velcro for lower base layer	3
13	Buckle loop for lower base layer	3
14	Bottom velcro assembly for lower base layer	1
15	Upper velcro assembly for lower base layer	2
16	Bottom velcro assembly for upper base layer	1
17	Loop velcro for upper base layer's middle velcro assembly	1
18	Anti-kink cord	3
19	Upper base layer	1
20	Loop velcro for upper base layer	1
21	Bottom buckle loop for upper base layer	1
22	Buckle	6
23	Top buckle loop for upper base layer	1
24	Middle buckle loop for upper base layer	1
25	Top velcro assembly for upper base layer	1
26	Middle velcro assembly for upper base layer	1

In addition, as seen in Figure 5B, the SLAK was stitched to jeans that were internally padded (Neoprene rubber sheet, RS-stocknr. 506-3157; RS Components, Corby, United Kingdom). The jeans located the SLAK in the correct position behind the knee, and the padding increased the grip between the jeans and the smooth artificial leg that the SLAK was tested on. This reduced the amount the SLAK shifted downward during actuation. However, the padding also made the SLAK difficult for a human to don and doff, hence a zipper allowed the front of the jeans leg to open. This made donning and doffing easier.

Actuator Characterization

A series of experiments were performed on the SLAK to determine its performance and behavior. This was useful for determining the SLAK's suitability for STS assistance (using the requirements in Table 1 as a benchmark), comparing the SLAK's PPIAs to the state-of-the-art in soft, high torque actuators, and gaining knowledge that could be applied to the future modeling and design of PPIAs. Experiments were conducted to measure the SLAK's extension torque production during standing, the sensitivity of its torque production to misalignment of the pleat and the knee joint, its hysteresis, the effect of pressure on torque production at different angles, the bending stiffness of the deflated actuator (backdrivability), and its speed. The next sections will explain the mechanics of the test rig, how torque was calculated, and the experimental methods.

Test rig

The test rig is schematically shown in Figure 6 and its key components are listed in Table 5. The test rig consisted of an instrumented test leg (11) that wore the SLAK. The leg was based on a 3D scan of the leg of a 1.8-m tall, 76 kg male and made from Necuron 651 (Necumer GmbH, Bohmte, Germany). These gave it hip–knee joint and knee–ankle joint distances of 0.45 m. The leg was weighted such that it had a similar weight distribution to the biological limb it was modeled after. The foot of the leg was fixed, and the hip was able to translate in a straight line along a linear guide (8).

FIG. 6.

A schematic of the test rig showing how the SLAK was tested. The numbered labels indicate components listed in Table 5. In dynamic experiments, the test leg (11) was inverted, the winch (4) disconnected, and a weight connected to the load cell (7). Color images are available online.

Table 5.

Key Components Used in the Test Rig (Numbering Corresponds to That in Fig. 6)

Number	Component	Part description
1	Air reservoir with integrated regulator	Batavia 7061061 VOLUMIA 15 L portable air pressure tank
2	Manual deflation valve	Festo HE-2-QS-8, 2/2 pneumatic manual control valve
3	Manual inflation valve	Generic ball valve, 0.004 m orifice diameter, Festo 0.008 m diameter push-in fittings
4	Winch	Generic trailer winch, unbraked, bidirectional ratcheting, 6 m long $\times$ 0.05 m wide band with 636 kg capacity
5	End stop	Custom (wooden block clamped to the guide rail)
6	Pressure sensor (0–1 MPa)	Festo SPTE-P10R-S6-B-2.5K
7	Load cell (500 or 100 kg)	1% full-scale maximum error, generic S-beam 500 kg, China or 0.03% full-scale linearity, LCM101-100 S-beam 100 kg, Omega Engineering, Inc., Norwalk, CT
8	Linear guide	SBI20-1000L rail with SBI20-FL linear bearing and HK2001A clamp
9	Encoder	AMS AS5048A
10	SLAK PPIA	Custom (see Actuator Fabrication section)
11	Test leg	Custom (see Experiment Methods section)

PPIA, pleated pneumatic interference actuator; SLAK, soft lift assister for the knee.

During an experiment, the SLAK was donned by the leg, pressurized by using components (1–3), and the resulting motion and/or force measured with the leg's encoders (9) and load cell (7). This was done with the test rig shown as in Figure 6 for all the experiments but the dynamic experiments. In these (nondynamic) experiments, the leg was upside down and the leg's position was imposed by a winch (4) connected to the load cell. In the dynamic experiments, the whole test rig was set upright and the load cell was connected to weights instead of the winch. Further, the SLAK was pressurized directly with a compressed air blow gun.

The test rig was not designed to simulate STS or another particular leg movement, but rather to test how much torque the attached actuator could generate at a particular angle. The consequence is that it is difficult to simulate dynamic loading conditions of STS with the current test rig. However, a compromise was to quasistatically test STS and compare it with STS datasets^16,26,27 based on dynamic torque analyses that account for the inertia and movement of all body segments. If the actuator tested could provide sufficient torque at a given angle as indicated by those datasheets, it is reasonable to assume it could completely assist slow STS movements.

The reason the SLAK was tested upside down in the static and quasistatic cases was that this was the most simple way (compared with mechanisms that compensate for the mass of the test leg) to characterize the torque generation of the SLAK over the complete standing ROM of the knee when using a realistic setup. The test leg was not tested on its side because its joints were not designed for side loading, and bearing friction would have hindered its movement in this orientation. Thus, the leg was inverted, where gravity acting on the test leg fully extended the knee and the winch flexed the knee. This method could measure low actuator torques over the whole test leg ROM, hence enabling a more complete characterization of the SLAK.

In contrast, if the SLAK was tested in an upright position, its whole ROM could not have been tested, as even when pressurized at the highest test pressure of 350 kPa the SLAK could not generate enough torque to fully extend the test leg. This was because the flexion torque due to the mass of the test leg's moving components was greater than what the SLAK could generate when the leg was fully extended. For example, at 350 kPa and a flexion angle of 17° the torque due to the leg's mass was 170% of that generated by the SLAK (in the tests of Fig. 7).

FIG. 7.

The SLAK quasistatic torque-angle characteristic compared with the STS requirements of Figure 1. The mean pleat misalignment $p_{a} \approx 0 m$ . Results are shown with bands of $\pm$ two standard deviations ( $n = 6$ experiments). Color images are available online.

Torque calculation

The knee torque was calculated by using statics equations, including all the external vertical and horizontal forces acting on the test rig arm, thigh, and calf. These included bearing reaction forces, thigh and calf weights, and the force measured by the load cell. This compensated for the mass of the test leg's moving parts. Note the passive torque component due to the SLAK's highly reproducible deflated bending stiffness (including the pinching effect) was subtracted from the compensated torques to generate all plots of the SLAK's quasistatic torque generation.

In torque calculations for the dynamic experiments, compensation for the test rig's inertia was done, but not subtraction of the SLAK's passive bending stiffness characteristic. This was because in this case the load cell was measuring the torque required to hold the leg in its given position. The torque calculated was not always a direct reflection of the torque generated by the SLAK. If the actuator torque was less than that required to lift the test leg off the end stop, the torque calculated was greater than the torque delivered by the actuator. Thus, for dynamic experiments the moving mass compensated torque is noted as the load torque, and the corresponding power, the load power. The term “load” is used, because the test rig consists of an actuator, the SLAK, that is coupled to a load, the moving parts of the test rig (load weight included). Hence, if the SLAK was moving in dynamic experiments, the load torque/power was the total torque/power delivered by the SLAK (due its passive bending stiffness and pressurization of its PPIAs) to the load.

In most experiments, the 500 kg load cell was used. Only in experiments where the SLAK was unpressurized or fixed at a low flexion angle was the 100 kg load cell used instead (to measure low torques with a higher accuracy).

Experiment methods

In this work, the SLAK was characterized with two different types of constant pressure, quasistatic experiments: a constant angle, quasistatic experiment and a constant load, dynamic experiment.

The first type of constant pressure experiment measured the torque-angle characteristic of the SLAK for direct comparison with the STS torque and ROM requirements in Figure 1. The SLAK was pressurized in its flexed position and slowly allowed to extend the knee by manual unwinding of the winch. This was done at the pressures of $P = 230, 350 k P a$ . The second constant pressure experiment also measured the SLAK's torque-angle characteristic, but over multiple cycles and with two different pleat misalignments. This data showed the hysteresis of the SLAK. Three cycles in each of these experiments were recorded, with the data of the first cycle being removed, as this cycle was required for the SLAK's hysteresis behavior to converge to consistent loops.

The constant angle pressure experiment ( $P = 100 k P a$ ) measured the torque-pressure hysteresis curves with the SLAK fixed at various angles. Combined with the constant pressure hysteresis loop experiments, these were meant to characterize the linearity of the SLAK's torque production. This is useful for considering challenges that may be encountered in advanced modeling or closed-loop control of the SLAK.

Last, the constant load dynamic experiments provide an initial indication of the speed and power output of the SLAK for comparing with the requirements in Table 1. In these experiments, the SLAK was mounted in an upright flexed position and weights hung on the load cell (7). During the experiment, the SLAK was pressurized until the target pressure was reached. Then, it was depressurized.

Results

The following sections outline key results from each of the experiments described in the previous section.

Quasistatic: Constant pressure standing

Figure 7 shows that the SLAK can repeatably generate sufficient knee extension torque (after subtracting extension torques due to the SLAK's passive stiffness) for 93% of the STS motion at pressures of 230 and 320 kPa. At 320 kPa, a torque was recorded that decreased parabolically from a maximum of 324 Nm at 82° to 3 Nm at 7° flexion. A similar trend at 230 kPa was observed but with a starting torque of 248 Nm at 82°. The significant discrepancy between the corresponding model predictions, particularly around $θ = 0$ °, are discussed in the Modeling section. Data for higher flexion angles are not shown, as the maximum flexion angle for the test rig was 86° [where the end stop (Fig. 6, item 5) was placed], and recorded data did not always start with the linear guide against the end stop.

Figure 7 also shows the model torque parabolically decreasing from 320 Nm at 82° flexion to 160 Nm at 7° flexion. This torque was calculated by using the parameters $D = 0.065 m$ , P = 320 kPa, α = 70°, and Equation (5) and multiplying the result by three. The underlying assumption was that all the PPIAs equally contributed to the SLAK's torque production.

Quasistatic: Constant pressure misalignment

Increasing the mean pleat misalignment $p_{a}$ (Fig. 2C) from 0.0125 to 0.03 m reduced the SLAK's torque output from 215 to 144 Nm at an angle of 84° (Fig. 8A). The minimum torque-producing flexion angle increased from 25.5° to 30° (the center of the two line intersection points with the x axis). In both cases, the torque reduced parabolically as the flexion angle reduced for experiments with a pressure of 100 kPa. Note that in these experiments a mean $p_{a}$ value is given because the misalignment increased when the SLAK was initially loaded. That is, if the SLAK was aligned at the start of an experiment, over the course of the first extension and flexion cycle $p_{a}$ increased from 0 to 0.01–0.02 m due to load-induced shifting of the SLAK. During successive cycles, it tended to stay in approximately the same steady-state position. Thus, $p_{a}$ was measured before and after the experiments and the mean value was the arithmetic average of the final $p_{a}$ observed for the different experiments. This shifting of the SLAK is why the zero crossing of the torque-angle characteristics is less in Figure 7 (when $p_{a} \approx 0 m$ as only half a hysteresis cycle was completed) compared with Figure 8A (when $p_{a} > 0 m$ as multiple hysteresis cycles were completed).

FIG. 8.

The effect of PPIA misalignment ( $P = 100 k P a$ ) (A), and pressure (B) on the SLAK's torque. The torque required to bend the unpressurized SLAK (C). The right side of the hysteresis loop in (C) is not shown because at high flexion angles pinching of the SLAK in the knee pit of the test leg generated very high (up to 160 Nm) torques. These torques do not reflect the passive stiffness of the SLAK (when worn on a human it was not observed to pinch). Results are shown with bands of $\pm$ two standard deviations ( $n = 6$ : three experiments with two cycles each). Color images are available online.

Figure 8A also shows the SLAK's PPIAs exhibited moderate clockwise torque-angle hysteresis with a maximum hysteresis loop height of 63 Nm at 74° when $p_{a} = 0.0125 m$ and 50 Nm at 68° when $p_{a} = 0.03 m$ . Repeatability in these experiments was reasonable, with the most variation shown at high flexion angles when the SLAK was flexed.

Quasistatic: Constant angle

Figure 8B clearly shows the SLAK had the torque-pressure linearity predicted by Equation (5) at high flexion angles, but at low flexion angles, torque increased logarithmically with pressure. At high and low flexion angles, torque hysteresis was low compared with the full-scale torque: a maximum hysteresis loop height of 0.7 Nm at 14 kPa for $θ = 7 . 8^{\circ}$ (counterclockwise hysteresis) and a maximum loop height of 14 Nm at 150 kPa for $θ = 8 6^{\circ}$ (clockwise hysteresis). The repeatability decreased with increasing pressure at the higher flexion angle. In the latter case, increasing $p_{a}$ was observed. Pleat misalignment started at 0 and during the first cycle (not shown in the results, as explained in Experiment Methods section) increased to a mean value of 0.0325 m. In addition, the angle of the knee changed slightly (by a maximum of 3.5°) with the cyclic pressurization of the SLAK in these tests. Hence, the flexion angle shown is an average value.

Quasistatic: Passive bending stiffness

The unpressurized SLAK had the clockwise torque-angle hysteresis curve shown in Figure 8C. The general trend is piecewise linear, and the average of the hysteresis line x axis intersections is 35°. In the figure, the torque increased from −3.4 Nm at 13° to 3.3 Nm at 60°. In this region, the hysteresis had a maximum loop height of 4.2 Nm at 60° and the torque increased linearly for angles greater than 20°. The stiffness of the SLAK over this region was ∼0.1 Nm/°, as given by the slope of the average of the upper and lower hysteresis curves. Beyond 60°, the torque increased steeply due to pinching of the SLAK in the test leg's knee pit. This did not occur when the SLAK was worn by a human. A maximum torque of 160 Nm at 86° was recorded (beyond the y axis scale of the figure).

Dynamic

Last, Figure 9 summarizes the highly reproducible dynamic responses of the SLAK as it partially extended and then flexed with three different load and pressure cases. Extension was only partial as the torque-angle characteristics of the fixed weights were more demanding than that for STS in Figure 1. This is because the kinematics of the test rig were such that when it was upright, the SLAK had to generate an extension torque to hold the leg fully extended, whereas STS does not require this (Fig. 1). The test rig was designed this way so the load cell's force measurement direction was never parallel to the test rig's thigh, a case that would not enable torque calculation.

FIG. 9.

Pressure, angle, speed, load torque, and load power of the SLAK during inflation (left) and deflation (right). Results are shown for experiments with maximum pressures and weights hung on the load cell with blue (100 kPa, load = 0 N), red (200 kPa, load = 98 N), and green (350 kPa, load = 196 N) lines. The vertical dashed lines (gray) indicate that part of the experimental data in the standing phase was removed to synchronize all the experiments' transitions from standing to sitting. The bands indicate $\pm$ two standard deviations ( $n = 3$ experiments). Color images are available online.

In the results of Figure 9, pressurization took about 5 s independent of the target pressure, and depressurization, 1.2–2.3 s, increasing with pressure. During pressurization, the flexion angle began to decrease 0.7 s after air was applied to the SLAK. The SLAK moved to a steady-state equilibrium position with a flexion angle of 48°–36° with corresponding load torques of 27–47 Nm. This movement involved speeds of up to −45°/s, resulting in a maximum load power output of 64 W for the 350 kPa case. These preliminary results show that increasing pressure and load cases moved further, faster, produced more load torque, and hence more load power.

In the depressurization phase of Figure 9, the 100 and 200 kPa motion profiles were very similar. That of 350 kPa had a similar shape profile but took longer (by 0.4 s) to accelerate to its maximum speed. The 200 and 350 kPa cases had a maximum speed of 93/s. The final torque values reflected the loads applied to the load cell, with an overshoot observed at 200 and 350 kPa as the test leg abruptly decelerated against its end stop. As during pressurization, the power profiles closely mirrored those of the SLAK's speed, with a maximum negative power of −150 W recorded for the 350 kPa case.

Discussion

The results of the Results section show that the SLAK is a soft wearable structure that produces high torque. It generates approximately eight times the torque of the ExoBoot²⁰ at 70% of the pressure and 12.6 times the torque of Fang et al.'s¹⁸ Knee Exosuit at 8.75 times the pressure. This is more than enough to generate the peak torque required for STS of an 80 kg person. Further, it is a soft wearable with its fabric and rubber construction (materials frequently used in clothing), ensuring it has a similar impedance to its wearer in the directions it interacts with him/her. The only rigid components not commonly found in clothing are its anti-kink cord, metal valve stems, and hosing. The cord is flexible and is padded from interacting with the body or environment by the surrounding PPIA. The valve stems and hosing do not interact with the body and can, if needed, be replaced with flexible fiber-reinforced equivalents. These likely need to be custom made, a challenge.

Compared with Fang et al.'s¹⁸ Knee Exosuit, the SLAK's fabrication is difficult. This is because of the heavy-duty materials, sewing, and coupling system to the body that are required for the SLAK to generate its high torques. Its construction can be simplified (without compromising strength) with the advice of orthosis and backpack manufacturers who are familiar with industrial practices, a process we are now involved in.

Referring to Figure 7, the results show that the SLAK matches at least 93% of the ROM required for STS. It did not quite produce the torque for STS at small flexion angles, and therefore these results suggest that its ROM is insufficient for STS. However, our informal testing of the SLAK indicated that when it is worn by a human it produces a significant torque even when the knee is fully extended. This torque production is not captured with the current test rig, because the test leg does not have the compliance of human tissue and higher friction coefficient of skin. Both factors mean that the SLAK remains better located and thus aligned on a human leg than the hard, smooth test leg. As Figure 8A confirms, PPIA misalignment reduces its ROM. Second, Figure 1 shows that two of the three STS datasets require an extension torque starting at 16°, above the 7° of the SLAK. Directly demonstrating the SLAK can provide the complete torque-angle characteristic for STS requires it to be tested on a full paraplegic or a test rig that enables the SLAK to remain aligned throughout the STS movement (perhaps through a compliant outer skin).

A direct comparison that can be made is with another PPIA knee extension prototype tested on the same test rig—that from Ref.²¹ The previous prototype produced torque at angles greater than 28° and exceeded the torque-angle requirements for STS for angles greater than 44°. We suggest that the SLAK has an improved ROM at lower flexion angles, even when accounting for its use of three PPIAs (of the same size as the single PPIA used in Ref.²¹), because it did not need to laterally stabilize its pleats with cords as the previous prototype did (Fig. 10). These cords were necessary, because the previous prototype's single PPIA did not have the lateral support provided by the side PPIAs in the SLAK. When the previous prototype's PPIA was pressurized, it pressed against the pleat shell that the cords used to stabilize the pleat. This tensioned the cords and, as shown by Figure 10, they produced a flexion torque that counteracted the PPIA's extension torque. The net effect of this was significant reduction of the PPIA's torque, particularly at low flexion angles. Hence, laterally stabilizing the central PPIA with additional PPIAs in the SLAK not only increased its overall torque performance but also eliminated the counter-torque of the stabilizing cords. How much the side PPIAs of the SLAK contribute to its overall torque is unknown; it may well be less than the central PPIA, as they generate a moment about an axis that is not in parallel with the knee's rotation axis.

FIG. 10.

The previous PPIA-based STS pants²¹ required cords along the sides of the PPIA to support it laterally. Actuation of the PPIA generated tension forces in these cords, producing a torque that acted against the actuator's torque. This reduced the torque that the actuator applied to the leg. Color images are available online.

Comparisons can also be made to the other requirements in Table 1 and devices in the state-of-the-art (Table 2). The SLAK's speed and hence load power were significantly lower than that observed in STS of healthy subjects (Table 6). Whether the SLAK needs to provide full support at a rate observed in the STS of healthy subjects depends on its users' abilities (it may be dangerous for impaired wearers to perform STS this fast). The SLAK's low speed was due to its long inflation time, a function of its small (0.005 m) valve stem inner diameter and large volume (∼5 L). This was also a problem for the ExoBoot,²⁰ which required even faster inflation and deflation times for assisting gait. Fang et al.¹⁸ did not comment on the inflation time or dynamics of their actuator. The SLAK's speed could be increased in a number of ways. Chung et al. suggested reducing the ExoBoot's actuator volume by replacing the segments of the actuator that perform no mechanical work with rigid components (as done by Ref.⁶³). This compromises the softness of the actuator, and in the SLAK, could make sitting very uncomfortable. Other options include: larger diameter (or multiple) air inlet and outlet fittings, reduced-diameter PPIAs with a higher operating pressure, and foam padding inside the PPIAs to reduce their dead volume.

Table 6.

Key Performance and Ergonomic Figures of Merit for the Soft Lift Assister for the Knee

Category	Requirement	Max value	Met
Performance	ROM (°)	$\geq 86.7$	×
	Speed (°/s)	45	×
	Torque (Nm)	324	✓
	Power (W)	64	×
Ergonomic	Weight on knee (kg)	1.95	✓
	Inflation/deflation	$74.9 \pm 3.7$ /	×
	sound level [dB(A)]	$116.2 \pm 4.4$
	Don/doff time (s)	$53.7 \pm 12.9$ /	✓
		$20.4 \pm 3.2$
	Flexed/extended profile (m)	0.16/0.13	n/a
	Passive stiffness (Nm/°)	0.1	n/a

Generated sound levels and don/doff time recordings are given with bands of $\pm$ two standard deviations and “n/a” means there is no corresponding requirement, and hence direct comparison with Table 1 is not applicable. Note that sound recordings were made 0.3 m from the inlet and exhaust valves of the SLAK. They were the peak recorded values during inflation and deflation when using “fast” weighted averaging on the sound meter. In addition, the passive stiffness is for angles $< 6 0^{\circ}$ .

Ergonomics

Considering other factors listed in Table 1, the SLAK met the weight and don/doff requirements, but not the generated sound-level requirement (Table 6). Further, its maximum profile was greater than all the surveyed orthoses in Table 2 except for Witte et al.'s Knee Exoskeleton⁴¹ and the RoboKnee.³⁰ The sound levels were due to high velocity air jets at fitting leakage points and during exhausting of the SLAK. Compressor noise was not relevant as the air was supplied by a lab air line. Reducing the SLAK's sound level requires good sealing fittings and a silencer on the exhaust line. Additional sound-level reduction could be obtained by increasing fitting, hose, and valve orifice diameters so that the overall air velocities are lower.

The SLAK was tested tethered to a pneumatic pressure source, so although its PPIAs were wearable, they were not autonomous. The current implementation of the SLAK would be relevant to a rehabilitation or hospital operating environment with a fixed and limited working space. However, if it was to be used outside or in everyday living scenarios, a portable pressure source, such as Kim et al.'s⁶⁴ compressor coupled to a reservoir or a high pressure air tank,²² would be required. These approaches, when applied to the SLAK, would allow it to be filled in around 90–120 s or 11 times, respectively. The number of times and fill rate of these two approaches would depend on battery and valve orifice size, respectively. The disadvantage to making the SLAK autonomous is the added weight and bulk of the pressure source.

Hydraulic actuation of the SLAK could offer a number of benefits compared with a pneumatic pressure source. Pressurizing the SLAK with a closed-loop (hydro-static) hydraulic system⁶⁵ would eliminate pneumatic's exhaust noise generation completely. Hydraulic actuation is also a possible way to reduce the bulk of the SLAK. Hydraulic systems are able to safely operate at higher working pressures than pneumatic systems. This is because their fluid is incompressible compared with air and hence stores little energy when compressed. If the SLAK's PPIAs were able to operate at 3 MPa (low for hydraulic systems, but realistic given the operating pressures of flexible reinforced layflat hosing), their diameter could be theoretically reduced to about 0.03 m while maintaining the same torque production. The fluid in these tubes would increase the SLAK's weight by about 1 kg. The profile of the SLAK could be further reduced by streamlining its fluid connections, which in the current prototype protrude from the PPIAs by 0.04 m. Despite these remarks, a noteworthy advantage of the SLAK's soft construction is that it collapses to less than 0.04 m (excluding the valve stems) when deflated, such that the wearer can easily and comfortably sit on the device and it does not severely impede their movements when unpressurized.

The passive (unpressurized) backdrivability of the SLAK (Fig. 8C for angles $< 6 0^{\circ}$ ) is comparable to the backdrivable devices in Table 2 for which information is given about their passive backdrivability. It is higher than their active backdrivability. For example, Fang et al.'s¹⁸ Knee Exosuit has a passive backdrivability <0.5 Nm for flexion angles <60°, and the iT-Knee⁴⁰ has passive and active backdrivabilities of about 10 and 2 Nm, respectively, as recorded during walking. The Knee Exoskeleton of Shepherd and Rouse⁴⁵ has an active backdrivability of 0.5 Nm. In practice, the SLAK's backdrivability is noticeable and does affect gait kinematics. This is due to the thickness of the materials used in the PPIAs and the 3D structure of their fabric sleeve. It highlights a clear need to optimize the SLAK's materials and the way they are assembled for maximum flexibility as well as strength (e.g., for operation at higher pressures). Future testing of backdrivability should also be done with a test rig that does not cause pinching of the SLAK, so that its passive stiffness at large flexion angles can be properly characterized. Additional points related to the comfort of the SLAK were that its wide velcro bands did ensure comfortable force transfer (as suggested by Ref.¹⁹), the PPIAs mounted on the inside of the leg should not catch on the other leg, and the buckles should be placed and padded to ensure they do not dig into the skin.

Modeling

The simple PPIA model [Equation (5)] plotted in Figure 7 predicted a large positive extension torque for straight PPIAs whereas the SLAK produced no torque in this position ( $θ = 0^{\circ}$ ). Similarly, Nesler et al.⁵⁹ predicted a nonzero torque for nearly straight PIAs, but measured a torque of zero at flexion angles of and close to zero. Their torque converged to the predicted torque with increasing PIA flexion. They attributed the lack of torque offset at $θ = 0^{\circ}$ to PIA material deformation and the noncircular cross-section of the actuator's buckling region during flexion. In addition, the model does not account for the compression of the PPIA along its length that occurs when it is loaded. These are valid points for the discrepancies seen between the model and the data in Figure 7. Other loss factors are also applicable to the SLAK and its PPIAs. Misalignment between the SLAK's pleats and the knee joint reduce its torque and ROM (Fig. 8A). Further, the misalignment, and hence its negative effect on the SLAK's performance, increased with test leg movement and when the actuator was inflated. The bending instead of buckling of the PPIA at low flexion angles also occurs and could reduce the PPIAs' torque. This is due to compliance of the SLAK's coupling between the test leg and the PPIAs. The fabric shifts and stretches and cannot perfectly hold the PPIA firmly against the leg and aligned with the knee. Thus, the PPIA bends away from the leg before buckling.

Another difference between the PPIA model and the results of Figure 7 is that the model increases torque at a lower rate than the SLAK as flexion angle increases. This could be due to the model not accounting for changes in $α$ as a function of $θ$ , the side PPIAs deforming in a different manner to that predicted by the model, and squashing of the mountain fold of the central PPIA at high flexion angles (increasing $Δ V (θ) ∕ Δ θ$ and hence $τ$ ). These are all factors that could be accounted for in a more advanced model of the PPIA.

Other factors that could further improve model accuracy are extending the model to include a hysteresis component (such as Vo-Minh et al.'s Maxwell-slip model⁶⁶), passive flexural stiffness of the PPIA, and the coupling between the PPIA and the body it actuates (misalignment and compliance). Figure 8C shows that SLAK alignment and hysteresis losses also affect its flexural stiffness. In this case, negative torques were recorded because the SLAK was imperfectly aligned, with its neutral (zero stiffness) position located at 35°. All these factors are important to improve the simple PPIA model so it can be used for sizing, simulating, and controlling the PPIA.

Although the model in this work is inaccurate, it demonstrates the dominant torque-generating mechanism in the PPIA, and it highlights the factors that additionally need to be accounted for to accurately model the PPIA. At some point in the modeling process, a compromise will need to be made between the model's accuracy and its computational time. This will depend on the PPIA's application. Only when given the application, a model can be found that optimizes accuracy and computational time with the available application requirements and actuator knowledge (dimensions, construction, and materials).

The results show that not all characteristics of the SLAK weigh equally in their effect on its behavior. For example, torque-angle hysteresis is much stronger than torque-pressure hysteresis. Thus, although it is not clear why the hysteresis loop of low flexion angle torque-pressure data moves counterclockwise and that of high flexion angle data clockwise (Fig. 8B), this effect is less important to model. It may be that at low flexion angles the torque calculated from data is dominated by loss factors, resulting in a different, and less linear behavior when compared with high flexion angles. The torque-pressure relationship is also less linear than that of Fang et al.'s Knee Exosuit. Compared with the maximum torque-angle hysteresis of Fang et al.'s¹⁸ Knee Exosuit (13–36%), its maximum of 29–35% (Fig. 8A) is similar. Thus, it is expected that the SLAK will be more challenging to control than Fang et al.'s Knee Exosuit.

A phenomenon observed that does not need modeling is the sharp increase on the extension torque of the unpressurized SLAK at angles greater than 60° (Fig. 8C). As mentioned, this was due to pinching of the SLAK in the test rig joint and requires a different test rig design to avoid. Pinching was not observed when the SLAK was worn by a human.

Lessons for PPIA and soft high torque actuator application

Moving forward from the SLAK with the PPIA and other soft high torque actuators, we can benefit by learning from a number of observations. For example, although the pleat of the PPIA may enable it to produce a torque when ( $θ = 0^{\circ}$ ), its torque production is sensitive to the pleat's location. Hence, we recommend that $p_{a}$ not be too small so that small misalignments of the actuator do not reduce its torque significantly. Another way to improve the pleat's location is to have a stiff coupling to the body actuated by the PPIA. Attaching the SLAK to pants helped prevent it from sagging under the weight of gravity or shifting due to shear forces generated during actuation. This attachment is important, but regardless of how stiff it is made, the PPIA-body coupling stiffness will always be limited by the compliance of human tissue, which limits the effective transfer of high torques between the two.

On a broader scale, the guaranteed safety of a soft actuator (in the sense described in the Introduction section) that can deliver high torques is not possible. First, realistic soft actuators need to increase their stiffness to deliver high torques. Thus, a soft actuator delivering high torques is stiff compared with its soft, passive state. This can also be seen in biological muscle. This means that any powered actuator, soft or hard, that is capable of delivering high torques cannot be guaranteed to yield compliantly in unexpected interactions with its environment. Instead, the actuator must rely on use within certain conditions, closed-loop control with sensor feedback (or at least intention detection of user feedback) to ensure it remains safe. Even given these provisions, other circumstances such as misuse and fatigue failure leave room for the risk of harm.

Conclusions and Future Work

This article presents a method for making wearable soft actuators that can produce high torques and transmit those torques to the body. Such actuators are needed to assist the completely paralyzed. This method is based on the concept of the PPIA and, after accounting for the SLAK's passive stiffness (including pinching), was verified to generate 324 Nm, more than the peak torque required for STS (180 Nm) and shown on a test leg to meet the STS torque requirements over 93% of the STS ROM. When worn by a real person, we believe it can provide complete support over 100% of the STS ROM. Characterizing the PPIA and STS orthosis, the SLAK, shows that the PPIA's torque-angle curve is sensitive to misalignment with the structure it is actuating and the compliance of the interaction between the two. Further, the same torque-angle curve has significant hysteresis.

The SLAK is promising as a proof-of-concept for an STS assistive device, but it has room for improvement in the design of the PPIA. Hence, we recommend that future research on the PPIA investigates maximization of its speed, power, and flexibility; and minimization of its bulk. This may require replacement of PPIA's pneumatic pressurization with hydraulic pressurization. Validation of the effectiveness of the SLAK and these improvements will eventually require testing it on human subjects. In addition, we suggest the PPIA model accuracy be improved by accounting for misalignment, torque-angle hysteresis, and prebuckling tube compression and bending effects.

Footnotes

Acknowledgments

The authors thank Martijn Grootens and Kester Meurink for their help in the development of the test rig.

Author Disclosure Statement

No competing financial interests exist.

Funding Information

This work was supported by the Netherlands Organisation for Scientific Research (NWO) (project no. 14429).

Supplementary Material

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