Pneumatic Exoskeleton Joint with a Self-Supporting Air Tank and Stiﬀness Modulation: Design, Modeling, and Experimental Evaluation

Electromechanical variable stiﬀness actuators (VSA) can store and reuse diﬀerent amounts of energy in the elastic element by varying the stiﬀness, but they are typically heavy for use in exoskeletons because they require more than one motor. At the same time, the use of pneumatic actuators in exoskeletons is suitable due to their high power-to-weight ratio and inherent compliance, where stiﬀness varies with applied pressure. However, the required air supply often compromises the portability of such systems. In this paper, a novel pneumatic exoskeleton joint mechanism (PEJM) is proposed that uses a pneumatic artiﬁcial muscle (PAM) as an air tank and a pneumatic cylinder to store and reuse energy and thus generate torque. The main innovation is that the PAM is independent of an external air supply; instead, compressed air from a cylinder is used to inﬂate the PAM. This is achieved by timely control of three air solenoid valves and air accumulation. Variable stiﬀness is achieved in two ways: by changing the pressure in the pneumatic cylinder and by contracting the PAM’s length. The mechanism and method of stiﬀness modulation are ﬁrst described analytically and then evaluated experimentally on an experimental platform where various functions, temperature eﬀects and leakage tests are investigated. The results show satisfactory performance and validate the theoretical concepts.

actuator but may exploit the body's dynamics to store the elastic energy and reuse it [5], [6].When the energy returns from the elastic elements, it generates a torque in the joints, thereby reducing metabolic cost and muscle strain [7], [8].To achieve this, the use of clutches in quasi-passive exoskeletons was introduced so that the elastic elements could be activated at precise intervals [9], [10].The optimal assistance for such devices relies on elastic elements with a proper stiffness that depends on mechanical properties.Moreover, if an elastic element has a lower stiffness, it can store little energy.Inversely, if it has a higher stiffness, it can store more energy, but it requires a greater force to deflect it, which may then hinder the motion during the energy storing phase.Therefore, selecting the optimal elastic element is not trivial, and it is usually a heuristic process that is time-consuming and cumbersome.The advantage of VSA is that the elastic element can be actively modulated, and thus find the optimal output stiffness.The authors of [11] have demonstrated theoretically that humans could run faster and jump higher than biological limits, only by having a quasi-passive variable stiffness mechanism in the knee joint that enables the accumulation of kinetic energy.Importantly, such a device must be designed to maximize stored energy and torque density, thus minimizing its mass.
Typically, stiffness variation in electromechanical VSA is achieved in several ways.The most commonly known ways are by changing the spring pretension [12]- [16], and by modifying the transmission between the load and the spring [17]- [20].In an effort to integrate a variable stiffness mechanism into a portable exoskeleton, the authors of [21] devised a mechanism that slides the attachment point of a single stiffness spring and creates a variable torsional stiffness around the human ankle.This enables human in the loop control, which was previously used in active exoskeletons [22].However an additional motor with a slider adds complexity and mass to the distal limbs, which is detrimental to metabolic cost [23].
As an alternative to electromechanical actuators, pneumatic actuators offer a very attractive solution.The properties of pneumatic actuators resemble biological muscles due to the inherent compliance and high weight-to-power ratio, where stiffness is usually varied by applying different pressure to the actuator.One type of actuators used in pneumatic exoskeletons are pneumatic muscles (PAM) arranged in an antagonistic configuration [24], with on-board compressor [25], and custom designed with variable stiffness [26].Work by [27], [28] showed how air can be used as an elastomer and that the stiffness of the actuator can be modulated by feeding controlled air masses into the chambers.Although these actuators offer many appealing options, the need for an air tank is often a challenge for the portability of exoskeletons.While it is not immediately obvious how to use pneumatic actuators without an air supply, some groups have shown that the stiffness of the pneumatic cylinder in passive use can be changed without an air supply and with minimal energy consumption simply by changing the effective length of the cylinder [29], [30].
Based on the given overview and in line with the usercentred approach of [31], we sought to understand what features are needed to design an appealing joint mechanism for wearable robotic applications.The research in [31] was based on interviews with participants using exoskeletons in an industrial environment and led to the conclusions that the main problems are related to comfort, adaptation to the body, independence in putting it on and taking it off.Some participants would have liked a mechanism for gradual support adjustment.Users also liked the versatility of introducing a clutch to manually turn the support on and off.
Focusing on the shortcomings related to actuation, this article, builds on our previous work [32] and presents the design, modeling, development, and experimental validation of a novel pneumatic exoskeleton joint mechanism (PEJM), which introduces some important innovations.Key contributions are as follows: 1) A novel PEJM uses the synergy of a pneumatic cylinder, solenoid valves, and a pneumatic muscle (PAM) that acts as an air tank independently of the external air supply, enabling a compact integration into a new lightweight exoskeleton design that can adjust the level of support and turn it on or off with low energy costs.
2) An upgrade of the previous method for stiffness modulation and the development of a new improved methodology, where the accumulated air from the atmosphere circulates in the PEJM, and the stiffness is adjusted by adapting the effective length of the cylinder.

II. THEORETICAL ANALYSIS
In this section, the PEJM is presented by elaborating on the working principle and the mathematical model.

A. System Overview
The PEJM can be coupled to an exoskeleton for any body part where a torque acting in the opposite direction to the joint rotation would provide support, as it works against gravity, such as during squatting, forward bending, arms lowering, etc.These movements store energy in the mechanism, which then supports the limbs in a flexed position or assists to return them to the starting position.Fig. 1 shows the PEJM integrated with the knee exoskeleton.The working principle is based on the timely opening/closing of three air solenoid valves while using a pneumatic cylinder as a passive elastic element, allowing different behaviors, such as pressure increase or transparent free motion.For example, transparent movement can be achieved by opening valve 1, or pressure can be increased if valve 2 is timely opened, resulting in air suction due to negative pressure.Furthermore, air can be pumped into the PAM by timely opening valve 3, which is deeper 140 explained later in this paper.The PAM allows for varying the 141 geometry, i.e., the effective length of the pneumatic cylinder.142 Moreover, the PAM can serve as a reservoir of compressed 143 air that can be used to drive the cylinder.The synergy of 144 both allows the torque and stiffness of the mechanism to 145 be modified.Crucially, the compressed air needed to pump 146 the PAM is generated within the cylinder by exploiting the 147 dynamics of the body, so no external air supply is required.148 The upper end of the PAM is fixed, while its lower end can be 149 repositioned on a linear slide.As compressed air is supplied 150 to the PAM, it expands radially, becomes shorter in length 151 and thereby changes the position of the pneumatic cylinder 152 base.The PAM also introduces additional compliance in event 153 of a mechanical singularity during joint rotation.Namely, the 154 pneumatic cylinder has a limited stroke length after which a 155 hard stop occurs.In this case, the PAM will begin to stretch 156 when the end of the cylinder is reached.

B. Kinematic Analysis 158
In order to calculate the theoretical torque of the joint, it 159 is necessary to identify the length change of the moment arm 160 r during the joint rotation (Fig. 2).Therefore, this subsection 161 deals with the mathematical modeling of r.

162
Let us define three points in the Cartesian coordinate system 163 P b (0, 1), P j (0, 0) and P l (0, −1).Additionally, it is necessary to 164 define the two endpoints of the cylinder; A with coordinates 165 x A and y A , and B with coordinates x B and y B .The coordinate 166 y B can be modified by shrinking the length of the PAM, whose 167 length contraction is denoted by δy.Bearing in mind that the 168 positive theta angle θ corresponds to the clockwise rotation 169 direction of the joint, the rotation matrix is given by 170 Assuming that the upper leg rotates while the lower leg is 171 stationary, the vectors ⃗ v b and ⃗ v l are given by the expression The coordinates of the point A ′ are obtained by adding the 174 vectors ⃗ v r and ⃗ v o which are formulated as where R +90 is the rotation matrix for 90 degrees clockwise, therefore the vector ⃗ v o is perpendicular to ⃗ v b .Finally, the By following similar steps, the vector ⃗ v B ′ can be expressed as 180 the sum of the vectors ⃗ v i and ⃗ v j as follows 182 183 where R −90 is the 90 degree counterclockwise rotation matrix.

184
Subtracting the vectors ⃗ v A ′ and ⃗ v B ′ gives the vector ⃗ l whose length can be calculated using the Euclidean norm To obtain the coordinates of point C, so that ⃗ r is always 187 perpendicular to ⃗ l, the expression for the minimum vertical 188 vector between the point and the line is used where |C−A ′ | means magnitude, and the unit vector l is given Since the point P j is the origin of the coordinate system, the coordinates of the point C are equal to the components of vector ⃗ r.Thus, by extracting C from Eq. 12 and drawing the vector ⃗ r between the points P j and C the expression for ⃗ r is given whose length is computed as

C. Torque modeling
The torque T totn of the PEJM can be adjusted in steps denoted by the subscript n, which is introduced for easier distinction in the stiffness modulation strategy.In this subsection, the analytical torque model is derived, and the next subsection explains its modulation with steps and the PAM influence.
To analytically model the torque T totn , it is first necessary to establish the correlation between the cylinder force and the chamber pressure during the joint rotation.The force F totn Fig. 3.As the joint rotates in the positive direction of θ, a negative pressure pu n is generated in the light blue chamber, creating a force Fu n , while in the red chamber, the air pc n is compressed, creating a force Fc n .The sum of the two forces is denoted as Ftot n , which at the moment arm r generates a counter-torque Ttot n that tends to return the mechanism to its initial state if all three valves are closed.By pressurizing the PAM, it expands radially dn > d 0 , causing δy increase.This leads to an increase in the force Ftot n due to the increased z.
necessary to compress the pneumatic cylinder from the initial position z 0 to position z, with all three valves closed, is formulated according to Fig. 3: ) where F cn denotes the force produced by the compressed air p cn that acts on the cross-sectional area A c , and F un is the pulling force generated due to the underpressure p un that acts on the cross-sectional area A u in the blue colored chamber.Supposing isothermal compression and neglecting 213 the thickness of the piston, the pressure p cn can be written as where p in is the initial pressure in both cylinder chambers, Using the general gas equation, the initial pressure is given by 222 the expression where N totn represents the total amount of air in both cylinder 224 chambers together, T is the air temperature in Kelvin, R m = 225 8314 J/kmolK is the universal gas constant, and V cyl equals The pressure change in the cylinder, starting from p in = p atm , is shown in Fig. 4.
The initial position z 0 is subject to changes depending on The change in force, moment arm, and torque with respect to 236 the angle is shown in Fig. 5.

D. Stiffness modulation
Stiffness modulation in the proposed mechanism is possible in two ways: 1) by changing the effective length of the pneumatic cylinder, i.e., by shortening the PAM, and 2) by changing the pressure p in inside the pneumatic cylinder.Usually, both are combined and allow tuning of joint stiffness and torque.The behavior of the mechanism is determined by the valves, which open and close in a timely manner as the joint rotates (Fig. 6).The change in pressure of the cylinder chambers during rotation is exploited to modulate the initial pressure.As p in increases, the joint becomes stiffer and can store more energy when deflected.The pressure increase is a process done in n steps where it is necessary to open valve 2 when the underpressure occurs, so that the atmospheric air ∆N n enters the blue chamber at a pressure p atm (see Fig. 6).Thus ∆N n is given by the expression A new amount of air ∆N n is now added to N un that was already inside, given by the expression where N un is the amount of air in the blue (underpressure air) chamber.The amount of compressed air in the red chamber N cn can be analogously expressed as By returning to the initial position and opening valve 1, the air from both chambers is merged.Now the total increased amount of air in the whole pneumatic cylinder is An increased amount of air in the same volume will cause a change in pressure.Fig. 7 depicts an increase in the initial cylinder pressure p in with steps.The value converges as soon as the pressure in the blue chamber becomes equal to p atm , after which the air can no longer be sucked in.
After the desired number of steps, the pressure can be pumped and stored in the PAM by opening valve 3.As the PAM is inflated, its volume increases and can be calculated using the expression given in [33], as follows   where n tu is the number of thread turns, L f is the thread length which can be calculated according to [34].Assume that the initial pressure in the PAM is equal to p atm , and δy = 0, meaning that the length of the PAM is at the initial length L m0 and volume V m0 .Then the initial amount of air in the PAM can be calculated as By merging the volume of the cylinder V cyl and assuming the volume of the PAM in the moment of opening valve 3 equals V mn = V m0 , the total pressure in the system after n steps can be calculated as Now the initial pressure in the cylinder and also the pressure in the PAM is p mn .Fig. 7 shows the increase in pressure when the PAM is pressurized in a volume-coupled manner.
This means that the PAM maintains the pressure in the cylinder once increased and is acting on the cross-sectional area A c .
If now valve 3 closes, the PAM pressure can be computed only if the exact relation V mn (L mn ) is known where L mn = f (p mn , F mn ).With a known PAM pressure its length L mn can be estimated by using FESTO table or any other PAM models [33], [34].Of course, once the force in the cylinder exceeds the static force of the PAM, it starts to stretch in a non-linear Fig. 7.By gradually drawing air to the system, the initial pressure p in in the cylinder increases.The value converges when pu n becomes equal to patm which means that air cannot be drawn into the chamber.The pressure can be increased through the desired number of steps n, after which, by opening valve 3, the pressure is shared with the pneumatic muscle.This pressure is denoted by pm n .
way.Modeling this dynamic behavior is beyond the scope of 292 this paper.The theoretical model within the scope of this paper 293 does not consider the dynamics of the PAM, but only considers 294 the PAM as an element that has the role of modifying the 295 effective length of the cylinder in the same way as it was a 296 rigid slide without elastic properties.Experimental results will 297 identify the dynamics of the mechanism as whole.

298
The derivative of torque with respect to the deflection can 299 be used to determine the stiffness of the mechanism In order to obtain the value of storable energy, the following 301 expression is used to calculate it The following figures show the theoretical torque, stiffness, and energy modulation in two different ways: 1) by changing the initial pressure p in , shown in Fig. 8, and 2) by changing the effective length of the pneumatic cylinder, i.e., by shortening the PAM, shown in Fig. 9.

III. EXPERIMENTAL EVALUATION
This section discusses the mechatronic design of the mechanism and the experimental setup.Furthermore, the section gives an insight into the control and explains the experiments.

A. Mechatronic Design of the Experimental Setup
In order to test the behavior of the mechanism and validate the theory, an experimental test platform was made with a schematic depicted in Fig. 10.In the following text, each unit is briefly described.

1) Load:
The dynamics of the human joint is replaced by a DC motor (80 W Maxon) with a planetary gear (ratio 113:1).
The motor driver, ESCON 50/5, allows high fidelity control in either velocity or current mode as the reference is sent from an external device to its analog input pins.
2) Sensors: The torque sensor (RT-500, Tovey Engineering) is placed at the output of the gear and connects it to the exoskeleton mechanism.On the same axis, there is also a rotary encoder (RLS RoLin RS422) for measuring the rotation angle.The same type of readhead is mounted to measure the linear displacement of the PAM.A ZMME-S 100 force sensor with a nominal force of 1000 N is installed on the piston rod to measure the force in the pneumatic cylinder during rotation.
Two sensors are set up to monitor the pressure; one to measure the compressed air in the cylinder and the other to measure the pressure in the PAM.The sensors collected the data throughout the measurement.
In the post-analysis, the data were filtered using a Butterworth filter, after which stiffness and stored energy were calculated as the derivative and integral of the torque and deflection angle, respectively.In the following text, the algorithm within the stateflow is given only for more complex experiments, while less complex ones are described in words.The remainder of this section explains the experiments and results.
1) Basic Mechanism Verification: The basic function of the mechanism was evaluated for different valve states and  13).The graphs indicate that the 404 theoretical models adequately approximate the experimental 405 results for all three cases.Since the stiffness is derived from 406 the measured torque, the noise and the filter noticeably change 407 the shape of the curve.Therefore, a small discrepancy between 408 theoretical and measured results is expected.Furthermore, the 409 isothermal assumption and the inaccurately known air volume 410 in pneumatic connectors affect the accuracy of the theoretical 411 model.In accordance with theory, when only valve 2 is open, 412 the cylinder force has a progressive characteristics due to 413 compressed air in the bottom chamber, with torque peaking 414 at ∼3 Nm (Fig. 13b).However, when only valve 3 is open, 415 the cylinder force has a degressive characteristic with a peak 416 torque of ∼1 Nm (Fig. 13c).Finally, in the third case, with 417 all valves closed, the values are the highest with a peak torque 418 of ∼4.5 Nm (Fig. 13a).

419
The basic function of the mechanism was further inves-420 tigated for different initial cylinder pressures with all three 421    15.Pneumatic cylinder pressure increase.In (a) with shown motor angle, valve states, and pressure in the cylinder.For valve 1 and valve 3 the "high" state opens the airflow, while for valve 2 the "high" state closes the airflow.The amplitude of valves is scaled.In (b) measured force and torque with the calculated torsional stiffness and stored energy versus deflection.same applies to valve 3, as the valve is the same.Conversely, a "high" state of valve 2 means the airflow is closed, while a "low" state means an open airflow.In the experiment, the target cylinder pressure was set to higher than 1.5 bar, after which the experiment stopped.After four strokes, the pressure in the cylinder increased from 0 bar to ∼1.6 bar (relative pressure) in equilibrium and to ∼4.7 bar in compression due to joint rotation.This results in a stiffness change from a peak value of ∼3.4 Nm/rad to ∼9 Nm/rad and a change in torque from ∼3 Nm to ∼10 Nm.These values support the concept of cylinder pressure increase.3) PAM pumping: There are different methods to pump the PAM.For example, by pumping after an increase in cylinder pressure, by increasing it even several times before pumping, or not increasing cylinder pressure at all.Two different ways of pumping PAM have been experimentally performed: without increasing the cylinder pressure and by increasing the cylinder pressure for two strokes beforehand, where the target cylinder pressure was set to higher than 0.8 bar.The algorithm for the first experiment is given in Fig. 16b, while the second experiment can be understood as a combination of (a) and (b) in Fig. 16.In addition, the opening time of valve 3 is conditioned by p cyl > p m , which ensures smooth pumping without jerking of the PAM during rotation.The results for the former are shown in Fig. 17a, and for the latter in Fig. 17b.The results indicate that when the cylinder pressure was increased, PAM pumping occurred faster (peak ∼3.4 bar at 68 sec), while when there was no previous pressure increase, the PAM pressure peaks ∼1.6 bar at 68 sec.In (a), the slight increase in cylinder pressure with each stroke is finely seen.This was due to the PAM contraction δy, which also progressively increased.
The PAM contraction δy peaks ∼2.1 mm at 70 sec without cylinder increase, while with the previous increase, it peaks ∼5.9 mm at 70 sec.These results further extend our knowledge of PAM pumping.

4) PAM as air tank:
The third variant of PAM pumping is where the PAM keeps the cylinder constantly pressurized and thus acts as an air tank with compressed air.The algorithm used in the experiment is given in Fig. 16c.Before the experiment, the desired PAM pressure was set to 2 bar (relative pressure), and when this pressure was reached, the experiment stopped automatically.The results show that the target pressure was reached after six steps (Fig. 18a).The results in Fig. 18b show the measured cylinder force and joint torque with stiffness and stored energy.From the stiffnessdeflection graph, it can be seen that the peak point moves slightly to the left with each step.This is achieved by PAM length contraction, meaning that the joint is stiffer for the smaller angle.As a result, the joint torque increased from a peak ∼1.3 Nm without PAM pressure to a peak ∼10Nm for PAM pressure of 2 bar.6) Leak Analysis: The leak test was performed for 180 min-508 utes with a constant joint rotation, where the initial pressure 509 was atmospheric.The motor was set to a repeating sequence 510 as before.The maximum pressure at the end of compression 511 was monitored during the experiment to check if the pressure 512 decreased with time.The results in Fig. 20 show that the 513 pressure decreased from ∼1.55 bar to ∼1.47 bar over 180 514 min, suggesting that the air leakage has a small impact on the 515 performance of the device, especially considering that the air 516 can be recovered from the atmosphere by opening the valve.The first and most noteworthy observation is the very low 522 weight, only 0.76 kg for one side.This is the weight of the 523 entire exoskeleton without the leg shells and electronic system.524 However, it should be noted that the device's portability 525 requires a small 24V battery to operate valves.The valves 526 require small amounts of current for trigger signals (0.09-0.44 527 mA).The peak torque is achieved for a peak pressure in the 528 cylinder of 8 bar, for which maximum stiffness and energy 529 storage capacity are also achieved.

530
In Table II, only the PVSA actuator is pneumatic, while the 531 other actuators use mechanical stiffness modulation methods.532

Fig. 1 .
Fig. 1.In (a) the PEJM CAD model applied to the knee exoskeleton, in (b) an exploded view.

Fig. 2 .
Fig. 2. Kinematic model of the proposed mechanism.The point P j marks the center of rotation and the origin.The perpendicular distance, denoted by r, between P j and l represents the moment arm, and l is the length between the endpoints of the cylinder.(a) With θ = 0 • , (b) with θ ̸ = 0 • , and (c) the triangle ∆A ′ B ′ P j shows a more detailed representation of vectors.

215
the numerator equals the initial volume of the red chamber, 216 where A t l is the volume inside the air hose and the pneumatic 217 connectors, and the denominator equals the final volume of 218 the red chamber after joint rotation, and z max is the maximum 219 stroke of the cylinder.Equivalently, the pressure p un in the 220 blue chamber equals 221

Fig. 4 .
Fig.4.Pressure change in both cylinder chambers starting from the atmospheric pressure p in = patm.Underpressure is generated in the blue chamber, while air is compressed in the red chamber.

232
the length L mn of the pneumatic muscle, while the p in can 233 be varied by adding the extra air quantity in the pneumatic 234 cylinder.Finally, the torque of the mechanism is given by 235 T totn = F totn ∥r∥.
Atmospheric pressureT tot n p c >p c N c >N c p u >p u N u >N u

Fig. 6 .
Fig. 6.Mechanism's stiffness modulation is a process done in n steps.For different valve combinations, different mechanism behavior is obtained.The blue marked cylinder chambers represent underpressure, while the red represents compressed air.When underpressure is generated, air ∆Nn enters the blue chamber by opening valve 2. When the amount of air in the cylinder increases, it can be pumped and stored in the pneumatic muscle by timely opening valve 3. Valve 1 acts as a clutch, by allowing free movement without generating force, as the air passes from one chamber to the other.

Fig. 8 .
Fig. 8.The increase in the initial cylinder pressure p in increases the torque Ttot n , torsional stiffness kn, and storable energy of the mechanism Hn.

Fig. 9 .
Fig. 9.The contraction of the pneumatic muscle δy causes a change in the effective length of the cylinder, and thus the force.This modulates the torque Ttot n , torsional stiffness kn and storable energy Hn of the mechanism.

Fig. 10 .
Fig. 10.Schematic overview of the experimental platform with a location of standard components.The control system is highlighted in yellow, with the output signals highlighted in red and the input signals in black.

338 4 )Fig. 11 .
Fig. 11.The control block scheme of the experimental setup.Sensor signals are inputs in the stateflow, where the algorithm inside decides when to open/close valves and when to switch the motor from the repetitive sequence to the standby state.A PD controller with a feedforward term realizes the desired motor position.The signal from the encoder is used for the position feedback loop.The valve amplitude is the same, but for ease of illustration, valve 2 is scaled by 2, and valve 1 is scaled by 3.

Fig. 13 .
Fig. 13.Basic mechanism verification; (a) With all three valves closed, (b) valves 1 and 3 closed and valve 2 open, and (c) valves 1 and 2 closed and valve 3 open.Red line: theoretical values, blue line: measured values.

424
and compared with the analytical ones.The values correlate 425 favorably for each pressure increase.

Fig. 16 .
Fig. 16.An algorithm within stateflow for experiments: (a) Pneumatic cylinder pressure increase, (b) PAM pumping without cylinder pressure increase, (c) PAM as an air tank.

Fig. 17 .
Fig. 17.Two different ways of PAM pumping; (a) Without cylinder pressure increase, (b) With two strokes of cylinder pressure increase.Valve 1 is red, valve 2 is green, and valve 3 blue.In the graphs, δy is the PAM contraction.

Fig. 18 .
Fig.18.The third variant of PAM pumping, where the PAM acts as an air tank by keeping the bottom chamber of the cylinder constantly under pressure.In (a) with shown motor angle, valve states, pressure in PAM, and contraction.In (b), measured force and torque with the calculated torsional stiffness and energy stored versus deflection.5)Temperature Variation Effect: An increase in temperature in the same volume leads to pressure increase and can affect the torque of the joint.To investigate the impact of this phenomenon, a temperature experiment was done by heating the PEJM from room temperature ∼22 • C to ∼65 • C for 60 sec.The heating was performed with a hair dryer with all valves closed and a joint angle of 0 • .An analog temperature sensor, TMP36, was used and glued to the PAM.The pressure in the cylinder, PAM, and temperature are shown in Fig.19.The results show the relative pressure increase from 0 bar to ∼0.07 bar in the cylinder and to ∼0.04 bar in the PAM.Since the PAM inflates the volume due to the pressure increase, its pressure increase was lower than in the hard shell pneumatic cylinder with a constant volume.These values show that the temperature change has a low impact on the pressure of the mechanism.

Fig. 20 .
Fig. 20.Cylinder pressure loss by constant joint rotation over 180 min. 521 Table I details the relevant parameters of the proposed 519 PEJM mechanism, and Table II provides an overview of other 520 variable stiffness actuators compared to this study.