Design and Characterization of a Compact Rotary Series ElasticActuator for Knee Assistance During Overground Walking

Fabrizio Sergi, Dino Accoto, Giorgio Carpino, Nevio Luigi Tagliamonte and Eugenio Guglielmelli

Abstract— In wearable robotics applications, actuators arerequired to satisfy strict constraints in terms of safety andcontrollability. The introduction of intrinsic compliance canhelp to meet both these requirements. However, the high torqueand power necessary for robotic systems for gait assistancerequires the use of custom elements, able to guarantee highperformances with a compact and lightweight design.

This paper presents a rotary Series Elastic Actuator (SEA),suitable to be used in an active orthosis for knee assistanceduring overground walking. The system includes a commercialflat brushless DC motor, a Harmonic Drive gear and a custom-designed torsion spring.

Spring design has been optimized by means of an iterativeFEM simulations-based process and can be directly connectedto the output shaft, thus guaranteeing high torque fidelity.With a total weight of 1.8 kg, it is possible to directly includethe actuator in the frame of a wearable orthosis for kneeflexion/extension assistance. The presented design allows toobtain a large-force bandwidth of 5 Hz and to regulate outputimpedance in a range compatible to locomotion assistance of el-derly subjects with an age-related decay of motor performances.

I. INTRODUCTION

In robots interacting with humans for assistive or rehabili-tation purposes, traditional stiff and high-precision actuatorsare being replaced by systems with intrinsic compliance,in order to improve the level of adaptability and safety[1]. In wearable robotics, the assistance to human move-ments should be imparted by opportunely modulating theinteraction forces, thus avoiding to rigidly move subjects’limbs through prescribed kinematic patterns. The necessity ofstably and robustly regulating human-robot interaction, alsoon the basis of the variable level of assistance required bythe subjects, entails the use of actuators operating in an idealforce (or torque) mode control, with a low output impedance.

Several actuation solutions have been proposed to meetsuch requirements [2]. The Series Elastic Actuator (SEA)[3], [4] is a simple and effective solution, where elasticityis intentionally introduced in series between a gearmotorand the load. This allows to decouple motor inertia andother nonlinearities from the output and to obtain highfidelity in force control by measuring the deflection of theelastic element. Physical series elasticity intrinsically limitsthe maximum impedance in the whole frequency spectrum:for external perturbations at frequencies above the actuatorbandwidth, the impedance of the system reduces to thestiffness of the spring thus avoiding unsafe behaviors.

All the authors are with the Laboratory of Biomedical Robotics andBiomicrosystems, Center for Integrated Research (CIR), Universita CampusBio-Medico di Roma, Via Alvaro del Portillo, 21 - 00128 Roma, Italy.Corresponding author: fabrizio.sergi@unicampus.it

SEAs were originally employed in bipedal walking andrunning robots [5] in which unavoidable high frequencydisturbances due to impacts with the ground must be re-jected. SEAs are now being widely adopted also in wearablerobotics for gait assistance [6]. In the specific case of actu-ated orthoses for knee support during walking, SEA architec-tures have been employed in different implementations, thatcan be divided in two categories. The first category includestreadmill-based systems such as the one presented in [7]. Inthis system, only the elastic element is placed on the kneeorthosis, while a high-power servomotor is mounted on aframe away from the user and regulates the interaction torquethrough Bowden cables. The second category comprises fullywearable actuation systems, in which the whole actuatoris mounted in the frame of a modified knee orthosis [8],[9]. The main advantage of remotely-driven series elasticactuation is the minimization of the mass and inertia added tothe orthosis. Conversely, fully wearable systems are appeal-ing because they require a less structured environment, andcan constitute an autonomous wearable robotic system forlocomotion assistance. However, there is no known designwhich allows to directly include a fully wearable SEA witha torsion spring in direct drive configuration to provideassistance to a knee orthosis during walking. For example,in [8] a linear SEA in triangular configuration was usedto render a desired torque, while in [9] a further reductionstage was placed between the elastic element and the actuatoroutput, thus compromising torque rendering fidelity due totransmission non-linearities. A direct drive wearable SEAconfiguration would nonetheless allow to match both torquefidelity and wearability requirements.

This paper presents a novel compact rotary SEA, designedto provide partial support to knee flexion/extension duringwalking. The basic requirements of the pursued design aredescribed in Sections II and the main design choices arereported in Section III; the control architecture and prototypecharacterization are presented in Sections IV and V, while adiscussion and conclusions are presented in Section VI.

II. DESIGN REQUIREMENTS

The SEA presented in this paper is designed to providepartial support to knee flexion/extension during gait in el-derly subjects with an age-related decay of motor perfor-mances.

A number of gait features are influenced by aging, such asdecreased gait velocity, caused by decreased step length [10]and increased stance time [11]. Elderly people have generallya more conservative gait pattern than normals, i.e. a lower

The Fourth IEEE RAS/EMBS International Conferenceon Biomedical Robotics and BiomechatronicsRoma, Italy. June 24-27, 2012

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preferred walking speed and shorter steps [12]. Consideringthe slow-walking data set described in [13], the maximuminstantaneous power exerted by the knee joint is about 40W with a maximum torque of 29 N·m and an RMS valueequal to 20 N·m. In order to provide an assistive torque equalto the 30% of the peak torque required during overgroundwalking, a target of 10 N·m for actuator torque is imposed asdesign requirement. However, the reduction in the durationof the swing phase requires torque control to be fast enoughto provide rapidly changing assistance levels during walking.To this aim, considering that more than 90% of the powerspectral density of knee torque is in the frequency rangebetween 0 and 4 Hz (as obtainable from data in [13]), aminimum bandwidth of 4 Hz is set as a requirement to torquecontrol.

In SEAs , the compliant element is required to withstandthe maximum output torque supplied by the actuator andto provide a linear torque vs. rotation relationship bothin static and dynamic conditions. Moreover, such elasticcomponent should be connected to the load in direct driveconfiguration, so to avoid the reduction of force fidelitycaused by transmissions non-linearities. The target stiffnessvalue can be selected by trading off between the requirementof providing a sufficiently high intrinsic compliance andthat of obtaining an accurate torque control in a givenfrequency bandwidth. Physical stiffness values of SEAs forlocomotion assistance range from 100 to 300 N·m·rad−1 [6],[9], [14], [15]. Both theoretical analyses [4] and our previoussimulation studies [16] show that the aforementioned targettorque control bandwidth can be obtained using a stiffnessof 150 N·m·rad−1, considering realistic velocity and currentlimitations for reasonably sized DC motors. Combining suchconsiderations, a stiffness value of 150 N·m·rad−1 is taken asspecification for the series elasticity of the actuator developedin the present work. Finally, actuator dimensions and weightmust be reduced as much as possible. For our design, wespecified a maximum weight of 2 kg and dimensions of 150× 150 × 200 mm3.

III. DESIGN

The design architecture of the developed SEA has beenconceived in order to obtain the highest possible level ofmodularity. A commercial 90 W brushless DC motor (MaxonEC90-flat) has been selected, with a weight of 648 g and amaximum continuous torque of 494 mN·m. The electric mo-tor also includes Hall sensors for current commutation and a500 counts per turn (cpt) optical incremental encoder AvagoHEDL5540, to measure motor rotation with a resolution of0.18 deg when using quadrature reading. A Harmonic Drivegear (CSD-20-50-2A-GR, reduction ratio of 50:1, weight of130 g) has been included in the design. An ASM magneticincremental encoder, composed by a PMIS4 reading sensorhead and a PMIR4 magnetic code wheel, is used to measurethe actuator output with a resolution of 3·10−3 deg andallows to estimate spring deflection used for SEA torquecontrol. Fig. 1 depicts a cross section of the final design.The overall dimensions are: 120 mm (diameter) × 165 mm

Fig. 1. Cross section of rotary SEA. 1: optical incremental encoder, 2: flatDC motor, 3: Harmonic Drive, 4: torsion spring, 5: magnetic incrementalencoder, 6: output shaft. Dimensions: 120 mm (diameter) × 165 mm (axiallength). Total mass is 1.8 kg.

(axial length) and the resulting mass is 1.8 kg, thus fulfillingthe requirements reported in Section II.

A. Custom torsion spring

There are no commercially available and sufficiently com-pact rotary components able to simultaneously fulfill boththe torque and stiffness requirements mentioned in SectionII (peak torque: 10 N·m, stiffness: 150 N·m·rad−1).

For this reason a monolithic disc-shaped design has beenpursued in order to minimize weight and dimensions, sinceit allows reducing the bulk in the radial direction, stillmaintaining an acceptable thickness. This shape implies thatthe transfer of torque is between an outer annulus (externaldiameter of 85 mm) and an inner annulus (internal diameterof 12 mm). Compliance is obtained by interposing flexible el-ements between the two rings. The shape and dimensions ofsuch flexible elements were defined through an iterative Fi-nite Element Method (FEM) simulations-based optimizationprocess. The morphology selected for the spring comprisesthree replications of two couples of arched lamellae, arrangedat 120. Lamellae provide the required compliance actingas a curved thin beam mainly undergoing a pure bendingload. Holes on the outer and inner rings allow to connectthe gearmotor output and the SEA output shaft respectively,thus embodying the SEA architecture.

Static FEM stress-strain analyses (COMSOL Multiphysics3.5, Comsol AB) have been performed in order to optimizethe mechanical design. In the static analysis, the lateral sur-face of the outer ring was loaded with a tangential distributedforce applying a desired equivalent torsional moment, whilethe inner ring was fixed to the ground frame. VACO 180T(maraging steel 300, Young modulus of 186 GPa) was thematerial selected for the strength analysis, due to his highnominal yield stress of 1.32 GPa and ultimate tensile strengthof 1.35 GPa. In the described conditions, the maximum vonMises stress as obtained by the FEM simulation under an

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6 4 2 0 2 4 610

8

6

4

2

0

2

4

6

8

10

Deflection [deg]

Torq

ue [N

m]

Experimental dataLinear regression

R2=0.997

R2=0.994

Fig. 2. Characterization of the torsion spring. Loading and unloadingphases are reported, both for positive and negative deflection. R2 coeffi-cients refer to the fitting of both positive and negative torque vs. deflectioncurves to the global stiffness curve, reported in solid line.

applied torsional moment of 10 N·m is 0.93 GPa. Said S.F.the safety factor, a S.F. of 1.4 is achieved. The resultantexternal ring rotation was equal to 0.063 rad, thus implyinga torsional stiffness value, as predicted by FEM simulations,Ks,FEM =159 N·m·rad−1.

The spring, shown in Fig. 3, has been manufactured byWired Electrical Discharge Machining (WEDM) and under-went an aging treatment of 4 hours at 482C, to guaranteethe nominal yield stress value. Total dimensions are 85 mmfor the outer diameter and 6 mm for the thickness.

Experimental characterization of the spring was performeddirectly by mounting the spring on the SEA assembly, andconnecting the SEA output shaft to a torque sensor (LorenzMesstechnik GmbH DR-2), fixed to the test-bed frame. Toavoid spurious forces deriving from radial misalignmentsbetween SEA and sensor shafts, a flexible coupling (RodoflexATMK60L77) was used. The SEA was commanded to tracka position profile consisting of a sequence of steps (amplitude0.2 deg, duration 2 s), in both loading and unloading condi-tions, while the applied torque was measured via the torquesensor. The resulting torque vs. deflection plot is shown inFig. 2.

It is possible to observe the presence of a non-negligiblebacklash (amplitude: 1 deg), determined by the shaped shaft-hub coupling of the elastic element. Two one-coefficientlinear regressions, for positive and negative spring deflectionswere performed. The two calculated regression coefficientsdiffered in less than 0.5%. The overall stiffness value wascalculated as their average, providing an estimation of springstiffness equal to 119 N·m/rad.

The value of Ks determined experimentally is 22% lowerthan the one predicted by FEM simulations. Similar discrep-ancy (29%) was previously reported by other researchersusing different FEM methods and different geometries [14].It is worth to note that this discrepancy cannot be inputed tothe series compliance of the characterization setup. Basedon components datasheets, we could determine that theequivalent series stiffness between the motor and spring

Fig. 3. Picture of the custom torsional spring. Dimensions: 85 mm (externaldiameter) and 12 mm (internal ring diameter) × 6 mm (axial length). Ashaped shaft-hub coupling is used as connection between the spring internalring and the output shaft.

under characterization is around 20 times higher than theone to be measured.

IV. CONTROL

A. Control hardware

The control hardware includes the following components:- Maxon EPOS2 50/5 control unit to drive the brushless

DC motor, capable to provide a 45 V constant voltageand 5 A maximum continuous current.

- National Instruments (NI) CompactRIO-9022 embed-ded control and acquisition system, which includes areconfigurable Field-Programmable Gate Array (FPGA)module and an embedded controller running LabVIEWReal Time (RT) (533 MHz processor, 2 GB non-volatilestorage, 256 MB DDR2 memory). The device alsocomprises a NI 9401 digital I/O module to acquire thequadrature signals from the output incremental encoder,and a NI 9853 high speed CAN module for communi-cation with the EPOS2 control unit.

The FPGA module of the CompactRIO system is pro-grammed to acquire SEA output encoder quadrature signals

Fig. 4. Test-bed used for spring characterization. 1: torque sensor, 2:flexible coupling, 3: SEA.

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($%&$

!

!!m

d! !!m,d

)*+,-.$/*01+*22.+$

3.2*/415$/*01+*22.+$

!out, !!out%6$&78.9:0/.$/*01+*22.+$

'$($

!out,d, !!out,d

Fig. 5. SEA torque control scheme. The delivered torque is measuredas τ = Ks(θm − θout), being θout the SEA output angle and θm thegear motor rotation. θm,d is the desired motor velocity as generated by thetorque controller.

and to execute CAN bus low level communication with theEPOS2 controller. SEA torque and impedance controllers runon the RT level on the CompactRIO device, programmedthrough LabVIEW RT software using an hosting PC. Thecontrol loop of the SEA runs continuously at 1 kHz.

B. Control architecture

SEA torque regulation is performed by measuring thedeflection of the elastic element, i.e. the difference betweenthe SEA output angle θout and the gearmotor rotation θm.Said Ks spring stiffness, the torque delivered by the actuatorcan be estimated as τ = Ks(θm − θout).

The control scheme used in the present work followsthe approach proposed in [17] and [18]. The correspondingblock diagram is reported in Fig. 5. In the implementationused for this work, the desired velocity command generatedby the torque and impedance controllers, implemented onthe CompactRIO, is transmitted to the velocity controller,implemented on the EPOS device, through the CAN bus(CANopen protocol). Both control loops run at 1 kHz.

The measured spring deflection signal is filtered through a2nd order lowpass Butterworth filter with a cut-off frequencyof 40 Hz and torque is estimated taking into account thedeadband of the torque vs. deflection characteristic intro-duced by the couplings backlash (ref Fig. 2). The computedtorque is then fed back to the torque controller, closing thetorque control loop. An outer impedance control loop isthen implemented to regulate the interaction of the torquecontrolled SEA with the environment.

V. EXPERIMENTAL CHARACTERIZATION

A. Position control

As a preliminary validation of the described design, theactuator was position-controlled to track a typical knee angleprofile during locomotion, as retrieved from the slow walkingdataset in [13], for a gait cycle duration of 1.6 s, with theactuator output unloaded. Fig. 6 shows a position regulationperformance in the described conditions, where an RMSerror of 2.7 deg is obtained.

B. Torque control

Torque control performances of the developed SEA werecharacterized using the method proposed in [4], which in-volves the connection of the actuator output shaft to the

Time [s]

out [d

eg]

0 0.5 1 1.5 2 2.5 310

0

10

20

30

40

50

60

70StanceConf. int.ActualReference

Fig. 6. SEA position tracking for a typical knee profile during overgroundwalking (gait cycle duration: 1.6 s), with superimposed confidence intervals(p <0.05). RMS error is 2.7 deg.

ground frame (blocked output conditions). In this config-uration, different metrics were considered to measure theperformances of the torque controller, as described in thefollowing sections.

1) Step response: PI torque controller gains were regu-lated based on the system response to a step commandedtorque, in order to have an overshoot lower than 5% of thesetpoint and a rise time lower than 10 ms. Fig. 7 shows theresponse of the system to commanded steps with differentamplitudes: 3 and 10 N·m. The system responds with a4% overshoot and with a maximum rise time of 6 ms, forthe largest commanded input. Actuator non-linearities (motorvelocity saturation) in the response to the largest input implya 2 ms lag between the rise time calculated at 3 and 10 N·mand a difference in the overshoot in these two situations.

2) Torque control bandwidth: Torque control bandwidthis defined as the transfer function between the desired torqueτd and the actual torque τ delivered by the actuator, whenthe output is fixed [4]. In the frequency domain, it can bewritten as Gtor(f) = T (f)/Td(f), being T (f) and Td(f)the Fourier transforms of τ and τd respectively.

The transfer function Gtor(f) has been estimated usingsystem identification method, based on the following:

G(f) =Puy(f)Puu(f)

, (1)

being Puy(f) the cross-spectral density and Puu(f) andPyy(f) the auto-spectral density of the input (u) and output(y), which in this case are τd and τ respectively. Theestimation coherence function Coh(f) is defined as:

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.52

0

2

4

6

8

10

12

Time [s]

Torq

ue [N

m]

ActualReference

Fig. 7. Response of the system to torque step commands (amplitude 3N·m and 10 N·m, with blocked actuator output.

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10 1 100 10115

10

5

0

5|G

tor(f)

| [dB

]

10 1 100 101200

150

100

50

0

Frequency [Hz]

Gto

r(f) [d

eg]

Fig. 8. Bode diagram of torque control, desired signal is a Schroedermultisine, peak amplitude 10 N·m (RMS value: 5.45 N·m). Torque controlbandwidth is 5.3 Hz. At this frequency, the phase lag is 106 deg.

Coh(f) =|Puy(f)|2

Pyy(f)Puu(f). (2)

In order to determine the transfer function Gtor(f), theSEA has been stimulated with a Schroeder multisine [19],with a flat power spectral density between 0.1 and 10 Hz,negligible power content above 10 Hz, and amplitude scaledto generate a peak desired torque of 10 N·m (correspondingto a RMS value of 5.45 N·m). Fig. 8 shows the performancesof the implemented controller, demonstrating a bandwidth of5.3 Hz for the maximum deliverable torque.

C. Impedance control

Characterization of impedance control was performed bymanually perturbing the actuator output shaft through oscil-latory movements imposed by a human operator grasping theoutput link.

The following position- and velocity-dependent torquefield around the desired kinematic status (θout,d, θout,d) wasimplemented:

τd(t) = −Kv[θout(t)− θout,d]− cv[θout(t)− θout,d], (3)

10 1 100 1010

1

2

3

4

|Z(f)

| [N

mde

g1 ]

10 1 100 101200

180

160

140

120

100

Frequency [Hz]

Phas

e [d

eg]

kskv=0.25 kskv=0.5 kskv=0.75 kskv=1 ks

Fig. 9. Bode diagram of the estimated transfer function Z(f) =T (f)

Θout(f),

when rendering a pure elastic behavior with different elastic constants Kv ,defined as a fraction of the physical spring stiffness constant Ks.

where Kv and cv are the desired virtual stiffness anddamping coefficients. Characterization of the performancesof impedance control was performed in two stages: firsttackling the problem of rendering a pure stiffness Kv , andthen rendering a desired damping cv . Impedance transferfunction was calculated using the same system identificationtechnique described in Section V-B, considering θout as inputsignal and τ as output signal and calculating the transferfunctions Z(f) = T (f)/Θout(f) for stiffness control andY (f) = T (f)/Ωout(f) for damping control.

1) Stiffness control: In order to assess stiffness regulationperformances, different tests were done, imposing the controllaw expressed in (3), by setting θout,d = 0, cv = 0 andθout,d = 0, and varying Kv in the range [0.25Ks,Ks], withincrements of 0.25Ks.

Stiffness regulation performances increase with the valueof Kv . Defining stiffness control bandwidth as the frequencywhere

∣∣ |Z(f)|−Kv

Kv

∣∣ ≥ 0.5, a minimum bandwidth of 1.5 Hzis obtained for Kv = 0.25Ks, while theoretically infinitebandwidth (limited only by motor thermal limitations) canbe obtained when Kv = Ks. At frequencies lower than thestiffness control bandwidth, the actuator actually behaves asa pure spring, where the transfer function Z(f) has a phaselag of -180 deg. Above the stiffness control bandwidth, atten-uation of torque control is responsible for increased stiffnessand for the reduction in phase lag, thus introducing dampingin the response. At higher frequencies, where the action ofactuator control can be neglected, all curves converge againto a pure spring-like behavior, with phase lag of -180 degand virtual stiffness magnitude close to the stiffness of thephysical spring Ks.

2) Damping control: A similar protocol was implementedto assess damping regulation performances, imposing thecontrol law expressed in (3), by setting θout,d = 0,Kv = 0 and θout,d = 0, and varying cv in the range[0, 0.4] N·m·s·deg−1, with increments of 0.1 N·m·s·deg−1.The frequency content of the applied perturbation was neg-ligible for frequencies above 2 Hz.

The desired damping behavior is obtained up to 1 Hz, with

10 1 1000

0.1

0.2

0.3

0.4

0.5

|Y(f)

| [N

ms

deg

1 ]

10 1 100280

260

240

220

200

180

Frequency [Hz]

Phas

e [d

eg]

0 N m s deg 1

0.1 N m s deg 1

0.2 N m s deg 1

0.3 N m s deg 1

0.4 N m s deg 1

Fig. 10. Bode diagram of the estimated transfer function Y (f) =T (f)

Ωout(f),

when rendering a pure viscous behavior with different damping constantscv .

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a frequency-independent ratio between torque and velocityand a 180 deg phase lag. However, the damping valueestimated by system identification is higher than the onedesired, with a discrepancy of 0.075 ± 0.002 N·m·s·deg−1,due to the parasitic damping of the motor. This demonstratesthat there is an intrinsic value of damping in the system,that is not compensated by control. However, the measureddiscrepancy is more than two orders of magnitude lowerthan that of human knee [20], allowing to conclude that thisintrinsic damping does not introduce significant drawbacksfor the selected application.

VI. DISCUSSION AND CONCLUSIONS

This paper presented the design of a novel rotary SeriesElastic Actuator (SEA) suitable to be included in a wearableorthosis for knee assistance. The chosen application fieldposes significant challenges to the design of an actuator, sinceit requires high performances in terms of both amplitudeand bandwidth of torque regulation, and also the additionof limited mass and inertia in order to minimally perturbthe wearer’s natural movements. The novelty of the pursueddesign consists in the fact that the developed SEA has adirect-drive custom torsion spring which allows its integra-tion in a fully wearable orthosis for knee assistance duringoverground walking.

The presented design has been carried out with the aim offulfilling a set of requirements defined on the basis of gaitanalysis data of target users. A major element of the pursueddesign is the torsion spring, which was purposively optimizedand fabricated, since no commercial component would havebeen able to provide the desired torque and stiffness prop-erties in such a compact and lightweight configuration. Themanufactured component has a significantly lower stiffnessthan the one required, probably due to the material actualelastic modulus being slightly different from the nominal oneused for the FEM simulations. Also fabrication inaccuraciesexpectedly contributed to such discrepancy, given the sen-sitivity of the torsional stiffness to lamellae thickness. TheSEA weighs 1.8 kg, thus allowing to directly include theactuator on the frame of a wearable knee orthosis.

Performances of the developed prototype have been char-acterized experimentally using system identification tech-niques. A velocity-source type torque control scheme allowsto regulate a continuous torque of 10 N·m with a bandwidthof 5 Hz. Impedance control was also implemented andperformances in response to externally applied perturbationswere measured, demonstrating that the actuator is able torender virtual stiffness and damping fields in ranges po-tentially useful in human-robot interaction schemes for gaitassistance. Future work will involve the integration of thedeveloped actuator in a wearable knee orthosis.

VII. ACKNOWLEDGMENTS

This work was supported by the FP7 FET ProactiveInitiative “Embodied Intelligence” of the European Commis-sion, project no. ICT-2007.8.5-231451 - EVRYON (EVolvingmorphologies for human-Robot sYmbiotic interactiON).

The authors wish to thank Bohler Uddeholm Italia S.p.A.for the kind availability to supply the maraging steel used inthis work.

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