IEEE/ASME TRANSACTIONS ON MECHATRONICS 1 Compliant …dyros.snu.ac.kr/wp-content/uploads/2013/05/TMECH2260554.pdf · IEEE/ASME TRANSACTIONS ON MECHATRONICS 1 Compliant Joint Actuator

IEEE/ASME TRANSACTIONS ON MECHATRONICS 1

Compliant Joint Actuator with Dual Spiral SpringsYongtae Kim,Student Member, IEEE,Jimin Lee, and Jaeheung Park,Member, IEEE

Abstract—The main motivation behind the creation of acompliant actuation system is to provide safety, capability ofstoring energy, and improved performance levels in dynamictasks. The choice of the proper compliance level pertainingtorobots depends on the specific purposes of the robots. In thispaper, a dual-spiral-spring actuation system (DSSAS) is proposedto provide high compliance and deformation values for wearablerobots. Among many different applications of wearable roboticsystems, we aim for systems in which safety and complianceare more important than the control bandwidth of the joints. Aspiral spring is selected to take advantage of the characteristicsof high levels of compliance and deformation compared to otherelastic components. The proposed dual-spiral-spring actuationsystem uses two spiral springs in opposite directions, as the spiralspring generates torque only in one direction. First, we presentthe characteristics of the spiral spring for a compliant joint. Then,the design and performance of the DSSAS are demonstrated byexperiments.

Index Terms—Compliant Actuator, Spiral Spring, Low Stiff-ness, Large Deformation, DSSAS.

I. I NTRODUCTION

Compliant actuation systems have received a great amountof attention in robotic systems to ensure intrinsic safety andstoring energy for dynamic tasks. Intrinsic safety is a criticalissue when robotic systems interact with humans, and thecapability to store energy can improve the efficiency of theperformance of robots.

Series Elastic Actuators (SEAs) are systems that providecompliance for the joints [1]. Robinson et al. applied a serieselastic actuator to a biomimetic walking robot [2], Prattdeveloped low-impedance walking robots with series elasticactuators [3]. To secure the safety of a compliant actuationsystem, Wyeth demonstrated the safety and performance ofseries elastic actuators [4]. Moreover, a compliant actuationsystem was applied to rehabilitation applications. Kong etal.used rotary series elastic actuator for human-robot interaction[5]. Lagoda et al. designed SEA joints for gait rehabilitationtraining [6]. Tsagarakis et al. developed a small scale SEA unitfor a small human friendly robot [7]. Ihrke et al. developeda compact rotary SEA unit for an upper-limb humanoid robot[8]. Laffranchi et al. proposed energy-based control strategyfor SEA [9]. Recently, Kong et al. developed cRSEA forhuman assistive system [10]. Abe et al. developed elastomer-based SEA for biped robot [11].

Yongtae Kim and Jimin Lee are with the Department of Transdisci-plinary Studies, Seoul National University, Republic of Korea. e-mail: [email protected], [email protected]

Jaeheung Park is with the Department of Transdisciplinary Studies, SeoulNational University, Republic of Korea and with the Advanced Insti-tute of Convergence Science and Technology, Republic of Korea. e-mail:[email protected]

Jaeheung Park is the corresponding author.

However, compliant actuators have limits in terms of thebandwidth of the joint motion. This can be regarded as a trade-off between safety and performance. The purpose of VariableStiffness Actuation (VSA) is to overcome this limitation. Thatis, the stiffness varies depending on the situation. English andRussell defined stiffness limitations using a variable stiffnessactuator for prosthetic limbs [12]. Like other studies [2] and[3], Hurst et al. attempted dynamic legged locomotion usingvariable stiffness actuators [13]. The actuation mechanismsof the variable stiffness actuators were also varied accordingto their elastic components. Tonietti et al. developed variablestiffness actuators using timing pulleys and belts [14]. Schiaviet al. used two springs for the variable stiffness actuatorVSA-II [15]. Wolf and Hirzinger developed variable stiffnessactuators using an extension spring [16]. Choi et al. developeda variable stiffness actuator using a leaf spring [17]. Moreover,elastic components are included for better performance. Kimand Song attempted to utilize hybrid variable stiffness actua-tors based on such mechanisms [18]. Tsagarakis et al. utilizedSEA[7] for a compact variable stiffness actuator (CompAct)using extension springs [19]. Jafari et al, developed a newadjustable stiffness mechanism using variable ratio lever[20].

There are other elastic joint systems that do not use springs.Klute et al. used artificial muscles for bio-robotic systems[21],and Zoss et al. developed an exoskeleton using a hydraulicactuator [22]. More comprehensive review for compliant ac-tuators can be found in [23].

In this paper, we propose a compliant actuation system usingspiral springs to provide high levels of compliance and defor-mation of the joint. It is aimed at wearable robots, especiallywhen they require high levels of compliance. There can bemany different types of wearable robots for specific purposes.Generally speaking, safety is one of the most important issuesfor wearable robots because the system directly interacts with ahuman. The safety of the system can be guaranteed in differentways by hardware and control algorithms. Stiff actuatorswould require the sensors for acquiring the intension of theuser and the control algorithms to provide the system withcompliance. However, if a specific system requires intrinsicsafety, the use of compliant actuators would be necessary.This is the main motivation of our research to develop in-trinsically highly compliant actuators to be used for specificwearable robots, such as the robots for gait rehabilitationofCVA(cerebrovascular accident) patient [24], cruciate ligamentinjured patient, and seniors needing assistance. In this type ofapplications, the main purpose is to assist humans in relativelyslow motion. Therefore, high levels of compliance can providegreater safety and comfort than conventional low-complianceactuators without losing their support capability.

Although a spiral spring has the advantage of large com-pliance, it produces torque in only one direction. Thus, we

This is the author’s version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available athttp://dx.doi.org/10.1109/TMECH.2013.2260554

Copyright (c) 2013 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].


propose a dual-spiral-spring actuation system (DSSAS) inwhich two spiral springs are installed in opposite directionsto provide bi-directional torque. In the following section,we present the characteristics of a spiral spring when it isused for a compliant actuation system. The development andexperimental results of the DSSAS are then discussed inSection III. The paper is concluded in Section IV.

II. CHARACTERISTICS OFSPIRAL SPRING

Spiral springs have long been used in different applications,such as clocks, toys, and seat belts. Spiral springs are usedin these applications due to their compactness and becausethey provide high levels of compliance and deformation. Theyare relatively compliant compared to other types of elasticcomponents such as helical and extension springs. The figureof spiral spring and its variables are shown in Fig. 1. In thissection, the properties of spiral springs are discussed in termsof robotics applications.

Fig. 1: The configuration and parameters of spiral spring.The outside diameter of spring, width of spring strip, insidediameter of spring, thickness of spring strip, number of turnsof spring, and moment/torque on spring are denoted byD, b,d, t, n, and,M, respectively.

A. Large Compliance and Deformation

Spiral spring provides high levels of compliance with a largeamount of deformation. The output torque is the product ofstiffness and deformation; thus, the compliant actuator withsmall magnitude of deformation would have a limited torquecapability. The spiral spring’s characteristic of high deforma-tion enables to provide high levels of torque even with smallstiffness. It would be difficult to implement such a compliantactuator with other conventional elastic components or with acombination of them. Elastic components that directly producetorque typically have high stiffness, for example, couplers andhelical springs. Alternatively, extension springs can be usedto compose a compliant joint, but doing so cannot easilylead to large rotational deformation. Moreover, an additionaladvantage of large deformation can be an increased resolu-tion for torque sensing when the torque is measured by themultiplication of deformation angle and stiffness.

The stiffness and stress of the spiral spring can be computedby the following equation [25]:

ks =Ebt3

12L, Ss =

6Mbt2

(1)

Here, E is the Young’s modulus,b is the width of springstrip, t is the thickness of a spiral spring,L is the length ofthe strip, andM is the moment applied on the spring.

The spiral spring can be chosen or designed given the spec-ifications of the dimensions, maximum torque, and stiffness.The design of a spiral spring has more flexibility than othertypes of springs due to their unique structural characteristics:the strip length can be different in a fixed volume. Forexample, the stiffness of the spiral spring can be chosen withina feasible range given the dimensions of the spring and themaximum torque. This characteristic contrasts with that ofahelical spring whose stiffness is uniquely determined for thegiven dimension and maximum torque.

It should be noted that the maximum rotational deformationwill also change depending on the different stiffness levels thatare selected for a fixed dimension of the spiral spring. A largerstiffness of the spiral spring leads to a shorter deformationrange of the spring due to the maximum stress of the material.They are inversely proportional. In practice, the choice ofthestrip length or the stiffness is limited due to the volume of thecase and the friction between the strips. The recommendedstrip length can be referred to [26].

Fig. 2 shows the analysis of the spiral spring in this sense.The feasible range of the stiffness and the correspondingdeformation angle are plotted for one fixed size of the springas an example. The size of the spring set equal to the helicalspring used in an earlier study [5] (D: 33mm, d: 8mm, b:30mm). The maximum stress(S) is 1.2∗ 109N/m2, and theYoung’s Modulus(E) is 2.11∗ 1011N/m2 from the propertyof the spring steel. In [26], the following three conditionsarerecommended:

Lmax= (D2−d2)/(2.55∗ t) (2)

15< d/t < 25 (3)

L/t > 1000 (4)

The upper boundary of the strip length in Fig. 2(a), which isdenoted as 1, is determined by (2). The lower boundary ofL,denoted as 2, is defined by (4). The upper and lower limits ofthe thickness are determined by (3) and are denoted as 3 and4 in Fig. 2(a). From these boundaries of the strip length andthickness, the feasible ranges of the maximum deformationand torque are plotted using (1) in Figs. 2(b) and (c).

The characteristics of the helical spring from the aforemen-tioned study [5] are as follows. The stiffness is 13.2Nm/rad,the maximum deformation is 0.44rad, and the maximumtorque is 6Nm. It can be observed that the spiral spring, inthis example with the same size, can provide 25∼ 102.2 timesthe maximum deformation of the helical spring, 1.21×10−3

∼

0.0113 times the maximum stiffness of the helical spring, and0.1 ∼ 0.28 times the maximum torque of the helical spring.The comparison result is shown in Table I.

B. Directional Properties

Springs in general have different stiffness levels when theyare compressed or decompressed (wound or unwound). Thischaracteristic also applies to spiral springs. The greatertheamount of torque that is applied, the more pertinent this




1.5 2 2.5 3

x 10−4

0

0.5

1

1.5

2

2.5

Spring Thickness(m)

Str

ip L

en

gth

(m)

1

4

2

3

0 0.05 0.1 0.1510

15

20

25

30

35

40

45

Stiffness(Nm/radian)M

axim

um

De

form

atio

n(r

ad

ian

)

1

2

3

4

0 0.05 0.1 0.150.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Stiffness(Nm/radian)

Ma

xim

um

To

rqu

e(N

m)

3

2

1

4

Fig. 2: Example of feasible ranges for one fixed size of a spiral spring. (a) thickness-length (b) stiffness-deformation(c)stiffness-torque. Line 1 and 2 are drawn using the upper and lower boundaries of strip length, respectively. Line 3 and 4 arecomputed using the upper and lower limits of thickness, respectively.

TABLE I: Characteristics of a spiral spring that has the samesize as that of RSEA in [5]. Given dimensions of the spiralspring, it can be designed to have different properties as shownin Fig. 2.

System Min.∼Max. Max. Max.

Stiff.(Nm/rad) Deform(rad) Torque(Nm)

Spiral Spring 0.016∼ 0.15 11∼ 45 0.6∼ 1.7

RSEA[5] 13.2 0.44 6

characteristic becomes. The experimental result in Fig. 3shows these characteristics. In this experiment, winding andunwinding are repeated to observe the characteristics of thespring, as follows: winding to 9 radian and then unwinding to6 radian, continuously winding to 12 radian and unwinding to9 radian, and finally winding to 12 radian and unwinding to theinitial position. In Fig. 3, solid lines and dotted lines representthe plots for the winding and unwinding steps, respectively.Each trial is denoted with a different color. It can be observedthat there are two main curves: the upper and lower curves.When the spring is wound or unwound, its response convergesto either of these curves depending on whether the spring isbeing wound or unwound. This characteristic of spiral springis due to the asymmetric structure of the spring. Therefore,the generated torques by a spiral spring are different whenit is wound or unwound. This phenomenon is similar to thatof hysteresis. These experiments were conducted with a spiralspring which has the same dimension as the one designed forDSSAS in the following section. The properties of the springare as follows: spring thickness (1mm), strip width (12mm), 8turns, outer diameter (90mm), and inside diameter (23mm).

Another important characteristic of a spiral spring is thatitproduces torque in one direction. That is, it generates torqueonly when it is wound. In fact, the spiral spring can beunwound past the initial configuration, but its characteristicsare unpredictable and it is easy to be broken. These twocharacteristics are the main motivation behind the developmentof the dual-spiral-spring system. Two spiral springs installedin opposite directions would resolve the problem of unidirec-tional torque.

0 2 4 6 8 10 12−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Angular Displacement(Radian)

Torque(Nm)

Unwinding after 1st windingFirst winding

Unwinding after 2nd windingSecond winding

Unwinding after 3rd windingThird winding

Fig. 3: Characteristics of single spiral spring in winding andunwinding.

III. D UAL SPIRAL SPRING ACTUATION SYSTEM

The proposed dual-spiral-spring actuation system (DSSAS)is composed of two preloaded spiral springs in oppositedirections (Fig. 4). It utilizes the characteristics of thelargedeformation and compliance while overcoming the directionalproperties of the spiral spring.

Fig. 4: Installation of two springs with preloading in oppositedirections.

The experimental setup is implemented to investigate theproposed dual-spiral-spring actuation system, as shown inFig.5. The centers of two spiral springs are fixed at the sameaxis of rotation. The other ends of the two spiral springs areattached to the outer case of the spring. To apply torque on




the shaft through the springs, the outer case is rotated by amotor which is directly connected to the case. We installed atorque sensor in between the link and the spring so that thejoint torque can be measured. Also, an encoder is installedto measure the joint angle. The difference between motorangle and joint angle is the twist angle of the dual-spiral-spring system. The design procedure of spring starts with

Fig. 5: Experimental setup and diagram of DSSAS.

the specifications on the stiffness and maximum torque ofthe DSSAS. Since the DSSAS has two preloaded springs inopposite directions, the stiffness of one spring is one halfof the required stiffness. The maximum torque of one spiralspring can be determined once the preloading angle is chosen,which is explained in the following subsection. Once thespecifications on the stiffness and maximum torque of thesinglespiral spring are determined, the parameters of the width(b), thickness (t), length (L), outside diameter (D), and insidediameter (d) can be obtained using (1) given the material.Since there are more parameters to be determined than thenumber of equations, the dimension can be selected withinthe conditions in (2)-(4) to meet the specifications on the size.

In this experiment, we aimed to compare the performanceof DSSAS with that of VSA-CUBE [29]. Therefore, the spiralspring in DSSAS has been selected such that the DSSAS hasa similar level of maximum torque with the VSA-CUBE andhas approximately 10% of the stiffness of the VSA-CUBE.The dimensions of the spiral spring and system parametersareD : 90mm, d : 23mm, b : 12mm.

The characteristics of the DSSAS in this experiment arethe followings. Stiffness:ks = 0.3Nm/rad, maximum torque:τmax = 2.4Nm, maximum deformation:∆θmax = 8rad. Asshown in Table II, our system has 80% of the maximum torqueof the VSA-CUBE [29], although the stiffness is 10%.

Direct comparison with other SEA or VSA is difficultbecause the systems greatly differ depending on the sizeof the elastic component and the selection of motors. Thecharacteristics of other systems are summarized in terms ofminimum and maximum stiffness, maximum deformation, andpeak torque in Table II for references. It can be observed thatthe proposed DSSAS has relatively low stiffness and largedeformation.

A. Preloading Angle of Spiral Spring

Two spiral springs are installed with preloading due tothe directional property of spiral springs. This is to avoid

TABLE II: Comparison of DSSAS with other elastic actuationsystems. The designed spiral spring is written as DSSAS andthe VSA-CUBE[29] is compared with DSSAS because ourgoal is designing spiral spring with 10% stiffness of the VSA-CUBE[29].

System Min.∼Max. Max. Max.

Stiff.(Nm/rad) Deform(rad) Torque(Nm)

DSSAS 0.3 8 2.4

VSA-CUBE[29] 3∼ 14 0.28 3

RSEA[5] 13.2 0.44 6

eSEAJ[6] 219 0.55 110

CompAct[19] 0∼ ∞ 0.35 117

AwAS[27] 30∼ 1300 0.20 80

MACCEPA[28] 5∼ 110 1.05 70

FSJ[30] 52.4∼ 826 0.26 67

unwinding that exceeds the initial configuration. Fig. 4 showsthe preloaded spiral springs in the DSSAS.

The preloading angle of the spiral spring can be determinedby the design specification and by the linear region of thespring. It is preferred to use only the linear region, i.e., thearea with a constant stiffness. Therefore, half of the maximumlinear area can be the maximum preloading angle. The othercriteria can be the maximum deformation angle that is requiredfor the purpose of the robot. These two criteria determine theminimum and maximum preloading angle of the spiral spring.

The maximum torque is proportional to the maximumdeformation. Therefore, the maximum torque is the greatestwhen the preloading angle is set to half of the maximumdeformation of one spiral spring. We selected approximately 8radian as the preloading angle in this experiment. Preloadingof 8 radian in the DSSAS generates 2.4Nm with deformationof 8 radian.

B. Stiffness

The stiffness of the DSSAS is experimentally verified in thissection. First, the torque generated by the DSSAS is measuredwhen the link is not installed. That is, the torque sensor isattached to the fixture so that the torque generated by theDSSAS is directly measured when the spiral spring deforms.

The stiffness of DSSAS is the addition of its stiffnesses atwinding (kwinding) and at unwinding (kunwinding) because thestiffness of a spiral spring changes depending on winding orunwinding as presented in Section II-B.

kdssas≃ kwind+ kunwind (5)

Fig. 6 shows the experimental result of the dual-spiral-spring system compared to the result of the single spiral spring.For a fair comparison, the two spiral springs used in the dual-spiral-spring system are installed in the same direction forthe experiment involving the single spiral spring. It is notedthat the stiffness of two spiral springs installed in the samedirection shows nonlinear property in the region of negativeangular displacements. This is because the springs are pasttheir initial configurations, a region the spiral springs are not




−8 −6 −4 −2 0 2 4 6 8−4

−3

−2

−1

0

1

2

Angular Displacement(Radian)

To

rqu

e(N

m)

DSSAS

Two spiral Spring in the Same Direction

Winding+Unwinding Stiffness

Fig. 6: Stiffness of dual spiral spring system.

supposed to operate. Therefore, its characteristics are typicallyunpredictable and the springs are easy to be broken.

The stiffness of our DSSAS system is approximately0.3Nm/rad. The maximum rotational deformation and max-imum torque are approximately 8 radians and 2.4 Nm, re-spectively. These large deformation and low stiffness levelsare the main advantage of the DSSAS given the size and themaximum torque of the spring.

C. Joint Torque Control

Compliant actuation systems generate the desired torquethrough the spring. The performance of tracking the de-sired torque is experimentally investigated for the developedDSSAS.

Fig. 7: Block diagrams of joint torque control.

The block diagram of the system and controls in thisexperiment is shown in Fig. 7. The motor is controlled in avelocity mode using a commercial motor driver (maxon motordriver). Then, a PD controller is implemented to track thedesired torque.

θm,desired= Km,p(τdesired− τestimated)−Km,vτestimated (6)

whereθm,desired, τdesired, andτestimatedare the desired values ofmotor velocity(rad/sec), the desired torque, and the estimatedtorque (kdssasθm), respectively. The control gainsKm,p andKm,v were set to 392.4 and 52.32, respectively. The velocitycommand to the motor is updated at 100Hz.

In this experiment, the axis of the DSSAS is directlyattached to the torque sensor to measure the spring torque.The desired torque and measured torque are plotted in Fig. 8.

Figure 8 plots the response to a sine command. The fre-quency of sine command is set to 0.7 Hz, which corresponds

to the maximum main walking frequency of CVA patients [24].The output amplitude decreases to approximately 95% and thephase delay decreases to approximately -24.5 degrees.

0 1 2 3 4 5−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Time(sec)

Torque(Nm)

Desired Torque

Actual Torque

Fig. 8: Torque responses of DSSAS.

D. Joint Position Control

A link is installed to demonstrate the performance of theDSSAS for control of position. The block diagram for theposition control is in Fig. 9. The desired velocity of the motoris computed by a PD controller using the error of the linkposition.

Fig. 9: Block diagram of joint position control.

θm,desired= K j ,p(θ j ,desired−θ j ,measured)−K j ,vθ j ,measured(7)

whereθ j ,desired and θ j ,measuredare the desired and measuredangle of the joint (rad). The termθ j ,measuredis calculated bythe finite difference on encoder readings with a low pass filter.

0 0.5 1 1.5 20

0.05

0.1

0.15

0.2

0.25

0.3

Time(sec)

Angle(radian)

Joint Angle(Kj,p

:7.325, Kj,v

:1.308)

Motor Angle(Kj,p

:7.325, Kj,v

:1.308)

Joint Angle(Kj,p

:3.663, Kj,v

:0.654)

Motor Angle(Kj,p

:3.663, Kj,v

:0.654)

DesiredAngle

Fig. 10: Step response of joint angle using DSSAS.




Figure 10 shows step responses of 0.261 radians (15 de-grees) with two different sets of gains. The position gainK j ,p and velocity gainK j ,v were set to 7.325 and 1.308 forthe first experiment, and 3.663 and 0.654 for the secondexperiment. The solid lines represent the measured joint anglesand the dashed lines represent the motor angles. The settlingtimes of the joint angles are approximately 0.45 and 0.90seconds, respectively and the rise times of the joint angle areapproximately 0.40 and 0.75 seconds, respectively.

IV. CONCLUSION

A dual-spiral-spring actuation system (DSSAS) is developedand its characteristics are investigated. The DSSAS is com-posed of two spiral springs in the opposite directions and amotor. The use of a spiral spring exploits the characteristicsof large compliance and deformation. The directional propertyof the spiral spring is then surmounted by the two oppositespiral springs on the same axis.

In this paper, the characteristics of spiral spring are pre-sented from the viewpoint of robotics applications. In additionto the characteristics of large compliance and deformation, itwas noted that a spiral spring has more design freedom interms of the specifications of the size, torque, and stiffness.Also, a spiral spring can in fact provide a maximum torquewith a similar order of magnitude compared to the other elasticactuators. Therefore, the DSSAS would be a good candidate toprovide large compliance without losing its torque capability.The experimental results of the joint torque control andposition control demonstrate the performance of the DSSASas a compliant robotic actuation system.

The DSSAS was developed for wearable robots. It isarguable as to whether high stiffness or low stiffness is betterfor general wearable robots. However, the joint compliancecan be different for specific wearable robots depending ontheir purposes. The large compliance of the DSSAS limits thebandwidth of the joint torque control, which is constrainedby the motor bandwidth. This is the trade-off between thecompliance and the bandwidth in joint actuation. Thus, theDSSAS can be used for several specific applications amongmany wearable robotic systems.

ACKNOWLEDGMENT

This research was supported by the National Research Foun-dation of Korea (NRF) funded by the Ministry of Education,Science and Technology (20110011341).

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