In the growing fields of wearable robotics, reha-bilitation robotics, prosthetics, and walkingrobots, variable stiffness actuators (VSAs) oradjustable compliant actuators are beingdesigned and implemented because of their
ability to minimize large forces due to shocks, tosafely interact with the user, and their ability tostore and release energy in passive elastic ele-ments. This review article describes the state ofthe art in the design of actuators with adaptablepassive compliance. This new type of actuator isnot preferred for classical position-controlledapplications such as pick and place operations butis preferred in novel robots where safe human–
robot interaction is required or in applicationswhere energy efficiency must be increased byadapting the actuator’s resonance frequency. Theworking principles of the different existingdesigns are explained and compared. The designsare divided into four groups: equilibrium-con-trolled stiffness, antagonistic-controlled stiffness,structure-controlled stiffness (SCS), and mechan-ically controlled stiffness.
In classical robotic applications, actuators arepreferred to be as stiff as possible to make preciseposition movements or trajectory tracking con-trol easier (faster systems with high bandwidth).The biological counterpart is the muscle that hassuperior functional performance and a neurome-chanical control system that is much moreadvanced at adapting and tuning its parameters.The superior power-to-weight ratio, force-to-weight ratio, compliance, and control of muscle,when compared with traditional robotic actua-tors, are the main barriers for the development ofmachines that can match the motion, safety, andenergy efficiency of human or other animals.One of the key differences of these systems is thecompliance or springlike behavior found in bio-logical systems [1]. Although such compliant
actuators are probably less suited for classical position-controlledapplications, they offer valuable advantages in certain novel appli-cations, e.g., safe human–robot interaction, comfortable actuatedprostheses, and orthoses, and in the design of legged robots.
It is worth mentioning that the range of compliance that isrequired depends on the application, as is the torque require-ment of the actuator. In this article, no specific torques aregiven for the actuators, because only the concepts of the actua-tors are described. Most actuators with controllable stiffnessconsist of two classical stiff actuators that can be easily dimen-sioned for the required torque.
Applications requiring adaptable compliance can bedivided into two groups: those for robot–human interactionand those to adjust natural dynamics. The distinction betweenthese groups depends on the primary use of the compliancewithin the application.
Adaptable Compliance inRobot–Human InteractionAdaptable compliance is used to make the interaction betweenrobots and humans safer and more natural. The following is anonexhaustive list of application examples.
u Industrial robots are heavy machines actuated by stiffsystems, and they do not give or comply in a collision,thereby inducing severe damage. Therefore, for safetyreasons, these devices are placed in a human-free envi-ronment. However, for some applications, it is useful tohave robots and humans fulfilling tasks together [2].This requires safer robots, which can be achieved bydesigning compliant joints. However, with a compliantjoint, it is harder to place the tool center point in anexact position or to track a specific trajectory accurately.In this case, an actuator with adaptable compliance canact stiff during precise positioning at low speeds (grasp-ing and placing an object) and compliant when posi-tioning is not as important when moving at higherspeeds (moving from one position to another) [3].
u Most robotic toys are actuated by stiff electrical drives.This inflexible movement results in the typical artificialway of moving and interacting. Especially for cuddlytoys such as Huggable [4] or Anty [5], a compliant,natural movement is preferred. When children playwith these toys, they can impose motions on it thatare different from the desired-controlled motion,which can damage the drive mechanism. Compliancein actuation can prevent damage from occurring andgive the cuddly toys a more natural feeling. Adaptable
compliance can also be used to emphasize emotions,e.g., anger by making the joints stiffer or fatigue bymaking the joints more compliant.
u Gait rehabilitation is generally aided by multiple physi-cal therapists, resulting in expensive sessions—limitedin time—which extends the overall rehabilitationprocess. Therefore, robots that can assist in the rehabil-itation process are being proposed, e.g., Lokomat [6]and Autoambulator, which impose gaitlike motionpatterns to the legs of a patient. Paraplegic patientsand stroke survivors often suffer from severe spasms.When using stiff actuators, undesired motions, such asthose caused by spasms, can cause large actuator forcesthat could potentially harm the leg. Adding compli-ance to the actuation system can naturally absorb largeposition errors, thus preventing damage to the systemand insuring safety of the wearer.
Additionally, in the beginning of the rehabilitation process,a relatively low stiffness might be preferred for safety, and stiff-ness could be gradually raised when the patient has regained acertain level of control over their legs. The Automated Loco-motion Training using an Actuated Compliant RoboticOrthosis project (ALTACRO) [7] intends to build a gait reha-bilitation robot with adaptable compliance. This field is grow-ing rapidly with many compliant systems: Bowden cables [8],gravity balanced systems [9], ankle devices that use series elasticactuators (SEAs) [10], and robotic tendons [11].
Adaptable Compliance to Adjustthe Natural DynamicsBy adjusting the natural dynamics of a mechanical system, itwill have a natural motion close to the desired motion toreduce energy consumption. Some application examplesinclude the following:
u Robotic prosthesis: many prostheses manufacturers focus onthe enhancement of comfort for the user, but the stiff-ness of their designs is fixed. For example, in a transtibialprosthesis, the compliance is fixed during the designphase and set to an average value, such that the naturalfrequency of the device is fixed. Thus, only for a certainstiffness of the ground and walking speed, this devicewill allow a comfortable feeling for the user. In contrast,when the compliance is adaptable, it can be chosen toobtain an optimal behavior for a wide range of circum-stances and desired motions. Besides the improvementsto enhance the comfort, research to optimize energyefficiency and avoid pathologies due to incorrect gaitpatterns has started. Today, most prostheses are still pas-sive, but more advanced systems are being developed,which have an actuator and a compliant element, suchas the work by Au et al. [12] and Hitt et al. [13].
u Walking and running robots: an actuator with adaptablecompliance extends the capabilities of these devices.The setting of the compliance can be used to maximizethe amount of energy, which can be stored duringtouchdown of the feet and released during push-off. Inaddition, by varying the stiffness of the joints, the natural
The equilibrium position of a
compliant actuator is defined as the
position of the actuator where the
actuator generates zero force
or zero torque.
IEEE Robotics & Automation Magazine82 SEPTEMBER 2009
frequency of the system can be adjusted to allow sloweror faster walking [14]–[17].
The goal of this article is to provide an overview of existingcompliant actuator designs and categorize the actuator designsinto four main groups to develop a standard terminology.Neither specific applications of these devices nor their appliedcontrol approaches will be discussed in any detail.
Compliant ActuatorsTo define what a compliant actuator is, a definition of a non-compliant actuator —better known as a stiff actuator—is use-ful. A stiff actuator is a device that is able to move to a specificposition or to track a predefined trajectory. Once a position isreached, it will remain at that position, whatever the externalforces exerted on the actuator (within the force limits ofthe device).
A compliant actuator, on the other hand, will allow devia-tions from its own equilibrium position, depending on theapplied external force. The equilibrium position of a compli-ant actuator is defined as the position of the actuator where theactuator generates zero force or zero torque. This concept isspecifically introduced for compliant actuators, since it doesnot exist for stiff actuators.
Some remarks must be made concerning terminology.Because compliance is the opposite of stiffness, both the termsare used to describe the compliant or nonstiff behavior of anactuator. To describe an actuator with a variable stiffness, theterm adjustable compliance can be used; variable compliance,adjustable stiffness, and controllable stiffness are also used.These examples are given to show that there is no standardterminology (yet) to describe these types of actuators. Through-out this article, a number of existing designs are described usingthe terminology used by the inventors. We prefer controlla-ble stiffness because the term fits with our groupings ex-plained later.
Passive compliant actuators contain an elastic element, i.e.,a spring that can store energy—which is not the case for actua-tors with active compliance, where the controller of a stiffactuator mimics the behavior of a spring [18]. The latter hasthe disadvantage that no energy can be stored in the actuationsystem, and because of the limited bandwidth of the controller,no shocks can be absorbed. An advantage of active complianceis that the controller can make the compliance online adapta-ble. Online adaptability means that the compliance can beadapted during normal operation. In this review article, wewill not focus on active compliant actuators.
The stiffness of an actuator is comparable with the stiffnessof a linear spring. The variation of the length of a linear springdepends on the force acting on the spring, according toHooke’s Law:
F ¼ k � (x� x0): (1)
This means that a spring with rest length x0 and an actuallength x generates a force F. If the actual length equals the restlength, zero force is generated. This is comparable with a com-pliant actuator at its equilibrium position. When a spring with
linear force-displacement characteristic is used, the stiffness—inverse of the compliance—can be defined as
k ¼ FDx¼ constant: (2)
When the force-displacement relationship is nonlinear, thestiffness is considered to vary with the position
k(x) ¼ dFdx6¼ constant: (3)
For a spring, the equilibrium position is fixed and is equalto its free length. However, a compliant actuator can changethis position by moving the attachment point of the spring.
An example of a passive compliant actuator is the originalSEA [19], which is a spring in series with a stiff actuator. Thecompliance of this actuator is fixed and determined by theselection of the spring; thus, the physical compliance cannotbe changed during operation. Further discussion about theSEA will be provided in a later section.
It is worth mentioning that this discussion about compliantactuators is restricted to conventional actuators used in themajority of robotic and automated mechanical systems, e.g.,hydraulic, pneumatic, and electric actuators. Recently, advan-ces in material technology have introduced new substances,making it possible to build structurally strong articulated mech-anisms that are compact and lightweight. Examples of suchmaterials that can be used to develop novel actuators are shape-memory alloys (SMAs) [20], electrorheological fluids (ERFs)[21], electrostrictive and magnetostrictive materials (includingpiezoelectric substances) [22], and electroactive polymers [23].The use of these new materials as compliant actuators is notobvious, since their current operational speeds are very low,with response times in the scale of tens of seconds.
Actuators with a fixed compliance can be used for forcecontrol [19] or safe human–robot interaction [3], but they donot control the natural frequency of a mechanical system. Asexplained in the ‘‘Adaptable Compliance to Adjust the NaturalDynamics’’ section, controlling the natural frequency can bedone by introducing adaptable, passive compliance.
One way to vary the compliance of an actuator is by softwarecontrol of a stiff actuator [17]. Based on the measurement of theexternal force or torque, a certain deviation is calculated by thecontroller and set by the stiff actuator. This type of compliantactuator requires an actuator, a sensor, and a controller that areall fast enough for the application, but it permits the adjustment
of the compliance during operation. Thus, the characteristic ofan imitated spring is programmed and as such is adjusted online;this is often referred to as active compliance. The main disad-vantage of active compliance is continuous energy dissipation,whereas energy could be stored and subsequently released againwhen a passive element (e.g., a spring) is used.
To combine energy storage and adaptable compliance, anelastic element to store energy is needed, together with a way toadapt the compliance. A substantial number of designs has beendeveloped. However, four main ideas can be distinguished.
u Equilibrium-controlled stiffness: these compliant actuatorsuse a fixed stiffness spring in series with a traditionalmethod of actuation, e.g., electric motors or hydraulicsystems. The SEA measures the displacement of theunit and force on the spring to adjust the torque sup-plied by the motor, otherwise known as impedancecontrol. To obtain variable stiffness, the virtual stiffnessof the actuator is adjusted by dynamically adjusting theequilibrium position of the spring as is explained inthe ‘‘Equilibrium-Controlled Stiffness’’ section.
u Antagonistic-controlled stiffness: two actuators with nona-daptable compliance and nonlinear force-displacementcharacteristics are coupled antagonistically, workingagainst each other. By controlling both actuators andusing nonlinear springs, the compliance and equilib-rium position of this antagonistic setup can be set. Tobe able to vary the compliance, it is required that thespring characteristic of the two actuators is non-linear,while the resulting spring characteristic is linear. Inthe ‘‘Antagonistic-Controlled Stiffness’’ section, thisprinciple is described in more detail and some exam-ples are given.
u Structure-controlled stiffness: unlike the previous twoconcepts, structure control modulates the effectivephysical structure of a spring to achieve variations instiffness. When using a beam as elastic element, thestiffness depends on material modulus, the moment ofinertia, and the effective beam length. During opera-tion, the stiffness can be controlled by adjusting one ofthese parameters. In the Jack Spring, the number ofactive coils in a helical spring is adjusted to vary the
stiffness. More about these types of designs can befound in the ‘‘Structure-Controlled Stiffness’’ section.
u Mechanically controlled stiffness: similar to structure con-trol, mechanical control also adjusts the effective physi-cal stiffness of the system. However, in this case, thefull length of the spring is always in use. The variationis done by changing the pretension or the preload ofthe spring, as is the case in the mechanically adjustablecompliance and controllable equilibrium positionactuator (MACCEPA) and the variable stiffness joint(VS-Joint). These actuators require only one compliantelement. The complete actuator behaves as a torsionspring where the spring characteristics and equilibriumposition can be controlled independently during oper-ation. The principles and designs are elaborated in the‘‘Mechanically Controlled Stiffness’’ section.
Passive, Controllable Stiffness Actuators
Equilibrium-Controlled StiffnessThis section starts with a description of the SEA, which isforce controlled and has a fixed compliance. Then, an exam-ple of a SEA variant with a second spring used in parallel isgiven. Finally, the concept of equilibrium-controlled stiffnessis explained.
Series Elastic Actuator
The SEA [19] is essentially a spring in series with a stiff actua-tor. The compliance is determined by the spring constant andis therefore not adjustable during operation. The SEA is acompliant actuator allowing force to be controlled in an easymanner. Figure 1 shows a typical setup of a SEA for force con-trol. The elongation of the spring is used as force measurementand fed back in the control loop.
SEA Variant
Au et al. at Massachusetts Institute of Technology (MIT) [24]developed a prosthetic ankle-foot device that uses a variant ofthe SEA in a parallel configuration with a passive unidirec-tional spring that is elongated when the ankle angle is less thanzero degrees (ankle dorsiflexed). The stiffness of the parallelspring is chosen by estimating the slope of the measured tor-que-angle curve and is also used to reduced shock loads. Theparallel stiffness is also selected to increase the required open-loop force-bandwidth.
Equilibrium-Controlled Stiffness Concept
Sugar has also developed a spring-based actuator, which usesthe concept of equilibrium-controlled stiffness. A linear springis added in series to a stiff actuator, and the equilibrium posi-tion of the spring is controlled to exert a desired force ordesired stiffness [11], [25]. The compliance is actively changedusing a control law instead of fixing the compliance by pas-sively adding springs. The force-control problem is convertedto a position-control problem using electric motors. Themotor position is adjusted based on the deflection of the springto alter the tension or compression of the spring.
Fdesired
Fload
+
−Controller Actuator
Spring Load
Sensor
Σ
Figure 1. Force control using a series elastic actuator.
The compliance adjustment of the
Jack Spring mechanism is achieved
by adding or subtracting the number
of available coils used in a spring.
IEEE Robotics & Automation Magazine84 SEPTEMBER 2009
The intrinsic spring stiffness cannot be altered, but the linkor limb stiffness can be selectively varied using an active con-trol law, therefore adjusting the virtual stiffness. Figure 2explains the control of a single actuator. The force applied bythe link is given by
F ¼ �Kact(l � s� a), (4)
where l is the length of the actuator, s is the length of the inter-nal ball screw that adjusts the equilibrium position of thespring, and a is the free length of the spring. Kact is the intrinsicspring stiffness. If a desired behavior is given by
F � Fo ¼ �Kdes(l � lo), (5)
about an operating point (Fo, l0), the desired actuator positionis given by
sdes ¼ l � aþ (F0 � Kdes(l � l0))=Kact: (6)
Thus, a position-control scheme achieves the stiffness con-trol of a single compliant limb. Controlling the position of dcmotors is very simple and differs from the work by Pratt wherethey controlled the torque on the motors and, in turn, con-trolled the impedance. The disadvantages of using an approachto control the virtual stiffness are that the performance islimited by the bandwidth of the controller (e.g., during impactthe hardware stiffness will be felt), and it consumes energy toadjust the position of the spring. One overlooked advantage isthat the compliant spring acts to passively change the transmis-sion ratio of the system. For example, if a force compresses thespring to the left and the desired behavior is to move the limbto the right, then as the spring compresses, the motor mustspin faster thus increasing the transmission ratio at the oppor-tune moment.
Antagonistic-Controlled StiffnessThe best-known example of an antagonistic setup is the combi-nation of biceps and triceps in the human arm. When thebiceps contracts and the triceps relaxes, the arm is flexed. Whenthe triceps contracts and the biceps relaxes, the arm extends.One of the reasons why an antagonistic setup is required is thefact that muscles can only pull and not push. However, morecan be achieved with this setup: when both biceps and tricepscontract, the elbow becomes stiff; when they both relax, theelbow becomes very compliant and the arm hangs freely. Inreality, the muscles in the human arm are controlled in acontinuous way and, thus, the system can cover a whole rangeof positions and compliant behavior. The biologically inspiredconcept of an antagonistic setup is used in a number ofmechanical actuators to obtain adaptable compliance.
The Necessity of Nonlinear Springs
The nonlinearity of the spring is essential to obtain the adapt-able compliance. To explain this, a simple linear antagonisticsetup (Figure 3) is used. The two springs are linear and havethe same spring constant. In Figure 3, x0A and x0B are the
controllable positions when zero force is applied by thesprings (the rest length of both springs is assumed zero). Eachposition can be independently controlled requiring twoactuators. The force on the block in the center is the sum ofthe forces of both springs:
F ¼ �k(x� x0A)þ k(x0B � x)
¼ �2kxþ k(x0A � x0B): (7)
The stiffness becomes
j ¼ dFdx¼ �2k: (8)
This result is independent of the controllable parametersx0A and x0B, and consequently, the compliance is uncontrol-lable if linear springs are selected.
When two springs with a quadratic characteristic are used,the force is
F ¼ �k(x� x0A)2 þ k(x0B � x)2
¼ 2kx(x0A � x0B)þ k(x20B � x2
0A): (9)
xx0Ax0B
Figure 3. Demonstration of the necessity of using nonlinearsprings.
a = Free LengthKact
s
l
(a)
(b)
(c)
Figure 2. System for one limb. The limb length is measuredby l, whereas the internal motor adjusts the length s. Thecompliance of the limb is adjusted by varying the length s.
As can be seen, the stiffness is a linear function of the differ-ence between the controllable parameters. The equilibriumposition is the position where no forces are generated:
2kx(x0A � x0B)þ k(x20B � x2
0A) ¼ 0, (11)
) x ¼ x20A � x2
0B
2(x0A � x0B)¼ x0A þ x0B
2: (12)
This result is the average of x0A and x0B. Thus, by control-ling the two positions x0A and x0B, both compliance andequilibrium position can be set. This principle is used in anumber of different designs, which are described in the follow-ing sections.
Biological Inspired Joint Stiffness Control
Migliore et al. [25] describe a device based on the antagonisticsetup of two nonlinear springs. This biologically inspired joint
stiffness control is a rotational joint, actuated by two SEAs asshown in Figure 4(a) and (b).
Figure 4(c) shows how the linear characteristic of the springis transferred into a quadratic characteristic, by using specialshaped pieces, over which two wheels roll. The centers of thewheels are interconnected by a linear spring.
When both servomotors rotate in the same direction, theequilibrium position of the joint is changed. When theyrotate in the opposite direction, the stiffness of the joint willbe changed.
The advantage of this design is that the force-elongationcharacteristic of the springs is chosen during the design phase,as well as the resulting compliance characteristic of the overallsystem. The drawback is the size, extra complexity, and fric-tion of the mechanisms to make the quadratic springs. Othersystems using antagonistic quadratic springs include the workby Koganezawa [26] and English [27].
Variable Stiffness Actuator
Tonietti et al. [28] describe the VSA. This design is based onthe same antagonistic setup. However, it is not as obvious as theprevious design. In Figure 5(a) and (b), two computer-aideddesign (CAD) views of the VSA are shown. The VSA consists
of three pulleys 1, 2, and 3 over which atiming (toothed) belt 10 is placed. Twoof the pulleys 2 and 3 are controlled,each by a servomotor 5 and 6. The otherpulley 1 is connected to the arm 4. Onthe belt between the pulleys, three ten-sioning mechanisms 7, 8, and 9 areplaced. Although all three tensioningmechanisms are equal, their function isdifferent. The two tensioning mecha-nisms 8 and 9, neighboring the pulleyconnected to the arm, form the nonlin-ear springs. The other mechanism 7 is
AntagonistServo
AgonistServo
RS RSX1X2
Tload
RJ
0°0°
0°
β αφ
θ
R F
NFS
Yc Yr
Xc
Xr
AppliedForce
Roller Guide
RollerTrajectory
Contact Point
Ball BearingRollerFrame
(a) (b) (c)
Figure 4. (a) Picture of setup. (b) Schematic drawing of the antagonistic setup of two SEA. (c) Schematic of a quadratic springdevice. With permission from Migliore.
4 4
1
18 9
82
2
3
3
7
7
5 6
9
10
a
D
hb,a
R, qa R, qb
bls ks
Lb,al2 Lb,al2rFsα
(a) (b) (c)
Figure 5. (a) and (b) Two CAD views of the VSA and (c) mechanism to make thesprings nonlinear in the VSA. With permission from Tonietti.
IEEE Robotics & Automation Magazine86 SEPTEMBER 2009
just a tension mechanism to keep the timing belt 10 against theother two pulleys.
One can see that the VSA is actually made with two SEAs:2, 5, 8 and 3, 6, 9. The two springs 8 and 9 of each SEA are lin-ear, but because of the tensioning mechanisms, they are madenonlinear. The mechanism that makes the springs nonlinear isshown in Figure 5(c). The big circle on the left represents thepulley with the radius arm 1, and the big circle on the right iseither pulley 2 or 3, depending on the considered SEA. As seenfrom Figure 5(c), the length of the spring is a nonlinear func-tion of the length of the belt between the two pulleys. Thecomplete formula for the torque can be found in [28].
To make the VSA stiffer, pulley 2 with motor 5 has to rotatecounterclockwise, and pulley 3 with motor 6 has to rotateclockwise. As a result, the two springs in the mechanism 8 and9 are compressed, and spring 7 elongates to keep the belt tightagainst the pulleys. When rotating both pulleys 2 and 3 in thesame direction, the spring’s length does not change, and assuch, the compliance will stay the same, but the equilibriumposition will change. As is the case for each antagonistic setup,both actuators have to be used to influence only one variable:compliance or equilibrium position.
The control of the VSA is more complicated than theprevious design, since the nonlinearity is more complex. TheVSA described in this section is the first generation concept.The researchers are working currently on a more compactimplementation, the VSA-II.
Other similar systems include an actuator, employing biomi-metic research that was developed by Kolacinski and Quinn[29]. Their actuator can modulate the position and stiffness,although the system’s stiffness law is very complicated. TheFlexCVA [30] uses a mechanism similar to that shown in Figure5(c) to create nonlinear springs.
Actuator with Mechanically Adjustable
Series Compliance
Another design based on the same principle is the actuator withmechanically adjustable series compliance (AMASC) developedby Hurst et al. [31]. As shown in Figure 6, the AMASC is arather complex mechanism with a great number of pulleys andcables. Nevertheless, the advantage is that only one actuator isused to control compliance or equilibrium position. Thus, eachof the actuators has its specific function, allowing different motortypes to optimize the weight of the com-plete system. The working principle isbased still on the antagonistic setup oftwo nonlinear springs.
In Figure 6(b), a schematic overviewof the AMASC is given. The springs FY
are two fiberglass leaf springs, which areplaced on both sides of the prototype[Figure 6(a)]. In the case of the AMASC,the nonlinear spring is formed by a set ofspiral pulleys. The reduction ratio of thepulleys varies proportionally with thefiberglass spring deflection to obtain thequadratic relationship. The pulleys are
also used to uncouple the control of compliance and equilib-rium position.
The leg of the actuator is placed on pulley J2. One motorcontrols the angle h1 of pulley J1, which is the setting for theequilibrium position. When this motor turns counterclock-wise, the set of floating pulleys ZA will move to the left, andthe set of floating pulleys ZB will move to the right. Thismotion will result in a counterclockwise rotation of the leg,which is connected to pulley J2. All this can be done withoutchanging the lengths of the springs, thus keeping the compli-ance constant.
On the other hand, when the displacement X3—controlledby the second motor—moves to the left, both sets of pulleysZA and ZB will also move to the left. This will elongate bothsprings, and thus make the joint stiffer, while the equilibriumposition is kept constant.
The AMASC is an actuator where the compliance and theequilibrium position can be controlled independently, each bya dedicated motor. This independence makes the control eas-ier and allows one to design the two motors separately to meetthe demands of a specific application, e.g., compliance variesslowly while the equilibrium position has to be set faster. Themain disadvantage of the AMASC is its complexity. Based onthis concept, the biped robot BiMASC is designed. Here, thestiffness of the whole leg can changed instead of the stiffness ofthe joints. Thorson [32] developed a linear variant where con-trol of equilibrium position and stiffness are adjusted by twoseparate motors.
Pneumatic Artificial Muscles
Instead of using a SEA, pneumatic artificial muscles (PAMs)are often used. When pressurized, the muscle contracts axiallywhile expanding radially. The compressibility of air makesthem inherently compliant, behaving in a spring-like fashion.The McKibben muscle [33] is the most well-known design.Its overall shape resembles a thin cylinder, which is easy to usein robotic devices. One of the drawbacks is the hysteresisintroduced by friction, which makes it difficult to control,and it has a substantial threshold of pressure, before any forceis generated. The pleated PAM (PPAM) [34] drasticallyreduces hysteresis and overcomes the threshold of pressure.Figure 7 shows an implementation of the PPAM in the bipedLucy [34].
X3
J1 J2r1 r2
B1 B2
θ1θ2
ZA, FZA
YA
YB
G(ZA)
G(ZB)FY (YB)
FY (YA)
ZB, FZB
leg
τ legτ motor
(a) (b)
Figure 6. (a) Picture of AMASC [31] and (b) schematic overview of AMASC, basedon [31].
Pneumatic muscles are actuators with a high power-to-weight ratio and can be directly coupled to the joint without aheavy and complex gearing mechanism. The drawbacks of ajoint actuated by two pneumatic muscles are the nonlinearcharacteristic of the joint, slow dynamics (especially depressu-rizing the muscle is slow), presence of hysteresis, and need forpressurized air.
Structure-Controlled StiffnessAs an alternative to the antagonistic setup of two nonlinearsprings, variations in stiffness can also be achieved throughmanipulation of the effective structure of a spring, also calledSCS [35]. As an example, bending a leaf spring is a form ofstoring energy. However, apart from simple loading (energystorage) and unloading (energy return) of the leaf spring, anextra step of altering the leaf spring’s effective stiffness is intro-duced. To understand the basic concepts of a SCS actuator,consider the small deflection beam equation
M ¼ EIL
� �3 h, (13)
where M is the bending moment, E the material modulus, Ithe moment of inertia, L the effective beam length, and h is
the angle of bending or slope. In this representation of bend-ing, the term EI/L represents the bending stiffness. To controlthe stiffness of the structure, any of the three parameters in thisbending stiffness can be manipulated.
The parameter E is a material property, which cannot becontrolled by a structural change, but for some materials, it canbe changed by changing the temperature. In most instances,the temperature of such a material cannot be changed fastenough to be useful to create adaptable compliant actuators forbipedal walking. Examples of mechanisms where the momentof inertia I and the length of the elastic element L are changedare discussed in the following sections.
Variation of Moment of Inertia by Axial Rotation
An actuator can be built that has a passive element withvariable mechanical impedance, resulting in an actuator withadaptable compliance. For example, when the aspect ratio of abeam differs from one, then compliance can be changed byrotating the beam over 90�. A prototype of a spring withvariable stiffness used in wearable robotic orthoses [36] isshown in Figure 8. The purpose of the helical spring in thisdesign is to reduce the effects of lateral buckling.
When the moment of inertia is calculated with the well-known formula, it can be seen that it varies, depending onthe width-to-thickness ratio of the beam. Depending on therotation, the thickness and width have to be exchanged inthe formula
Istiff ¼thickness 3 width3
12(14)
Icompliant ¼width 3 thickness3
12(15)
This is a very easy way to obtain a compliant element withtwo predefined settings of the compliance. Because of thelateral buckling, it is difficult to have intermediate settings.
Work by Seki et al. [37] have employed a concept similar tothe rotated leaf spring approach, although these authors didnot account for beam deflections beyond 15� in experimentsnor did they address the limitations because of lateral buckling.
Union Is Strength: Increasing the Moment of Inertia
Kawamur changed the moment of inertia by controlling theforce to press together an element consisting of many layeredsheets [38] as shown in Figure 9(a). When external forces act
on the element, the loose stack of sheetsbend, as is depicted in Figure 9(b).
However, if the sheets are firmlypressed together, they will not slip be-cause of friction. As a result, the elementstiffens, and larger forces are needed tobend the element. Different methods ofpressing the sheets together such as elec-trostatic [39] or vacuum [38] can beused. To be able to create a vacuum, thesheets are covered with a rubber or vinylsheet to make an airtight chamber. By
(a) (b) (c)
Figure 8. Variation of moment of inertia by rotating the beam.
High-PressureTubing
AngularPositionLimiter
To AirSupply
CompressedAir Buffer
Low-PressureTubing
Exhaust
Figure 7. Antagonistic setup of two PPAM.
IEEE Robotics & Automation Magazine88 SEPTEMBER 2009
decreasing the pressure in the chamber, the atmospheric pres-sure generates a normal force on the sheets. It should be notedthat holding the sheets together is very difficult because thetransverse shear forces are very high.
To estimate the variation of compliance of the element, themoment of inertia in both the normal and vacuumed state canbe calculated. Consider that the number of sheets is n. The sys-tem is compliant when the sheets are separated. When thevacuum is applied, the system is stiff.
Icompliant ¼n 3 width 3 thickness3
12(16)
Istiff ¼width 3 (n 3 thickness)3
12(17)
Consequently, the stiffness of the element can be increasedby a factor n2 when vacuum is applied. This is an effectivemethod to obtain a large stiffness range since the number ofsheets can be increased easily when using thin sheets such asfilms. Based on the same idea, a two-dimensional variant canbe made using wires with a square cross section [38].
The advantages of this system are the simple constructionand wide stiffness range that is possible. However, the frictionmakes the precise control of the compliance difficult. More-over, the compliance will depend on the deflection when thevolume is in a vacuum applied state.
Mechanical Impedance Adjuster
Another way to adjust the compliance is to vary the effectivelength of a compliant element. An active knee brace varies thelength of beam to adjust the stiffness [36]. Figure 10 depicts themechanical impedance adjuster [40]. The compliant elementis a leaf spring connected to the joint by a wire and pulley. Theeffective length of the spring can be changed by a slider. Aroller is placed on the slider to hold the leaf spring close to thestructure. The motor rotates the feed screw, which moves theslider, and thus changes the compliance.
A rotational version was developed [41] for implementationin a robotic joint. In Figure 11, a conceptual drawing of theproposed design is shown. Figure 11(a) and (b) shows the situa-tion when the mechanism is compliant and stiff, respectively.The two vertical spindles, which are actuated by a motor, canmove the slider up and down. The four wheels placed on theslider roll over the leaf spring. When the slider is movedupward, the effective length of the leaf spring is shortened.
An advantage of both of these mechanisms is that they areeasy to construct. They are easy to control because the settingof the compliance and the equilibrium position are com-pletely independent. This mechanism allows all possible
intermediate states between compliant and very stiff. Thisimplies one actuator for the compliance and one actuator forthe equilibrium position can be used to allow independentcontrol. Similar devices include the following example. DeUri Tasch designed a two-degree-of-freedom finger, whichagain uses leaf springs, but has the ability to control thecoupling compliance as well [42].
Jack Spring Actuator
Recently, a new type of actuator, based on the structure con-trolled stiffness concept, was presented in [43], named the JackSpring actuator. A helical spring is used as the compliant ele-ment. It should be noted that, because a helical spring has thesame geometry as a lead screw or jack screw, the mathematicsto describe a lead screw can be used to describe a Jack Spring.The main difference is that the lead of the Jack Spring changesunder an applied axial load.
The compliance adjustment of the Jack Spring mecha-nism is achieved by adding or subtracting the number ofavailable coils used in a spring. The basic concept for theadjustment of stiffness can be seen in the equation of thespring constant (stiffness):
K ¼ Gd4
8 3 D3na, (18)
where G represents a material property called shear modulus.Each of the parameters of (18) influences the stiffness of acoiled spring. In particular, an increase in wire diameter, d, willincrease stiffness, whereas either an increase in coil diameter,D, or number of active coils, na, will decrease spring stiffness.Therefore, to create a SCS device, based on the properties of a
Leaf Spring
Motor
Wire To Joint
Pulley
SliderFeed Screw
Figure 10. Conceptual design of mechanical impedanceadjuster.
(a) (b)
Figure 11. Conceptual design of rotational mechanicalcompliance adjuster.
(a) (b)
F
Figure 9. (a) Laminated structure and (b) deformation.
coil spring, any of these parameters could potentially beadjusted. The simplest parameter to change and adjust stiffnessis the number of active coils, na. A conceptual diagram of thisapproach can be seen in Figure 12.
The diagram shows an extending helical spring or JackSpring. Through a rotation of either the spring or the shaft/nut, coils can be added to or subtracted from the number ofactive coils, thus changing the effective stiffness of the structure.In this example, both displacement and stiffness are coupled.
The Jack Spring actuator is novel, compact, and easy toimplement. The external force can act in both directions. Incombination with a stiff actuator, both compliance andequilibrium position are adaptable. However, both are coupledin this first concept. Moreover, setting the compliance, whileforces are working on the spring, results in friction and defor-mation of the space where the surface has to slide but the tor-que that is required is reduced in compression. Also, if rollingpins are used, the system is similar to a ball screw instead of alead screw. In a second concept, a second motor can be used totranslate the Jack Spring. In this concept, one motor is used toadjust the equilibrium position of the actuator, and a secondmotor is used to adjust the stiffness.
Mechanically Controlled StiffnessSimilar to structure control, mechanical control also adjuststhe effective physical stiffness of the system. However,mechanical control adjusts stiffness by varying the pointswhere a compliant element is attached to the structure, thuschanging the pretension or preload of the spring.
Lever Arm Length Adjustment
A first type of actuator based on mechanical-controlled stiff-ness was developed at the Vrije Universiteit Brussel. As shownin Figure 13, the proposed system is a rotational joint consist-ing of grounded arm 1 and movable arm 2, connected by an
axis 8. The lever arm 3 is also placed onthe same rotational axis. The position oflever arm 3, relative to arm 1, can becontrolled by a servomotor 4. Thespring 7 generates a torque that tends toline up bodies 2 and 3. This restoringforce is transmitted by the cable 9 thatruns from a point on body 3 to a pointon body 2. Servomotors 5 and 6 rotatethe threaded spindles, which move thesepoints to or away from the rotationalaxis, resulting in shorter or longer lever
arms and thus a lower or higher torque (or torsion stiffness).The spindle, powered by servomotor 5, also moves the pointwhere the spring 7 is attached. Figure 13(a) shows the situationwith short lever arms, resulting in a joint with low stiffness. InFigure 13(b), the situation is shown where the lever arms arelonger, which makes the joint stiffer.
The variation of the compliance is based on the variation ofthe length of the lever arms and uses only one passive element,which is fundamentally different from the antagonistic setupor structural-controlled stiffness. This design has a number ofdrawbacks. The use of three motors, of which two are con-trolled together, is expensive but difficult to avoid. It is possibleto reduce the number of motors by connecting both slidersusing a cable running through the rotational axis. However,this will result in a complex mechanism with considerable fric-tion. For practical reasons, the two points that ensure tension-ing of the cable cannot be placed at the same distance from therotational axis, resulting in nonlinearity of the torque-anglecharacteristic for small angles. For larger angles, the torque-angle characteristic will become nonlinear since the cable willfollow a straight line (a chord) instead of an arc with the rota-tional axis as the center. This nonlinearity is because the lengthof an arc is a linear function of the angle, which is not the casefor a chord.
Also, the fact that friction occurs in the point where thecable is guided around arm 2, resulting in hysteresis, made thisdesign unfavorable, especially with respect to passive walking.A similar approach is presented in [44], where only the lengthof one of the lever arms is changed.
MACCEPA
Starting from the previous design, a new design was devel-oped, named MACCEPA [45]. In Figure 14, the essentialparts of the MACCEPA are drawn. As can be seen, there arealso three bodies pivoting around one rotational axis.Around the rotational axis, a lever arm is pivoting, depictedas a smaller body in Figure 14. A spring is placed between afixed point b on the lever arm and a cable that runs around c(a fixed point on the right body) and is attached to a preten-sion mechanism.
The angle j between the lever arm and left body is set by aclassical actuator (e.g., a servomotor). When a—the anglebetween the lever arm and right body—differs from zero, theforce due to the elongation of the spring will generate a torqueT that tends to line up the right body with the lever arm.
63 4
1
27
5
8
9
63 4
1
897
5
2
(a) (b)
Figure 13. Variation of the length of the lever arms.
ActiveCoil
Region
InactiveCoil
Region F
X
τDatum
Datum
(a) (b)
Figure 12. Active and inactive coil region in the Jack Spring actuator.
IEEE Robotics & Automation Magazine90 SEPTEMBER 2009
When the angle a is zero—this is the equilibrium position—
the spring will not generate any torque. The equilibrium posi-tion itself is determined by the value of j. A second classicalactuator present in the pretension mechanism at point b deter-mines the length of the piece of cable between points c and b,thus setting the pretension of the spring. This pretension willinfluence the torque for a certain angle a, thus controlling thespring constant of the equivalent torsion spring used to modelthe device. In Figure 15, a CAD drawing of the MACCEPAprototype is shown.
The advantages are that the MACCEPA actuator can bebuilt with standard off-the-shelf components and that it has alinear angle-torque characteristic. The control of complianceand equilibrium position are fully independent, and these con-trol signals are independent of the current position. However,the friction in the joint depends on the setting of the compli-ance, and the servomotors require some space in the structure.Recently, this novel concept is implemented on two bipedalwalking robots [14] and [46] and in an elbow rehabilitationdevice developed by Sulzer [47].
VS Joint
At DLR, the German Aerospace Center in Germany, anotherdevice based on mechanically controlled stiffness is devel-oped: the VS-Joint [48]. Figure 16 shows a picture of thevariable stiffness part. The cam disk (lower part) is connectedto the joint. The vertical position of the spring base slider isdefined by the spindle that is actuated by the small motor forthe stiffness setting. This upper plate compresses the springs.The angular position of the upper plate is controlled by theposition motor.
Figure 17 shows the unwinded schematic of the VS-Joint.The shaded part is one of the three cam disks, which are con-nected to the joint, whereas the linear bearing in the figure isconnected to the upper plate and position motor. A roller ispushed by a spring to the lowest position in the cam disk.When a torque is applied on the joint, there will be a jointdeflection of the roller, e.g., to the right, as shown in Figure17(b), and pushing the roller upward causing a translationaldeflection of the springs. The spring pushes the roller down-wards, which will generate a force in the direction of the low-est point of the cam disk. This lowest point is the equilibriumposition of the joint. By changing the position motor, theangle of the stiffness mechanism is adjusted, and thus also theposition where no torque is generated.
The advantage of this design is that can easily be integratedinto a robotic arm. The shape of the cam disk can be adjustedto obtain a progressive, degressive, or linear system behavior.Although one spring is enough, the VS joint uses three springsfor symmetry. It is also a design where two motors of differentsizes can be used: a small one for the stiffness preset and a morepowerful motor for the link position.
StifferPreset
TranslationalDeflection
JointDeflection Axis of Rotation
Spindle
Spring Base Slider
Connection toLinear Bearing
Roller Slider
Cam Rollers
Cam Disk (Fixedto Circular Spline)
Figure 16. VS-Joint mechanism.
Roller
LinearBearing
Roller Positionof UndeflectedJoint
Deflection
(b)(a)
Cam Disk
FΤ
α
Figure 17. (a) Unwinded schematic of the VS-Joint principle inequilibrium position and (b) deflected position.
Note that the VS-Joint and the MACCEPA actuator are ina way complementary, because, in the VS design, the spring isused in compression, whereas the latter uses the spring in ten-sion. Both designs use the pretension or preload of the springto vary the stiffness, and both have one motor for the stiffnesssetting and one for the equilibrium position.
Discussion and ComparisonComparing the different designs is not easy, because eachdesign might be optimized for a specific task or property.
Table 1 gives an overview of some of the properties for the dif-ferent groups of controllable stiffness actuators.
These properties of each group are a generalization.Within each group, there are differences, and the describeddesigns might be optimized for a specific application. Otherdesign criteria to be taken into account are the complexity ofthe design, cost, speed of the stiffness variation, maximumtorque, and size of the complete system. In addition, therequired power source, e.g., in case of pneumatic muscles, canalso be a criterion.
ConclusionsFour concepts to create adaptable, passive-compliant actua-tors, which can store energy and can be used for passiveapplications, are presented and examples are given. Thefirst concept, equilibrium-controlled stiffness, is based onadjusting the equilibrium position of springs. This conceptis simple to control but constantly requires energy to regu-late its actuator position. The second concept, antagonis-tic-controlled stiffness, covers the compliant actuatorsbased on the antagonistic setup of two nonlinear springs.Again, in this system, extra work is needed to adjust thestiffness, because two nonlinear springs must be controlled.
Table 1. An overview of some of the properties for the different groupsof controllable stiffness actuators.
Equilibrium-
Controlled
Stiffness
Antagonistic-
Controlled
Stiffness
Structure-
Controlled
Stiffness
Mechanically
Controlled
Stiffness
1) Minimum number of springs required
(can be more to obtain symmetry)
1 2 1 1
2) Can linear springs be used (related to
availability, linear spring are standard)
Yes No Yes Yes
3) Always using the full length of the spring
element
Yes Yes No Yes
4) Preload/Pretension in equilibrium posi-
tion (= forces acting on joint in eq. pos.)
No Yes No Yes
5) Completely stiff setting possible (limited
by the force of the spring elongation)
No No Yes No
6) Vary compliant setting possible (concep-
tual, can lead to large designs)
Yes No Yes Yes
7) Infinite bandwidth for shock absorbance
(compliant behavior at high speed)
Yes Yes Yes Yes
8) Infinite bandwidth for chosen compli-
ance (stiffness controllable at high speed)
No Yes Yes Yes
9) Independent control stiffness and
equilibrium position
No No/Yes Yes Yes
10) Possibility to vary linearity of the stiffness
curve
Yes No Yes Yes
Remark on 4: This can be either positive or negative. Preload/pretension is positive to reduce or even avoid play and backlash;
on the other hand, it generate forces on the structure and the bearings, which can lead to a heavier structure or wear.
Remark on 9: Some designs of antagonistic setups allow independent control, however this results in a relatively complex
designs.
Remark on 10: In this way, a progressive, degressive, or linear system behavior can be chosen. In equilibrium-controlled stiffness,
the motor feedback can be used to vary the desired stiffness curve as long as the control commands are within the bandwidth of
the motor. In a Jack Spring actuator, feedback can be used to add or subtract coils for a given deflection allowing the linearity
response to vary.
The variation of the compliance is
based on the variation of the length
of the lever arms and uses only one
passive element, which is
fundamentally different from the
antagonistic setup or structural-
controlled stiffness.
IEEE Robotics & Automation Magazine92 SEPTEMBER 2009
The third concept, structural-controlled stiffness, allowsadaptable compliance. The Jack Spring was presented,which actively tunes the intrinsic stiffness of the spring.The last concept is mechanically controlled stiffness, inwhich the MACCEPA and VS-Joint are novel actuatorswith independently controllable compliance and equilib-rium position.
We believe that adjustable, passive, compliant actuators willrise in importance for two reasons, safe human/machineinteraction, and energy savings. Although different designs ofcompliant actuators are currently under investigation, theultimate design combining a stiffness range from completelystiff to zero stiffness, lightweight and compact, and easy tocontrol has not yet been invented. One can conclude that, inthe field of compliant actuation, much research is still possibleon the actuator itself, applications, and how to control theadjustable compliance. We hope to see more roboticists de-signing the next generation of passive, compliant-actuatorsand their controller architectures.
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Ronald Van Ham received his degree in electromechani-cal engineering at the Vrije Universiteit Brussel in 1999and Ph.D. degree in applied science in 2007. He is cur-rently a postdoctoral researcher on the integration of theseactuators in rehabilitation robots. He performed research onpleated pneumatic muscles and later developed the MAC-CEPA actuator.
Thomas G. Sugar received his B.Sc. and Ph.D. degrees inbusiness and mechanical engineering from the University ofPennsylvania. He worked as a project engineer for W. L.Gore and Associates. He has been a faculty member in theDepartment of Mechanical and Aerospace Engineering andthe Department of Engineering at Arizona State University.His research interests include compliant wearable robotsusing tunable springs.
Bram Vanderborght received his degree in mechanicalengineering at the Vrije Universiteit Brussel in 2003 andPh.D. degree in applied sciences in May 2007. The focus ofhis research was the use of adaptable compliance of pneu-matic artificial muscles in the biped Lucy. From October2007 to September 2008, he worked as postdoctoral re-searcher at the Italian Institute of Technology (IIT). SinceOctober 2008, he works both at the IIT and the VUB. Hisresearch interests include humanoids, bipedal locomotion,compliant actuation, rehabilitation robotics, and safe andcognitive HRI.
Kevin W. Hollander has been involved in a variety of bio-mechanics and clinical-related research projects over the past17 years, including the areas of bone and tissue research andhuman gait. The JackSpring actuator concept and the basicRobotic Tendon design approach were developed as part ofhis Ph.D. thesis.
Dirk Lefeber received his degree in civil engineering andPh.D. degree in applied sciences at the Vrije UniversiteitBrussel in 1979 and 1986, respectively. He is currently a fullprofessor and head of the Mechanical Engineering Depart-ment and the Robotics and Multibody Mechanics ResearchGroup, Vrije Universiteit Brussel. His research interestsinclude new actuators with adaptable compliance, dynami-cally balanced robots, robot assistants, rehabilitation robotics,and multibody dynamics. He is a Member of the IEEE.
Address for Correspondence: Ronald Van Ham, Department ofMechanical Engineering, Vrije Universiteit Brussel, Pleinlaan2, 1050 Brussel, Belgium. E-mail: [email protected].
IEEE Robotics & Automation Magazine94 SEPTEMBER 2009
