Review of Actuators with Passive Adjustable Compliance ...

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High-PressureTubingAngularPositionLimiterTo AirSupplyCompressedAir Bufferthe angle of bending or slope. In this representation of bending,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.Pneumatic muscles are actuators with a high power-toweightratio 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 depressurizingthe 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 introduced.To understand the basic concepts of a SCS actuator,consider the small deflection beam equationM ¼ExhaustFigure 7. Antagonistic setup of two PPAM.Low-PressureTubingEI 3 h, (13)Lwhere M is the bending moment, E the material modulus, Ithe moment of inertia, L the effective beam length, and h is(a) (b) (c)Figure 8. Variation of moment of inertia by rotating the beam.Variation of Moment of Inertia by Axial RotationAn 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 wellknownformula, 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 formulathickness 3 width3I stiff ¼ (14)12width 3 thickness3I compliant ¼ (15)12This 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 InertiaKawamur 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 acton 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 becauseof friction. As a result, the elementstiffens, and larger forces are needed tobend the element. Different methods ofpressing the sheets together such as electrostatic[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. By88 IEEE Robotics & Automation MagazineSEPTEMBER 2009
decreasing the pressure in the chamber, the atmospheric pressuregenerates 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 systemis compliant when the sheets are separated. When thevacuum is applied, the system is stiff.n 3 width 3 thickness3I compliant ¼ (16)12width 3 (n 3 thickness)3I stiff ¼ (17)12Consequently, the stiffness of the element can be increasedby a factor n 2 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. Moreover,the compliance will depend on the deflection when thevolume is in a vacuum applied state.Mechanical Impedance AdjusterAnother 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 situationwhen 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 completelyindependent. This mechanism allows all possibleintermediate 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 ActuatorRecently, a new type of actuator, based on the structure controlledstiffness concept, was presented in [43], named the JackSpring actuator. A helical spring is used as the compliant element.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 mechanismis 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 ¼Gd48 3 D 3 n a, (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, n a , will decrease spring stiffness.Therefore, to create a SCS device, based on the properties of aLeaf SpringMotorWireFeed ScrewTo JointSliderPulleyFigure 10. Conceptual design of mechanical impedanceadjuster.F(a)Figure 9. (a) Laminated structure and (b) deformation.(b)(a)Figure 11. Conceptual design of rotational mechanicalcompliance adjuster.(b)SEPTEMBER 2009 IEEE Robotics & Automation Magazine 89
Page 1 and 2: BY RONALD VAN HAM,THOMAS G. SUGAR,B
Page 3 and 4: frequency of the system can be adju
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Page 7: just a tension mechanism to keep th
Page 11 and 12: When the angle a is zero—this is
Page 13 and 14: The third concept, structural-contr

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