The variation <strong>of</strong> the compliance isbased on the variation <strong>of</strong> the length<strong>of</strong> the lever arms and uses only onepassive element, which isfundamentally different from theantagonistic setup or structuralcontrolledstiffness.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 tension.Both designs use the pretension or preload <strong>of</strong> 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 <strong>of</strong> some <strong>of</strong> the properties for the differentgroups <strong>of</strong> controllable stiffness actuators.These properties <strong>of</strong> 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 <strong>of</strong>the design, cost, speed <strong>of</strong> the stiffness variation, maximumtorque, and size <strong>of</strong> the complete system. In addition, therequired power source, e.g., in case <strong>of</strong> pneumatic muscles, canalso be a criterion.ConclusionsFour concepts to create adaptable, passive-compliant actuators,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 <strong>of</strong> springs. This conceptis simple to control but constantly requires energy to regulateits actuator position. The second concept, antagonistic-controlledstiffness, covers the compliant actuatorsbased on the antagonistic setup <strong>of</strong> 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 <strong>of</strong> some <strong>of</strong> the properties for the different groups<strong>of</strong> controllable stiffness actuators.1) Minimum number <strong>of</strong> springs required(can be more to obtain symmetry)2) Can linear springs be used (related toavailability, linear spring are standard)3) Always using the full length <strong>of</strong> the springelement4) Preload/Pretension in equilibrium position(= forces acting on joint in eq. pos.)5) Completely stiff setting possible (limitedby the force <strong>of</strong> the spring elongation)6) Vary compliant setting possible (conceptual,can lead to large designs)7) Infinite bandwidth for shock absorbance(compliant behavior at high speed)8) Infinite bandwidth for chosen compliance(stiffness controllable at high speed)9) Independent control stiffness andequilibrium position10) Possibility to vary linearity <strong>of</strong> the stiffnesscurveEquilibrium-ControlledStiffnessAntagonistic-ControlledStiffnessStructure-ControlledStiffnessMechanicallyControlledStiffness1 2 1 1Yes No Yes YesYes Yes No YesNo Yes No YesNo No Yes NoYes No Yes YesYes Yes Yes YesNo Yes Yes YesNo No/Yes Yes YesYes No Yes YesRemark 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 <strong>of</strong> antagonistic setups allow independent control, however this results in a relatively complexdesigns.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 <strong>with</strong>in the bandwidth <strong>of</strong>the motor. In a Jack Spring actuator, feedback can be used to add or subtract coils for a given deflection allowing the linearityresponse to vary.92 IEEE Robotics & Automation MagazineSEPTEMBER 2009
The third concept, structural-controlled stiffness, allowsadaptable compliance. The Jack Spring was presented,which actively tunes the intrinsic stiffness <strong>of</strong> the spring.The last concept is mechanically controlled stiffness, inwhich the MACCEPA and VS-Joint are novel actuators<strong>with</strong> independently controllable compliance and equilibriumposition.We believe that adjustable, passive, compliant actuators willrise in importance for two reasons, safe human/machineinteraction, and energy savings. Although different designs <strong>of</strong>compliant 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 <strong>of</strong> compliant actuation, much research is still possibleon the actuator itself, applications, and how to control theadjustable compliance. 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