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資源目錄里展示的全都有，所見(jiàn)即所得。下載后全都有,請(qǐng)放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問(wèn)可加】 A New Mechanical Structure forAdjustable Stiffness Devices with Lightweight and Small SizeMitsunori Uemura and Sadao KawamuraDepartment of Robotics, Ritsumeikan UniversityAbstractIn this paper, we propose a new mechanical struc-ture for adjustable stiffness devices with lightweight and smallsize. The proposed structure utilize a ball screw mechanismto adjust a relationship between infinitesimal displacements ofjoint rotation and a linear spring. Then, stiffness around thejoint is adjusted. Unlike many of other adjustable stiffnessstructures, available elastic energy of the elastic element ismaximum when the stiffness of the proposed structure ismaximum. Therefore, the elastic element of this structure canbe smaller and more lightweight than the other structures.Another advantage of the proposed structure is to require fewerand smaller mechanical parts, because the proposed mechanismmostly requires the ball screw mechanism and the linear spring.We developed an actual hardware to test the proposed structure.IndexTermsAdjustableStiffness,NewMechanism,Lightweight, SmallI. INTRODUCTIONA. Stiffness Adjustment in Scientific and Technology FieldHuman beings and animals generate motions dexterously.A lot of factors seem contribute the dexterous motions. Sinceit has been investigated that human beings and animals movewhile adjusting stiffness of their muscles and tendons, oneof the factors may be utilization of the stiffness adjustment.Therefore, to adjust mechanical stiffness is an interestingissue from the scientific viewpoint.In the field of robotics, electric motors with high reductiongears have generated motions of robots traditionally. Re-searchers also have proposed control methods of the robotsactuated by such electric motors. Advancements of the elec-tric motors and the control methods have enhanced abilitiesof the robots. However, capabilities of electric actuators seemto be reaching almost limit, and strong advancements ofactuator capabilities may not be expected in the near future.In addition, since some recent robots perform tasks withhuman, very stiff joints of robots due to the high reductiongears seem not suitable for the recent robots 1. Therefore,researchers are recently trying to investigate alternative waysto generate robot motions. One of the important alternativeways seems to utilize mechanical elastic elements.From a viewpoint of energy efficiency, to utilize elasticelements is also effective, because resonance of mechanicalsystems can save energy while generating periodic motionsof the robots.B. Resonance-based Control MethodWe have proposed resonance-based control methods thatutilize online stiffness adjustment of mechanical elastic el-ements installed in each joint of multi-joint robots 2, 3,4, 5, 6. The proposed controllers can generate periodicmotions of multi-joint robots while minimizing actuatortorque by adjusting the stiffness. We have tried to extend theconcept of resonance to multi-joint robots 2, 3. The pro-posed controllers can guarantee global stability of controlledsystems 2. Not only stiffness adjustment but also motionpattern adjustment reduce actuator torque furthermore 3,4. This kind of controller could reduced more than 90%of actuator torque for walking motions 5. Application ofthe control methods are human walking support systems 6,energy saving industrial manipulators and walking/runningrobots. Now, we are developing a hardware of a legged robotas shown in Fig.1. The robot is aimed at running by usingthe resonance-based control methods. Therefore, the robotshould equip adjustable stiffness devices in every joint ofthe robot.However, if we use some structures of adjustable stiffnessdevices, it may be difficult for the robot to run due to largeweight of the adjustable stiffness devices. Therefore, we needadjustable stiffness devices with lightweight and small sizethat can be installed in joints of multi-joint robots.C. Related Work on Stiffness AdjustmentIn order to develop adjustable stiffness devices, manyresearchers have proposed mechanical structures 7, 8, 9,10, 11, 12, 13, 14.One simple approach for the stiffness adjustment is to varyeffective length of elastic elements. For example, effectivelength of a leaf spring can be adjusted by moving a linearslider 7.Another approach is to utilize two nonlinear elastic el-ements 8, 9. The two nonlinear elastic elements aremounted antagonistically on a joint. Then, by pulling thetwo elastic elements, stiffness around the joint is adjusted.Fig. 1.Developing Legged RobotThe 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems October 18-22, 2010, Taipei, Taiwan978-1-4244-6676-4/10/$25.00 2010 IEEE2364This structure is similar to that of human beings, becausehuman can adjust their joint stiffness by co-contractionof antagonistic muscles. For this structure, how to makethe elastic elements nonlinear becomes a key issue. K.Koganezawa realized the nonlinearity by using rotationalsprings and tapers 8. Rotating the rotational springs makesthe springs twine around the tapers. Then, the stiffness ofthe springs depends on the rotated angle of the spring. H.Noborisaka et al. realized the nonlinearity by using linearsprings and wires 9.In another approach, varying pretension and preload ofelastic elements brings about the stiffness adjustment. Thiskind of structure requires not two elastic elements but onlyone elastic elements for a joint. B. Vanderborght et al.proposed a simple structure called MACCEPA based on thiskind of mechanism 10. S. Wolf et al. also proposed thiskind of structure called VS-joint 11.However, in the case of the above structures, availableelastic energy of the elastic elements is minimum, when thestiffness is maximum. Then, we need larger and heavier elas-tic elements, because storable elastic energy is proportionalto weight and size of the elastic elements, and deformabledisplacement of the elastic elements is proportional to rootsquare of the storable elastic energy. Therefore, if we solvethis problem, we can develop smaller and more lightweightadjustable stiffness devices.Varying relationship between infinitesimal displacementsof joint rotation and elastic elements can be a solution of thisproblem, because available elastic energy of this structurecan be maximum even in the case of maximum stiffness.For example, varying a moment arm length of a spring forcecan adjust the infinitesimal relationship, and stiffness arounda joint. Then, no load acting on the spring is required inthe case of maximum stiffness. N. Takesue proposed anadjustable stiffness structure utilizing this kind of mecha-nism 13. This structure varies a position of one side oflinear springs to adjust the infinitesimal relationship. Then,available elastic energy of the linear spring is maximum evenin the case of maximum stiffness. However, this structureis designed for translational joints. Therefore, we can notdirectly use this structure for rotational joints of our leggedrobot. In addition, to vary the position of one side of thelinear spring seems to require large work space. V. Duindamet al. illustrated an idea of an adjustable stiffness structurethat utilizes the adjustment of the infinitesimal relationship14. This structure is composed of a flexible cam and alinear spring. In this case, the infinitesimal relationship isadjusted by varying the shape of the cam. However, this kindof flexible cam seems to be large and heavy, and requirelarge work space. In addition, this structure was stated asjust a conceptual idea. Therefore, there were no detaileddiscussions or concrete analyses, and actual hardware deviceswere not presented.Hence, if we can make small devices that vary the in-finitesimal relationship, we can develop adjustable stiffnessdevices with lightweight and small size.D. This StudyIn this paper, we proposed a new mechanical structurethat varies a relationship between infinitesimal displacementsof joint rotation and a linear spring by using a ball screwmechanism. Then, available elastic energy of the spring ismaximum, when stiffness around the joint is maximum.Therefore, the elastic element of the proposed structure canbe lightweight and small. Another advantage is that theball screw mechanism does not require a lot of mechanicalparts and large work space. In addition, the stiffness of theproposed structure can be adjusted from 0 to the maximumone theoretically. Therefore, range of the adjustable stiffnesscan be large.This paper analyzes some characteristics of the proposedstructure. We develop an actual hardware utilizing the pro-posed structure, and conducted an experiment to test thedeveloped hardware.II. PROPOSEDSTRUCTUREThis section describes details of the proposed mechanicalstructure.A. StructureThe proposed structure uses a ball screw mechanism and alinear spring as shown in Fig.2. The ball screw mechanism isrigidly attached to the rotating shaft, which is rigidly attachedto the base link at the joint. The one side of the spring isattached to the fore link. The other side of the spring isattached to the nut of the ball screw mechanism. The lengthfrom the joint to the one side of the spring should be longerthan the length from the joint to the nut l r. The positionof the nut can be adjusted by rotating the screw of the ballscrew mechanism. The motor rotates the screw.B. Principle of Stiffness AdjustmentThe principle of the stiffness adjustment is as follows.When we adjust the length from the joint to the nut r bymoving the nut position, relationship between infinitesimaldisplacements of the joint rotation q and the spring lsisvaried. Then, rotational stiffness around the joint is adjusted.Base LinkJointFore LinkNutScrewqrllsSpringMotorFig. 2.Proposed Mechanism2365C. Mathematical AnalysisHere, we analyze the stiffness around the joint of theproposed structure so as to clarify characteristics of thestiffness adjustment quantitatively,At first, we calculate the length of the spring ls(q) asls(q)=ql2sin2q + (lcosq r)2=pl2+ r2 2lrcosq,(1)where l is a length from the joint to the one side of the springattached to the fore link.Elastic energy U of the linear spring is given byU =12kl(ls ls0)2,(2)where klis stiffness of the linear spring, and ls0is naturallength of the spring.Torque from the spring around the joint is given bydifferentiating the elastic energy U with respect to the jointangle q.s=Uq= kllr sinq ls0sinqpl2+ r2 2lrcosq!(3)The stiffness around the joint kqis given by differentiatingthe torque swith respect to the joint angle q.kq=sq=kllr cosq ls0cosqpl2+ r2 2lrcosq+ls0lrsin2qpl2+ r2 2lrcosq3!(4)Threfore, the stiffness kqcan be adjusted by varying thelength r as shown in the equation (4). The stiffness kqis anonlinear function of the length r. However, if the inside of() of the right-hand side of the equation (4) does not changelargely by varying the length r, the stiffness is linearlyadjusted by varying the length r. The stiffness kqis alsoa nonlinear function of the angle q. The nonlinearity of thestiffness kqis shown in the section IV by using a concreteexample.D. Advantage of Proposed StructureThe proposed structure has the following advantages.1) Weight and Size of Linear Spring: The most importantadvantage is that we can use smaller and more lightweightlinear springs in the proposed structure because of the fol-lowing reason. At first, we consider available elastic energyUavaof the linear spring asUava= Umax U,(5)where Umaxis storable elastic energy that the spring canmaximally store without plastic deformation. In the case ofthe linear spring, the maximum length of the linear springlsmaxis determined from the storable elastic energy aslsmax= ls0+q2Umaxkl. As shown in the equation (2), thepotential energy of the spring U increases with deformationof the spring lsls0. If the available elastic energy Uavaissmaller, the spring plastically deforms by smaller additionaldeformation. Therefore, how to ensure large available elasticenergy Uavais important. However, to increase the storableelastic energy Umaxlinearly affects weight and size of thelinear spring. On the other hand, the stiffness of the proposedstructure is maximum when the length r is longest. In thiscase, the spring length lsat the equilibrium angle q = 0 isminimum as shown in the equation (1), and the elastic energyof the spring U is minimum as shown in the equation (2).Then, the available elastic energy Uavaof the proposed struc-ture is maximum when the stiffness is maximum. In many ofother structures, available elastic energy of elastic elementsis minimum when stiffness is maximum. For example, inthe case of the effective length adjustment 7, availableelastic energy decreases with increase of stiffness, becausethe stiffness is increased by shortening effective length ofelastic elements. In some of other structures 8, 9, 10,11, available elastic energy is also minimum when stiffnessis maximum, because the stiffness is increased by increasingloads acting on elastic elements. Therefore, the proposedstructure has the advantage that the linear spring can besmaller and more lightweight due to the above structuraleffect.We do not need to concern about low stiffness cases, be-cause deformation of the linear spring lsby joint rotation qbecomes smaller in the case of the low stiffness. Therefore,even the available elastic energy Uavain the case of lowstiffness is also decreased, we dont need to use large springs.2) Mechanical Simplicity: Another important advantageof the proposed structure is mechanical simplicity. Theproposed structure is composed of almost only the ballscrew mechanism and the linear spring. The ball screwmechanism can be not so large and requires not so manymechanical parts. Therefore, the proposed structure can beeasy to construct, and small.3) Range of Adjustable Stiffness: As shown in the equa-tion (4), the stiffness of the proposed structure can beadjusted from 0 to the maximum by varying the length rfrom 0 to the maximum. Therefore, range of the adjustablestiffness of the proposed structure can be large.If we vary the length r from negative one, we can realizeeven negative stiffness. This characteristic may be favorablefor some applications.4) Low Backdrivability: Low backdrivability of the ballscrew mechanism is favorable in some cases, because to keepconstant stiffness consume only small energy of actuators ofthe stiffness adjustment devices. It is known that ball screwmechanisms can have low backdrivability.5) Low Friction: When we keep a constant stiffness, theproposed structure has almost no slide portions. Therefore,low friction is also an advantage of the proposed structure.6) Work Space: The proposed structure requires not solarge work space, because the ball screw mechanism and thespring moves in not so large space. This may be an advantageof the proposed structure.2366Fig. 3.Developed HardwareIII. DEVELOPEDHARDWAREWe developed a hardware as shown in Fig.3 to verify theeffectiveness of the proposed structure.A. Mechanical PartThe mechanical parts of the developed hardware are shownin Fig.4. We adopted aerial aluminum frames as the base linkand the fore link. We used a NC machine tool to cut outthe base part and nut of the ball screw mechanism, and thebearing holder and shaft holder of the joint from aluminumblocks. The rotating shaft, linear spring, screws, bearings,wire and spring post were commercialized products. The ballscrew mechanism was attached to the rotating shaft rigidly.The rotating shaft was attached to the base link rigidly.B. Size and WeightThe sizes of the mechanical parts were as follows. Heightand width of the aluminum frames were 2cm respectively,length of the base link was 15cm, and length of the forelink was 18cm. Diameter of the wire of the spring was2.5mm, the total number of the coils of the spring was23, average diameter of the coils was 16mm, and lengthof the spring including the hooks was 9cm. Height, widthand length of the base part of the ball screw mechanism is14mm, 15mm, and 51mm.Weights of the mechanical parts were as follows. Weightof the links with the joint was 223g. Weight of the springwas 51g. Weight of the ball screw mechanism including thenut and the screw was 37g. Total weight of the all partswas 311g.The developed adjustable stiffness device was smaller andmore lightweight than the links with the joint. Therefore, thedeveloped device can be mounted on each joint of multi-jointrobots or walking robots like Fig.1.C. Specification of SpringThe spring can be extended by 52mm without plasticdeformations. Therefore, we can rotate the joint by morethan rad in the case of maximum stiffness. In the casesof lower stiffness, we can also rotate the joint by more thanrad. The length from the joint to the one side of the springl was 19.0cm. The stiffness of the linear spring klwas4.570N/mm. The natural length of the spring ls0was 9cm.Fig. 4.Mechanical PartsThe spring can passively exert more than 7Nm of torqueon the joint.D. Ball Screw MechanismThe ball screw mechanism can adjust the position of thenut by rotating the screw. Then, the length r can be adjustedfrom 34mm to 0.0mm.We can calculate necessary torque r, which is requiredto rotate the screw, by using the principle of virtual work.rqr= klls(6)where qr is a rotated angle of the screw. The nutmoves 0.8mm by rotating the screw 2rad. Then lsand qrsatisfieslsqr=0.00082. The spring maximally exertsof 234N force to the nut. Therefore, to rotate the screwmaximally requires 0.030Nm of torque theoretically.E. DC motor for Stiffness AdjustmentWe assume that the following DC motor with the gearboxrotates the screw of the ball screw mechanism. The productname of the DC motor is ”RE16” developed by MaxonCorporation. Specifications of the DC motor are as follows.Rated power is 4.5W, rated angular velocity is 1466 rad/s,rated torque is 0.00442 Nm, and maximum torque is0.035Nm. The product name of the gearbox is ”GP 16A”. Reduction ratio of the gearbox is 29:1.Then, we can exert 0.13Nm of rated torque and 1.0Nmof maximum torque to the screw by the DC motor with theFig. 5.Ball Screw Mechanism with DC Motor2367gearbox. Therefore, the motor with the gearbox can rotatethe screw enough.In the case of the rated angular velocity of the DC motor,the angular velocity of the screw becomes 8 revolutions/s.Then, the nut moves with 6.4mm/s of velocity. Therefore,to adjust stiffness from the minimum to the maximumrequires about 5s in the case of the rated angular velocity.The motor is assumed to have an optical encoder as anangle sensor. Radius of the motor with the gearbox and theencoder is 16mm, total length of them is 68mm, andweight of them is 80g. Therefore, we can attach the motorwith the gearbox to the ball screw mechanism like Fig.5.The total weihgt of the adjustable stiffness device includingthe motor is still 168g. This weight seems not unreasonablefor the kind of walking/running robots like Fig.1.F. Adjustment of Equilibrium AngleDepending on applications, we need to adjust equilibriumangle of the joint. In such cases, we can adjust the equi-librium angle by rotating the ball screw mechanism aroundthe joint. Then, the equilibrium angle is linearly adjusted bythe rotated angle of the ball screw mechanism. However, torotate the ball screw mechanism requires one more actuator.IV. EXPERIMENTWe conducted an experiment to test the developed hard-ware.A. ConditionWe measured torque from the developed adjustable stiff-ness device. Since the proposed structure is symmetric, thetorque of one side rotation of the joint is the same as theother side of rotation. Therefore, we measured the torque ofonly one side of rotation (q 0). The length from the jointto the nut r is adjusted as r = 34,23,17,11,8,4,0mm. Wemeasured the torque at the angles q from 0rad to2rad atFig. 6.Experimental Resultsthe18rad intervals. To compare the measured torque andthe theoretical one, we calculated the equation (4).We also measured torque, which is maximally required torotate the screw of the ball s