The DLR FSJ: Energy based design of a variable stiffness joint
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1 211 IEEE International Conference on Robotics and Automation Shanghai International Conference Center May 9-13, 211, Shanghai, China The DLR FSJ: Energy based design of a variable stiffness joint Sebastian Wolf, Oliver Eiberger and Gerd Hirzinger DLR - German Aerospace Center Institute of Robotics and Mechatronics D Wessling, Germany sebastian.wolf@dlr.de Abstract Bringing mechanically compliant joints to robots is in the focus of interest world wide, especially in the humanoid robotics community. Variable Stiffness Joints (VSJ) promise to gain a high performing and robust robotic system. The presented DLR Floating Spring Joint (FSJ) is a VSJ module designed for the first 4 axes of the anthropomorphic DLR Hand Arm System. The DLR Hand Arm System aims to match the skills of its natural archetype. For this purpose, the joints have to be extremely compact to fit into the arm. At the same time they require a high power density in order to approximate the human arm skills. The new DLR FSJ is designed completely from an energy based point of view. This addresses not only energy efficient components and low friction design, but also that the potential energy of the spring is used as good as possible. A demonstration of robustness is given by the investigation of a blunt impact to the tip of the arm. I. INTRODUCTION Mechanically compliant joints appear to be the key feature to build lean and lightweight robots which are robust and gentle to their environment. Furthermore, the possibility to store potential energy in the short term facilitates to extend the performance of the robot e.g. regarding maximum peak velocity [1], [2]. The mechanical compliance with its high bandwidth of reaction to external forces reduces the requirements to the bandwidth of control, because external forces due to contacts with the environment increase slower. Also, for the higher level control soft robot joints have advantages. They decrease the need for precise trajectory planning to avoid overload at rigid contacts, damage objects, or loose deliberate contacts. Humanoid robots with mechanical springs have been developed for almost two decades with increasing dexterity and performance. They can be divided into two types: robots with serial elastic joints (SEA) with a invariant spring characteristic like DOMO [3], the Twendyone the NASA Robonaut R2 or the upcoming generation of icup and those with variable stiffness joints (VSJ) like the Waseda robot Wendy [4]. SEA joints have only one actuator in every joint which results in less complex and most likely lighter and This work has been partially funded by the European Commission s Sixth and Seventh Framework Programmes as part of the projects SMERobot TM under grant no , PHRIENDS under grant no , and VIAC- TORS under grant no Fig. 1. DLR s new integrated Hand Arm System. smaller joints, but have the drawback that the joint s stiffness and thus its eigenfrequency are not adaptable to different tasks. The newly developed VSJ prototype is intended to operate in DLR s integrated Hand Arm System [5] [7] (see Fig. 1). The DLR Hand Arm System is aimed to come as close as possible to the dexterity and the capabilities of the average human arm. The proposed joint prototype is designed to serve as a modular basis for the arm. The nonlinear variable spring mechanism of the joint prototype is employed in axis 1 to 4. II. DESIGN GOALS The application of the Floating Spring Joint in the fist four joints (shoulder-elbow) of the Hand Arm System yields a number of requirements for the FSJ: To be extremely compact to fit into the arm. To be highly integrated to form a joint module including the joint motors, sensors, mechanics, and also the joint bearing itself. In Particular the weight of an human arm appears to be a tough goal to reach [8]. Thus the joint module has to be as light as possible. To compete with the performance of an human arm [9] the active equilibrium velocity of the joint should be above 5 /s whilst not to sacrifice maximum torque to reach that goal. Reasonable maximum torques appear /11/$ IEEE 582
2 to be about 6 Nm [1], [11]. Maximum human arm stiffness on joint level is still under investigation and a topic controversially discussed. Some indications lead to a value of about 35 Nm/rad on joint level in the elbow [12]. In order to achieve accurate positioning as well as robust and predictable dynamics the robot arm should have a stiff structure and high resolution position sensors. An important goal during the design process was to keep friction as low as possible. Application of absolute position sensors, in order to measure the complete joint state. III. ENERGY BASED DESIGN The layout of the DLR FSJ is derived from the energy point of view. In elastic joints the kinetic energy is stored in the connected links and the joint motor. Potential energy is stored in the elastic element and in the links due to gravitation. Energy is transformed between kinetic and potential energy repeatedly during arm movement. Therefore it is essential that the energy can be transformed efficiently. It is important that the amount of potential energy is well balanced with the intended tasks and the resulting dynamics. That implies at first that we keep the friction in general as low as possible so that we do not loose the energy unintentionally during operation. So we have to avoid friction bearings, and reduce the overall number of bearings. Secondly we require highly efficient motors and gears that also feature high peak energy throughput. Therefore we use Robodrive motors and Harmonic Drive gears. Finally the VSJ performance is mostly determined by the design of the spring mechanism. The proposed mechanism is designed to use the spring energy of a single mechanical spring efficiently to to generate the desired torque and to reduce losses due to pretension in order to alter the joint stiffness. A. Joint Mechanics The DLR FSJ (see Fig. 2 and 3) is designed as a variable stiffness joint device with two electromechanical actuators of significantly different size. The big Robodrive ILM 5x14 SP motor is dedicated to move the joint by setting the equilibrium point of the joint. The purpose of the smaller Robodrive ILM 25x8 SP motor (equipped with a n adj = 1 : 1 gear box) is to change the stiffness preset of the joint. However there is some coupling in between them (see section III-C) - not only with external load applied like other VSJ but also at zero external load. The variable stiffness mechanism is attached to the Harmonic Drive gear CSD-25 (ratio n main = 8 : 1) of the main motor in a series setup at its output shaft (see Fig. 4). The serial setup was chosen, because the presented joint mechanism could be kept more compact in that way. The serial setup is less advantageous compared to the differential setup of previous joint prototypes the VS-Joint and the QA-Joint regarding the link side inertia. So the full joint mechanism has to be accelerated by the main motor. Nevertheless the highly integrated design results in a link side inertia (see Table I) which is still an order of magnitude smaller than the whole connected individual links of the arm. Roller Base Joint Motor Harmonic Drive Gear Fig. 2. The DLR Floating Spring Joint (FSJ). Fig. 3. Harmonic Drive Gear Joint Motor Cross section of the FSJ. Stiffness Motor Rotational Supported Cam Disk Guide Hypoid Gear Cam Disks Cam Rollers Stiffness Adjusting Motor Variable Stiffness Mechanism Link Fig. 4. The spring mechanism of the FSJ is located in series between the harmonic drive gear box of the main actuator and the link. The core of the joint is the spring together with its surrounding nonlinear and adjustable transmission mechanics as depicted in Fig. 5. The spring pulls the two cam disks together with respect to each other. The spring is not attached to any part of the housing. In between the cam disks rotate the cam rollers, which are mounted to the roller base and with it to the gear output of the harmonic drive gear. The cam disks are guided by linear bearings in the axial direction. One cam disk is rotationally supported by the link output, the other by the stiffness adjusting motor. The stiffness adjusting motor rotates the cam disks with respect to each other to gain a stiffer joint setup. A passive joint deflection as well as an increase of the stiffness setup is pushing the cam disks apart. The joint is equipped with 5 position sensors, of which 2 pairs are redundant. The following positions are measured in 583
3 Max. Torque Max. Stiffness Max. Deflection Max. storable Energy Nominal Input Power Max. Velocity TABLE I JOINT PROPERTIES Min. Stiffness Adjusting Time Diameter ±67 Nm 826 Nm/rad ± J = 614 W 8.5 rad/s.33 s 92 mm Length 119 mm Weight (incl. motors) 1.41 kg Link Side Inertia kg m 2 Axis of Rotation Floating Spring Roller Base (connected to Gear Output Shaft) Linear Guides Cam Disks Cam Rollers Fig. 5. The FSJ mechanism. A passive joint deflection results in a rotational movement of the two cam disks relative to the cam rollers along the axis of rotation. The cam rollers are embraced by the two cam disks. The cam disks are axially pulled together by the spring and are rotationally supported by linear bearings (not shown). The cam disks are able to move in the axial direction guided by the linear bearings. the joint (see Fig. 4 for an overview of the joint setup): The joint motor axis q M1 The stiffness adjusting motor axis q M2 Link position vs. joint base q (absolute) Adjustable cam disk position vs. link side q adj (absolute) Cam rollers vs. link side q flex (absolute) The three absolute positions allow a full identification of the joint state directly at the startup of the system. It is important to mention that in contrast to previous robots developed at DLR, no torque sensors are included in the DLR Hand Arm System. The FSJ joint torque is calculated from the position sensor signals based on the joint model. This method was confirmed to have good performance with the VS-Joint [1], [6] and is assumed to have similar operational behavior due to the closely related construction of the mechanics. Additional details of the FSJ are published in the VIAC- TORS Variable Stiffness Joint Datasheet of the FSJ, which is published at the VIACTORS homepage [13]. The fist page of the FSJ datasheet is given in the Appendix. B. The floating spring The mechanical principle of the DLR FSJ (see Fig. 6) is a derivation of the two previous joint prototypes developed at DLR the VS-Joint [1] and the QA-Joint [2]. Like in the VS-Joint the torque is generated by a rotational cam disk and roller system which transmits the rotational joint deflection to an axial compression of a linear spring. The shape of the cam disks can be chosen according to the desired torque vs. displacement behavior. In contrast to the mechanics of the VS-Joint the new mechanics of the FSJ is not equipped with a single cam system but with two opposing cam profiles. This originates from the QA-Joint where two cam systems generate the torque of the output shaft by superposition of the two individual torques. In classical antagonistic systems [14] [18] as well as the in the QA-Joint two spring elements are used to generate the two torques, which sum up for the output torque. Variable Stiffness Joints which alter the stiffness by giving a preload to the spring element [19], [2] usually have only one. However VSJ with two opposing spring mechanics have some advantages in the range of stiffness (see section III-C to E). For a good joint performance (high torques, big stiffness range, high energy capacity) the spring has to be able to store as much energy as possible. Spring elements with high energy capacity tend to be bulky and mostly heavy. As a result the spring elements of most existing VSJ are a dominating factor in the mechanics regarding size and weight, especially if you count in the suspension and the structure to embed the spring elements. This is in contradiction to the design goals of compactness, lightweight, and low friction. To benefit from two opposing spring mechanisms, but keep a compact design, we designed a mechanism which acts like two opposing spring generating mechanisms, but employs only one spring. The two cam disks of the FSJ are coupled with each other by a single floating spring, which means that the spring has no connection to the joint base or output shaft. The spring forms a direct connection between the two cam disks and pulls them axially together. In between the cam disks is a pair of cam rollers directly attached to the gear output shaft of the harmonic drive gear which is axially and radially guided by a bearing. So the spring is only displaced by an axial movement of the cam disks relatively to each other and not with respect to the housing. The force generated by the spring is applied to both cam disks with different sign and thus is generating the two opposing torques at the same time. The floating spring mechanism facilitates us to use a high energy spring in an extremely compact package. C. Joint Model As mentioned before the spring mechanism of the FSJ is located in series with the main actuator. With q M1 being the rotor position of the main motor, the gear output position is θ 1 = n main q M1 = 1 8 q M1. (1) The gear output position of the stiffness adjusting motor, which is redundantly measured by q adj, is θ 2 = q adj = n adj q M2 = 1 1 q M2 (2) and sets the relative position difference between the two cam disks. The state of stiffness setup σ is given as: σ = 1 2 θ 2 (3) 584
4 Rest Position Passive Deflection Stiff Setup Cam Rollers Equilibrium Position φ 2 σ Cam Moved by Stiffness Actuator Deflection in Stiff Setup 2 σ φ x x F ext x x F ext Linear Cam Fixed to Link a) Cam Disks Bearings b) c) Fig. 6. The FSJ mechanism principle in a flattened view. The cam rollers are connected to the gear output shaft of the main actuator gear box (Harmonic Drive). One cam disk is fixed to the link side and the second to the stiffness actuator. In a) the mechanics is depicted in the rest position with the spring length x. In b) an external torque is applied to the joint and results in a passive deflection ϕ, and c) is the equilibrium position in a stiff joint preset where the upper cam disk is rotated with respect to the lower by the stiffness adjuster to the angle 2σ. Subfigure d) depicts the system in stiff preset with external load applied. d) The equilibrium position of the joint ε, i.e. the joint position with no external load applied, depends on both motor positions as given in: The passive joint deflection ϕ is D. The principle to gain stiffness ε = θ 1 σ = θ θ 2 (4) ϕ = q flex (ε θ 1 ). (5) The progressive output torque of the mechanism originates in the progressive cam shape. When the roller carrying base is deflected in a rotary direction, the (momentary) agonist cam disk is deflected axially (see Fig. 6 b) lower cam), thus increasing the deflection on one side of the floating spring. At the same time, the antagonist cam disk (see Fig. 6 b) upper cam) is releasing deflection on the other side of the spring. The shape of the cam disks ensures, that the derivation of the deflection/compression characteristics is progressive, thus the derivation in the contact point of the momentary agonist is always higher than the one of the antagonist. Since both cam disks apply the same axial force on the rollers, the difference in this derivation, multiplied with the momentary spring force, determines the output torque. Stiffness variation in this mechanism is accomplished by rotary pretension (see Fig. 6 c)), applied to one of the cam disks. This results in higher spring pretension in the equilibrium position. Moreover the progressive derivation of the deflection/compression characteristics is also resulting in faster growth of the output torque with rotary deflection. Since the drive, which operates stiffness adjustment, has to maintain the pretension or even sustain the external load, it has to be small, but powerful, and it should be placed in the less charged direction of the joint (i.e. due to gravity). E. Derivation of the cam disk profile The QA Design used two separate springs, resulting in two independent progressive torque deflection characteristics, which were opposing each other in adjustable distance, to deliver the desired output. The output torque was simply calculated as the addition of both (positive to negative) torques at a certain deflection and offset. The FSJ uses a single spring, which is compressed form one side and released from the other side at the same moment. If the stiffness is changed, both ends of the spring are compressed or released. As a result, the relation between spring preload, cam gradient and displacement of the mechanism are altered simultaneously, influencing not only the stiffness, but also the shape of the torque vs. deflection characteristics. To maintain the original characteristics as good as possible, the cam shape was calculated for a layout setpoint about the mid of the stiffness setup range (σ lay = 5 ) 1. As a next step the desired output torque and desired torque vs. deflection characteristics, which determine the amount of energy to be stored, were optimized to match available springs. The calculation of the mechanism starts from a desired torque characteristicsτ cam (ϕ) with 67.5 Nm as maximum output torque τ max of one cam disk. With the characteristics variable τ char = 12 and the maximum passive deflection ϕ max = 15 the torque characteristics of one cam disk is given as τ cam (ϕ) = τ max e τ char (ϕ (ϕ max σ lay )) (6) τ cam (ϕ) = 67.5 Nm e 12(ϕ π/18). (7) The sum of both opposing cam torques lead to ( τ ext (ϕ) = τ max e τ char (ϕ (ϕ max σ lay )) e τ char ( ϕ (ϕ max σ lay )) ) (8) ( τ ext (ϕ) = 67.5 Nm e 12(ϕ π/18) e 12( ϕ π/18)). (9) To generate a cam shape from a desired stiffness characteristics τ ext (ϕ), it is necessary to solve a differential equation, which incorporates the initial spring state and derivation of the cam faces, as well as deflection through both cam faces: ( ) x x τ ext (ϕ) = F spring (ϕ,x ) (ϕ) ϕ ϕ ( ϕ) (1) with F spring being the spring force. The solution for this equation originates in the energy balance inside the spring. 1 Note that for a more intuitive presentation, all angular data in the text and figures is presented in degrees, whereas all equations are in SI units, e.g. radians. 585
5 The applied torques alter the potential energy in the spring, as work has to be applied to deflect the joint mechanism. The stored energy is E store (ϕ) = ϕ ϕ abs(τ cam (ϕ) τ cam ( ϕ)) ϕ = J ( e 12(ϕ π/18) 2 e 12( π/18) +e 12( ϕ π/18)). (11) With this energy balance and the spring energy E store (ϕ) = 1 2 R ( x 2 x 2 ) (12) (with spring constant R, spring deflection x and pretension x ), the spring force results in F spring (ϕ) = 2 R(E store +E(x )). (13) With the derivative of the cam disk in dependency of ϕ x ϕ = τ cam(ϕ) F spring (ϕ), (14) finally, the differential equation can be numerically integrated along ϕ to derive the cam profile. Due to the simultaneous presence of root terms of the spring energy and exponential terms of the work energy, an analytic solution could not be found. The result was validated with the calculated spring length to match the cam profile for agonist and antagonist actuator face. External torque τ (Nm) Deflection φ (deg) σ = σ = 2.5 σ = 5 σ = 7.5 σ = 1.2 Fig. 7. Calculated torque vs. passive joint deflection ϕ. The maximum possible joint deflection is decreasing with higher stiffness preset σ. The layout torque curve with exponential characteristics is indicated in thick green. With the resulting cam shape, the output torques for different stiffness presets can be calculated (see Fig. 7, Fig. 8). The maximum passive deflection of the mechanism is decreasing with increasing stiffness. This is due to saturation effects of the spring combined with the potential energy stored in the spring through the stiffness preset. In the layout process the pretension of the spring, as well as the choice of the stiffness characteristics and stiffness setpoint for the cam layout, greatly influence the resulting stiffness characteristics curves. Even intersections of the stiffness curves are possible, which creates load states, where Stiffness K (Nm/rad) External torque τ (Nm) σ = σ = 2.5 σ = 5 σ = 7.5 σ = 1.2 Fig. 8. Calculated stiffness vs. external torque. At a given external torque the stiffness is always increasing with higher stiffness preset σ. stiffness is reduced when trying to stiffen up. This problem is due to the combination of linear increasing spring force and progressive deflection, and can be avoided by evaluation of several combinations of setpoint and pretension to find the best matching characteristics set. Compared to the resulting stiffness curves obtained with the QA-Joint, the stiffness variation is about 3% lower, and the motion range and maximum torque decrease faster with higher stiffness setpoint. This is counterbalanced by the more compact package, and the advantage of a single spring. A. System Identification IV. TESTS & APPLICATION In order to find out if the system performs well and to generate a joint model the real torque curve has to be experimentally evaluated. For this purpose a torque sensor and a lever arm were mounted to the link side of the joint. At the tip of the lever arm a force was applied in both directions until the passive deflection limits of the joins are approached. The torque was recorded with 5 different stiffness setups of σ = [,2.5,5.1,7.7,9.9]. The results are plotted together with the calculated torque τ calculated (ϕ,σ) in Fig. 9 and show a well predictable friction characteristic. Clearly visible is some kind of ripple in the torque curves. This ripple originates from manufacturing problems of the cam disks which resulted in a bumpy cam disk surface. This will be fixed in the next evolution step of the cam disks. The fast increase of torque when the passive deflection limits of the joint are exceeded are a result of the stiff mechanical end stops. The asymmetric joint design with the stiffness adjusting motor being much smaller than the main driving motor demands a closer look at the performance of the smaller motor. A step response of σ from minimum to maximum was recorded, where the spring has to be compressed during the movement (see Fig. 1). The step response is dominated by the maximum output velocity which is limited by control to the velocity limits of the harmonic drive gear. The whole trajectory is accomplished after.33 s. 586
6 Torque Msr. (Nm) τ calculated (ϕ, σ) σ = σ = 2.5 σ = 5.1 σ = 7.7 σ = Passive Joint Deflection ϕ (deg) Fig. 9. Measured Torque with respect to joint deflection ϕ. Five test rows with different stiffness setups σ form min to max. Stiffness Preset σ (deg) σ desired σ measured Fig. 1. Step response of the stiffness actuator from minimum to maximum with no external load applied. B. System performance Besides maximum joint velocity, which was addressed before e.g. with the VS-Joint in [1], the second main goal of system performance of the developed joint is robustness. Robustness especially in the sense of withstanding external impacts and fast collisions of the robot arm with rigid obstacles. Robustness of single DoF joint prototypes to impacts have been shown previously in [2], [21]. A short demonstration of robustness of a robot arm equipped with FSJ in the first 4 axes to impacts with a rigid object is given in the following (see also video attachment). For this demonstration the forearm and hand of the Hand Arm System have been replaced by a dummy lever with approximately the same mass and inertia of the forearm, see Fig. 11. This was necessary, because the current housing of the forearm is not able to resist the local force at the impact area. The dummy lever is padded with a 3 mm sheet of silicone rubber to distribute the contact force and avoid plastic deformation of the aluminum lever and the wooden impact object. Furthermore the padding spreads the impact in time and thus facilitates a more precise calculation of the impact Fig. 11. Setup of the demonstration to robustness. The dummy forearm is hit approximately at the position where the wrist of the real forearm is located. energy. The impact object is a3 baseball bat weighing768g and is equipped with a 1 khz acceleration sensor weighing 4 g. The joints in the arm are set to the softest stiffness preset σ =. The steady state joint torques are a result of gravity. At the instant of impact the arm is not moving and the joint motors are held in position by a PD controller. The acceleration of the bat during the impact is given in Fig. 12. The transferred energy during the impact is calculated by integration of the acceleration over the impact time and was identified to be 22 J. This impact can be considered as relatively hard and is most likely not outmatched during normal operation. The response of the arm in passive joint deflection and resulting joint torques are plotted in Fig. 12. The results show that the joint limits of ±15 and 67 Nm are not exceeded during the impact. Differences of position and calculated torque before and after the impact are caused by friction effects. V. CONCLUSION & FUTURE WORKS The design of the new FSJ from the energy point of view is presented. The new mechanism design with one floating spring and two superimposed cam mechanisms results in superior joint properties compared to the foregoing joint prototypes, the VS-Joint and the QA-Joint. As a result a compact and light weight, but still fast and strong joint was developed. The joint is fully integrated with the joint bearing, the two motors and position sensors and thus serves as a module to easily build up robotic arms with a serial kinematic and variable stiffness joints. The robustness of a robot arm equipped with FSJ is shown in a short demonstration of a blunt impact of a rigid object to the tip of the robot. Future works will focus on experimental evaluation of the presented mechanics in the Hand Arm System. Out of future applications and resulting trajectories typical requirements on joint level are to be investigated. New cam profiles adapted to those requirements will be developed. VI. ACKNOWLEDGEMENTS The authors gratefully acknowledge the fruitful discussions with Markus Grebenstein and Werner Friedl, and Ulrich Hagn. 587
7 Deflection ϕ (deg) shoulder 1 shoulder 2 Deflection ϕ (deg) upper arm elbow Acceleration (m/s 2 ) 1 5 Acc X Acc Y Acc Z Acc Sum x 1 3 Torque τ Ext (Nm) shoulder 1 shoulder 2 Torque τ Ext (Nm) upper arm elbow Speed (m/s) / Energy (J) Speed of bat Transmit energy Fig x 1 4 Passive joint deflection and resulting joint torques resulting from an impact with a baseball bat. REFERENCES [1] S. Wolf and G. Hirzinger, A new variable stiffness design: Matching requirements of the next robot generation, in Proc. of the IEEE International Conference on Robotics and Automation. Pasadena, CA, USA: IEEE, May 28, pp [Online]. Available: 1.119/ROBOT [2] O. Eiberger, S. Haddadin, M. Weis, A. Albu-Schäffer, and G. Hirzinger, On joint design with intrinsic variable compliance: Derivation of the dlr qa-joint, in Proc. of the IEEE International Conference on Robotics and Automation. Anchorage, Alaska, USA: IEEE, May 21, pp [3] A. L. 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Petit, B. Pleintinger, J. Reil, N. Seitz, T. Wimböck, S. Wolf, T. Wüsthoff, and G. Hirzinger, The dlr hand arm system, in Proc. of the IEEE International Conference on Robotics and Automation, 211. [8] R. Chandler, C. Clauser, J. McConville, H. Reynolds, and J. Young, Investigation of inertial properties of the human body, Aerospace Medical Research Laboratory, Tech. Rep. DOT HS-81 43, March [9] I. Herman, Physics of the Human Body. Springer Verlag, 27. [1] H. Bubb, F. Engstler, F. Fritzsche, C. Mergl, O. Sabbah, P. Schaefer, and I. Zacher, The development of ramsis in past and future as an example for the cooperation between industry and university, International Journal of Human Factors Modelling and Simulation, vol. 1, no. 1, pp , 26. [11] H. Panzer, O. Eiberger, S. Wolf, M. Grebenstein, P. Schaefer, and P. van der Smagt, Human motion range data optimizes anthropomorphic robotic hand-arm system design, in Proc. of the International Conference on Motion and Vibration Control (MOVIC), March 28. [Online]. Available: [12] K. P. Tee, E. Burdet, C. M. Chew, and T. E. Milner, A model of force and impedance in human arm movements, Biological Cybernetics, vol. 5, no. 5, pp , May 24. [Online]. Available: [13] VIACTORS. Viactors homepage. [Online]. Available: [14] K. Koganezawa and S. Ban, Stiffness control of antagonistically driven redundant d.o.f. manipulator, in Proc. of the IEEE/RSJ Intl. Conference on Intelligent Robots and Systems. Dep. ofmechanical Engineering TOKAIUniversityDep. of Mechanical Engineering TOKAI University 1117 Kitakaname, Hiratsuka,Kanagawa JAPAN: IEEE/RSJ, September 22, pp [15] J. W. Hurst, J. E. Chestnutt, and A. A. Rizzi, An actuator with physically variable stiffness for highly dynamic legged locomotion, in Proc. of IEEE International Conference on Robotics and Automation. New Orleans, LA, USA: IEEE, April 24, pp [16] S. A. Migliore, E. A. Brown, and S. P. DeWeerth, Biologically inspired joint stiffness control, in Proc. of the IEEE International Conference on Robotics and Automation. Laboratory for Neuroengineering, Georgia Institute of Technology, Atlanta, Georgia 3332: IEEE, April 25, pp [17] R. Schiavi, G. Grioli, S. Sen, and A. Bicchi, Vsa-ii: a novel prototype of variable stiffness actuator for safe and performing robots interacting with humans, in Proc. of the IEEE International Conference on Robotics and Automation. Pasadena, CA, USA: IEEE, May 28, pp , 61. [18] B.-S. Kim and J.-B. Song, Hybrid dual actuator unit: A design of a variable stiffness actuator based on an adjustable moment arm mechanism, in Proc. of the IEEE International Conference on Robotics and Automation. 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8 Rz 6 APPENDIX DLR Floating Spring Joint (FSJ) Adjustable Stiffness Joint Operating Data # (quantity) (unit) (value) Mechanical 1 Continuous Output Power [W] Nominal Torque [Nm] Nominal Speed [rad/s] Nominal Stiffness with no load [s].33 5 Variation Time with nominal torque [s].33 6 Peak (Maximum) Torque [Nm] 67 7 Maximum Speed [rad/s] Maximum Stiffness [Nm/rad] Minimum Stiffness [Nm/rad] Maximum Elastic Energy [J] Maximum Torque Hysteresis [%] 2 12 with max. stiffness [ ] 3 Maximum deflection 13 with min. stiffness [ ] Active Rotation Angle [ ] Angular Resolution [ ] Weight [Kg] 1,41 Electrical 17 Nominal Voltage [V] 48; Nominal Current [A] 1; 3 19 Maximum Current [A] 24; 9 Control 2 Voltage Supply [V] Nominal Current [A] 1 22 I/O protocol [] spacewire 48V 24V 12V Ground Spacewire φ Stiffness K (Nm/rad) Speed (rad/s) Deflection (deg) External torque τ (Nm) External torque (Nm) External torque τ (Nm) σ = σ = 2.5 σ = 5 σ = 7.5 σ = 1.2 σ = σ = 2.5 σ = 5 σ = 7.5 σ = 1.2 Fig. 13. First page of FSJ Datasheet. The VIACTORS Variable Stiffness Joint Datasheet was developed within the VIACTORS project, which is part of the EU 7th Framework Programme. It is intended to form a basis for the exchange of information of different VSJs on an objective basis. We presented a fist draft at the VIA Workshop at ICRA 1, and since then it was further expanded within the VIACTORS group. The datasheets of different Variable Stiffness Joints developed by the different partners of the VIACTORS group, as well as the template can be downloaded from the VIACTORS homepage 589
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