0
Research Papers

Design of Variable Stiffness Actuator Based on Modified Gear–Rack Mechanism

[+] Author and Article Information
Wei Wang

School of Mechanical Engineering
and Automation,
Beihang University,
37 Xueyuan Road,
Haidian District,
Beijing 100191, China
e-mail: jwwx@163.com

Xiaoyue Fu

School of Mechanical Engineering
and Automation,
Beihang University,
37 Xueyuan Road,
Haidian District,
Beijing 100191, China
e-mail: fuxiaoyue@buaa.edu.cn

Yangmin Li

Mem. ASME
Department of Electromechanical Engineering,
University of Macau,
Room 4067, Building E11,
Taipa, Macao S.A.R., China
e-mail: ymli@umac.mo

Chao Yun

School of Mechanical Engineering
and Automation,
Beihang University,
37 Xueyuan Road,
Haidian District,
Beijing 100191, China
e-mail: cyun18@vip.sina.com

Manuscript received January 7, 2016; final manuscript received June 24, 2016; published online September 6, 2016. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 8(6), 061008 (Sep 06, 2016) (10 pages) Paper No: JMR-16-1008; doi: 10.1115/1.4034142 History: Received January 07, 2016; Revised June 24, 2016

Variable stiffness actuators (VSAs) can improve the robot's performance during interactions with human and uncertain environments. Based on the modified gear–rack mechanism, a VSA with a third-power stiffness profile is designed. The proposed mechanism, used to vary the joint stiffness, is placed between the output end and the joint speed reducer. Both the elastic element and the regulating mechanism are combined into the modified gear–rack (MGR), which is modeled as an elastic beam clamped at the middle position. Two pairs of spur gears are engaged with the rack and considered as the variable acting positions of supporting forces. The joint stiffness is inversely proportional to the third power of the gear displacement, independent from the joint position and the joint deflection angle. The gear displacement is perpendicular to the loading torque, so the power consumed by the stiffness-regulating action is low (14.4 W). The working principle and the mechanics model are illustrated, and then, the mechanical design is presented. The validity of the VSA is proved by simulations and experiments.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Topics: Stiffness , Deflection , Gears
Your Session has timed out. Please sign back in to continue.

References

Grioli, G. , Wolf, S. , Garabini, M. , Catalano, M. G. , Burdet, E. , Caldwell, D. G. , Carloni, R. , Friedl, W. , Grebenstein, M. , Laffranchi, M. , Lefeber, D. , Stramigioli, S. , Tsagarakis, N. G. , Damme, V. M. , Vanderborght, B. , Albu-Schaeffer, A. , and Bicchi, A. , 2015, “ Variable Stiffness Actuators: The User's Point of View,” Int. J. Rob. Res., 34(6), pp. 727–743. [CrossRef]
Vanderborght, B. , Albu-Schäffer, A. , Bicchi, A. , Burdet, E. , Caldwell, D. G. , Carloni, R. , Catalano, M. , Eiberger, O. , Friedl, W. , Ganesh, G. , Garabini, M. , Grebenstein, M. , Grioli, G. , Haddadin, S. , Hoppner, H. , Jafari, A. , Laffranchi, M. , Lefeber, D. , Petit, F. , Stramigioli, S. , Tsagarakis, N. , Van Damme, M. , Van Ham, R. , Visser, L. C. , and Wolf, S. , 2013, “ Variable Impedance Actuators: A Review,” Rob. Auton. Syst., 61(12), pp. 1601–1614. [CrossRef]
Van Ham, R. , Sugar, T. , Vanderborght, B. , Hollander, K. W. , and Lefeber, D. , 2019, “ Compliant Actuator Designs,” IEEE Rob. Autom. Mag., 16(3), pp. 81–94.
Albu-Schäffer, A. , Eiberger, O. , Grebenstein, M. , Haddadin, S. , Ott, C. , Wimbock, T. , Wolf, S. , and Hirzinger, G. , 2008, “ Soft Robotics,” IEEE Rob. Autom. Mag., 15(3), pp. 20–30. [CrossRef]
Pratt, G. , and Williamson, M. M. , 1995, “ Series Elastic Actuators,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Pittsburgh, PA, Aug. 5–9, pp. 399–406.
Tsagarakis, N. G. , Laffranchi, M. , Vanderborght, B. , and Caldwell, D. G. , 2009, “ A Compact Soft Actuator Unit for Small Scale Human Friendly Robots,” IEEE International Conference on Robotics and Automation (ICRA), Kobe, Japan, May 12–17, pp. 4356–4362.
Laffranchi, M. , Tsagarakis, N. , and Caldwell, D. G. , 2011, “ A Compact Compliant Actuator (CompAct) With Variable Physical Damping,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, China, May 9–13, pp. 4644–4650.
Shafer, A. S. , and Kermani, M. R. , 2011, “ On the Feasibility and Suitability of MR Fluid Clutches in Human-Friendly Manipulators,” IEEE/ASME Trans. Mechatronics, 16(6), pp. 1073–1082. [CrossRef]
Kajikawa, S. , and Abe, K. , 2012, “ Robot Finger Module With Multidirectional Adjustable Joint Stiffness,” IEEE/ASME Trans. Mechatronics, 17(1), pp. 128–135. [CrossRef]
Du, Y. , Fang, Z. , Wu, Z. , and Tian, Q. , 2008, “ Thermomechanical Compliant Actuator Design Using Meshless Topology Optimization,” Asia Simulation Conference—7th International Conference on System Simulation and Scientific Computing (ICSC), Beijing, China, Oct. 10–12, pp. 1018–1025.
Choi, J. , Park, S. , Lee, W. , and Kang, S. C. , 2008, “ Design of a Robot Joint With Variable Stiffness,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 19–23, pp. 1760–1765.
Garabini, M. , Passaglia, A. , Belo, F. , Salaris, P. , and Bicchi, A. , 2011, “ Optimality Principles in Variable Stiffness Control: The VSA Hammer,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA, Sept. 25–30, pp. 3770–3775.
Koganezawa, K. , Inaba, T. , and Nakazawa, T. , 2006, “ Stiffness and Angle Control of Antagonistially Driven Joint,” First IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob), Pisa, Italy, Feb. 20–22, pp. 1007–1013.
Tonietti, G. , Schiavi, R. , and Bicchi, A. , 2005, “ Design and Control of a Variable Stiffness Actuator for Safe and Dast Physical Human/Robot Interaction,” IEEE International Conference on Robotics and Automation (ICRA), Barcelona, Spain, Apr. 18–22, pp. 526–531.
Schiavi, R. , Grioli, G. , Sen, S. , and Bicchi, A. , 2008, “ VSA-II: A Novel Prototype of Variable Stiffness Actuator for Safe and Performing Robots Interacting With Humans,” IEEE International Conference on Robotics and Automation (ICRA 2008), Pasadena, CA, May 19–23, pp. 2171–2176.
Hurst, J. W. , and Rizzi, A. , 2008, “ Series Compliance for an Efficient Running Gait,” IEEE Rob. Autom. Mag., 15(3), pp. 42–51. [CrossRef]
Chou, C. P. , and Hannaford, B. , 1996, “ Measurement and Modeling of McKibben Pneumatic Artificial Muscles,” IEEE Trans. Rob. Autom., 12(1), pp. 90–102. [CrossRef]
Bicchi, A. , Rizzini, S. L. , and Tonietti, G. , 2001, “ Compliant Design for Intrinsic Safety: General Issues and Preliminary Design,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Maui, HI, Oct. 29–Nov. 3, pp. 1864–1869.
Zhou, X. , Jun, S. K. , and Krovi, V. , 2015, “ A Cable Based Active Variable Stiffness Module With Decoupled Tension,” ASME J. Mech. Rob., 7(1), p. 011005. [CrossRef]
Jafari, A. , Tsagarakis, N. G. , Vanderborght, B. , and Caldwell, D. G. , 2010, “ A Novel Actuator With Adjustable Stiffness (AwAS),” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, Oct. 18–22, pp. 4201–4206.
Kim, B. S. , and Song, J. B. , 2010, “ Hybrid Dual Actuator Unit: A Design of a Variable Stiffness Actuator Based on an Adjustable Moment Arm Mechanism,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 1655–1660.
Kim, B. S. , and Song, J. B. , 2012, “ Design and Control of a Variable Stiffness Actuator Based on Adjustable Moment Arm,” IEEE Trans. Rob., 28(5), pp. 1145–1151. [CrossRef]
Visser, L. C. , Carloni, R. , Unal, R. , and Stramigioli, S. , 2010, “ Modeling and Design of Energy Efficient Variable Stiffness Actuators,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 3273–3278.
Jafari, A. , Tsagarakis, N. G. , Sardellitti, I. , and Caldwell, D. G. , 2014, “ A New Actuator With Adjustable Stiffness Based on a Variable Ratio Lever Mechanism,” IEEE/ASME Trans. Mechatronics, 19(1), pp. 55–63. [CrossRef]
Groothuis, S. S. , Rusticelli, G. , Zucchelli, A. , Stramigioli, S. , and Carloni, R. , 2014, “ The Variable Stiffness Actuator vsaUT-II: Mechanical Design, Modeling, and Identification,” IEEE/ASME Trans. Mech., 19(2), pp. 589–597. [CrossRef]
Hollander, K. W. , Sugar, T. G. , and Herring, D. E. , 2005, “ Adjustable Robotic Tendon Using a ‘Jack Spring’,” International Conference on Rehabilitation Robotics (ICORR), Chicago, IL, June 28–July 1, pp. 113–118.
Van Ham, R. , Vanderborght, B. , Van Damme, M. , Verrelst, B. , and Lefeber, D. , 2007, “ MACCEPA, the Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator: Design and Implementation in a Biped Robot,” Rob. Auton. Syst., 55(10), pp. 761–768. [CrossRef]
Wolf, S. , and Hirzinger, G. , 2008, “ A New Variable Stiffness Design: Matching Requirements of the Next Robot Generation,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, May 19–23, pp. 1741–1746.
Park, J. J. , and Song, J. B. , 2010, “ Safe Joint Mechanism Using Inclined Link With Springs for Collision Safety and Positioning Accuracy of a Robot Arm,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, AK, May 3–7, pp. 813–818.
Alazmani, A. , Keeling, D. G. , Walker, P. G. , Abbas, S. K. , Jaber, O. , Sivananthan, M. , Watterson, K. , and Levesley, M. C. , 2013, “ Design and Evaluation of a Buckled Strip Compliant Actuator,” IEEE/ASME Trans. Mechatronics, 18(6), pp. 1819–1826. [CrossRef]
Morita, T. , and Sugano, S. , 1995, “ Development of One-DOF Robot Arm Equipped With Mechanical Impedance Adjuster,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Pittsburgh, PA, Aug. 5–9, pp. 407–412.
Yalcin, M. , Uzunoglu, B. , Altintepe, E. , and Patoglu, V. , 2013, “ VnSA: Variable Negative Stiffness Actuation Based on Nonlinear Deflection Characteristics of Buckling Beams,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan, Nov. 3–7, pp. 5418–5424.
Choi, J. , Hong, S. , Lee, W. , Kang, S. , and Kim, M. , 2011, “ A Robot Joint With Variable Stiffness Using Leaf Springs,” IEEE Trans. Rob., 27(2), pp. 229–238. [CrossRef]
Groothuis, S. , Carloni, R. , and Stramigioli, S. , 2014, “ A Novel Variable Stiffness Mechanism Capable of an Infinite Stiffness Range and Unlimited Decoupled Output Motion,” Actuators, 3(2), pp. 107–123. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematics of vsaMGR with one-end clamped. MGR is modeled as a beam: (a) top view and (b) side view.

Grahic Jump Location
Fig. 2

Mechanics model of MGR, considered as an Euler–Bernoulli beam with constraints

Grahic Jump Location
Fig. 3

CAD design of vsaMGR. Four components are serially connected.

Grahic Jump Location
Fig. 4

Exploded view of vsaMGR: 1—base, 2—timing belt for driving, 3—harmonic gear reducer, 4—stiffness-regulating motor (2), 5—MGR, 6—deep groove ball bearing (6), 7—spur gear (4), 8—linear guide, 9—right half housing (inner bushing, connected with #20), 10—hollow output flange (outer bushing), 11—potentiometer, 12—potentiometer housing, 13—solid flange (connected with #8 and #9), 14—timing belt for measuring, 15—output link (connected with #10), 16—slider (2), 17—brackets for slider (2), 18—gear housing (2), 19—regulating motor housing (2), 20—left half housing (connected with #3), 21—joint motor, 22—spacer, 23—locking nut (2), 24—eccentric shaft, and 25—tension wheel

Grahic Jump Location
Fig. 5

Stiffness-regulating mechanism of vsaMGR, exploded view and assembly: 1—left half housing (connected with #5), 2—stiffness-regulating motor on the right, 3—MGR, 4—linear guide (connected with #8), 5—right half housing (connected with 8), 6—hollow output flange, 7—potentiometer, 8—solid flange (connected with 9 and 5), 9—timing belt for measuring (the bigger pulley is connected with 8), 10—slider (2), 11—brackets for slider (2), 12—gear housing (2), 13—active gear 1#, 14—passive gear 1#, 15—regulating motor housing (2), and 16—stiffness-regulating motor on the left

Grahic Jump Location
Fig. 6

Prototype of vsaMGR with its controller

Grahic Jump Location
Fig. 7

vsaMGR stiffness as a function of adjusting displacement and beam length

Grahic Jump Location
Fig. 8

Joint stiffness relating to the effective height of rack. The height of 1.23 mm is selected in our prototype to satisfy future applications.

Grahic Jump Location
Fig. 9

Potential energy of vsaMGR as a function of adjusting displacement and deflection angle, simulated by Eq. (13)

Grahic Jump Location
Fig. 10

FEM simulation of vsaMGR's stress and strain. (a) Stress of MGR (MPa) to investigate if it works in the elastic range. The maximum stress is at the engagement point. (b) Strain of MGR to compute how much the simulated angular deflection is.

Grahic Jump Location
Fig. 11

Stiffness profile of vsaMGR with regulating displacement 17–39 mm with the interval of 2 mm. (a) Torque versus deflection by static experiments and (b) theoretical, simulation, and experimental joint stiffness.

Grahic Jump Location
Fig. 12

vsaMGR's response of position step at different stiffness: (a) joint position of step move, (b) joint speed of step move, and (c) history of potential energy stored in MGR during step move

Grahic Jump Location
Fig. 13

Sine trajectory tracking in the vertical plane: (a) tracking setup in the vertical plane and (b) tracking position of vsaMGR in the vertical plane with three periods

Grahic Jump Location
Fig. 14

Kicking-ball experiments are done to investigate the colliding performance: (a) schematic diagram of kicking experiment is shown in the vertical plane and (b) a ball is kicked by the output link of vsaMGR in the kicking experiment

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In