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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.

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Copyright © 2016 by ASME
Topics: Stiffness , Deflection , Gears
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References

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.

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Fig. 2

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

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Fig. 3

CAD design of vsaMGR. Four components are serially connected.

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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

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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.

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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.

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Fig. 9

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

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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.

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Fig. 7

vsaMGR stiffness as a function of adjusting displacement and beam length

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Fig. 6

Prototype of vsaMGR with its controller

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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

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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

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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

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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

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