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Research Papers

Effects of Load Connection Form on Efficiency and Kinetics of Biped Walking

[+] Author and Article Information
Yuanhao Wu

State Key Laboratory of Tribology,
Beijing Key Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China
e-mail: wu-yh14@mails.tsinghua.edu.cn

Ken Chen

State Key Laboratory of Tribology,
Beijing Key Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China
e-mail: kenchen@mail.tsinghua.edu.cn

Chenglong Fu

State Key Laboratory of Tribology,
Beijing Key Lab of Precision/Ultra-Precision
Manufacturing Equipments and Control,
Tsinghua University,
Beijing 100084, China
e-mail: fcl@mail.tsinghua.edu.cn

1Corresponding author.

Manuscript received February 17, 2016; final manuscript received August 1, 2016; published online September 9, 2016. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 8(6), 061015 (Sep 09, 2016) (10 pages) Paper No: JMR-16-1041; doi: 10.1115/1.4034464 History: Received February 17, 2016; Revised August 01, 2016

This paper investigates the influence of the load connection form on the walking energetics and kinetics with simple models. Four load connection forms including rigid connection (RIC), springy connection (SPC), swingy connection (SWC), and springy and swingy connection (SSC) were modeled. The step-to-step transition of periodic walking was studied through an analytical method. The toe-off impulse magnitude and the work done by toe-off were derived. Simulations were performed to study the walking performance of each model and the effect of model parameters on the gait properties. The analysis and simulation results showed that compared with RIC, SPC and SSC can significantly improve the toe-off efficiency and change the ground reaction force (GRF) profile by reducing the burden during the step-to-step transition, which may lead to reduction of walking energy cost. Energetics and kinetics of SWC are closely related to the swing angle of load at the transition moment. The load swing may decrease the walking speed, and it is not beneficial to walking efficiency.

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Figures

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Fig. 1

Powered walking model [17]. Body velocities just before and after the step-to-step transition are perpendicular to trailing leg and leading, respectively. The toe-off impulse P is along the trailing leg and the heel strike impulse I is along the leading leg.

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Fig. 2

Four loaded walking models

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Fig. 3

Geometry of toe-off and body mechanics during step-to-step transition for loaded powered walking models. (a) RIC model: vb− and vb+ are perpendicular to the trailing leg and the leading leg, respectively, and their magnitudes should be equal. (b) SPC model: As the spring force is limited, spring can isolate the impulse between the load and the body during instantaneous transition. (c) SWC model: The tensile force of rigid cord could be infinite and the force only exists along the cord direction. In this model, magnitudes of P and I could be not equal for periodic walking. (d) SSC model: The SSC model can be regarded as a RIC model with a massless load during the step-to-step transition.

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Fig. 4

‖P‖/‖P0‖ and ‖I‖/‖I0‖ versus swing angle of load q4, where ‖P0‖ and ‖I0‖ are the magnitude of toe-off and heel strike impulse, respectively, when q4 = 0. By fixing vb− and mass ratio (Ml=40%Mb), this figure shows ‖P‖ will decrease while ‖I‖ will increase as q4 increases: (a) ‖P‖/‖P0‖ versus swing angle of load q4 and (b) ‖I‖/‖I0‖ versus swing angle of load q4.

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Fig. 5

Effects of spring stiffness k on gait properties of the SPC model when Mb = 75 kg, Ml = 30 kg, α = 0.35 rad, and v = 1.4 m/s: (a) fspring/fw versus k, (b) COT versus spring stiffness k, and (c) vibration amplitude q4 versus spring stiffness k

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Fig. 6

Effects of cord length S on gait properties of the SWC model when Mb = 75 kg, Ml = 30 kg, α = 0.35 rad, and v = 1.4 m/s: (a) fpendulum/fw versus S, (b) COT versus S, and (c) maximal horizontal load displacement Ah versus S

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Fig. 7

COT of each model with k = 1500 N/m, c = 10 Nm/s, and S = 0.5 m. As the walking speed v or half step angle α increases, COT increases for all models: (a) COT versus average walking speed v with α = 0.35 rad and (b) COT versus average walking speed v with preferred α.

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Fig. 8

Angular velocity of stance leg q˙1 versus stance leg angle q1 in a gait cycle with α = 0.35 rad and v = 1 m/s

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Fig. 9

GRF and load force during the single stance phase, when v = 1.4 m/s and α = 0.3 rad: (a) GRF in the single stance phase and (b) load force in the single stance phase

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