Research Papers

Variable Stiffness Legs for Robust, Efficient, and Stable Dynamic Running

[+] Author and Article Information
Kevin C. Galloway

Wyss Institute for Biologically
Inspired Engineering,
Harvard University,
Cambridge, MA 02138
e-mail: kevin.galloway@wyss.harvard.edu

Jonathan E. Clark

Department of Mechanical Engineering,
Florida A&M University/
Florida State University,
College of Engineering,
Tallahassee, FL 32310
e-mail: clarkj@eng.fsu.edu

Daniel E. Koditschek

GRASP Laboratory,
Department of Electrical and
Systems Engineering,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: kod@seas.upenn.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanisms and Robotics. Manuscript received August 2, 2011; final manuscript received September 1, 2012; published online January 24, 2013. Assoc. Editor: Vijay Kumar.

J. Mechanisms Robotics 5(1), 011009 (Jan 24, 2013) (11 pages) Paper No: JMR-11-1087; doi: 10.1115/1.4007843 History: Received August 02, 2011; Revised September 01, 2012

Humans and animals adapt their leg impedance during running for both internal (e.g., loading) and external (e.g., surface) changes. To date, the mechanical complexity of designing usefully robust tunable passive compliance into legs has precluded their implementation on practical running robots. This work describes the design of novel, structure-controlled stiffness legs for a hexapedal running robot to enable runtime modification of leg stiffness in a small, lightweight, and rugged package. As part of this investigation, we also study the effect of varying leg stiffness on the performance of a dynamical running robot.

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Fig. 2

Illustrations of the different spring models used to understand C-leg compliance under load a load, P. (a) Linear model, (b) 2-orthogonal spring model, (c) pseduo-rigid-body model where stiffness is characterized by a single torsional spring.

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Fig. 3

Pseudo-rigid-body model applied to the C-leg. Adapted from Ref. [44].

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Fig. 5

Application of PRB-model to tunable leg where leg stiffness can be defined by the slider position and the loading point

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Fig. 1

EduBot [22], a hexapod robot considered for studying the effect of the legs with variable stiffness on the robot's dynamic stability

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Fig. 4

An implementation of a structure-controlled stiffness mechanism applied to a C-leg

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Fig. 6

Relaxed and compressed images of a C-leg in the experimental set-up

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Fig. 9

Proposed new design: side view of tunable stiffness composite leg design. (a) Rotation directions of gears. (b) Slider adjusted to a higher stiffness setting.

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Fig. 10

Photograph of the prototyped variable stiffness C-leg

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Fig. 11

Close-up of the active component

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Fig. 12

Older design alternative: C-leg with a Nitinol spring element

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Fig. 7

Experimental validation of the PRB model for estimating torsional spring constant

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Fig. 8

Experimental validation of the cantilever beam bending model for estimating lateral leg stiffness

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Fig. 14

Spring force response at four different leg stiffness settings each with a curve fit (dotted line) applied to the loading phase

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Fig. 13

Top view of experimental set-up. (a) Linear stage is in the home position and leg is undeflected. (b) Platform has been moved a distance, d, and the leg is deflected.

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Fig. 16

Preliminary experimental results showing specific resistance against relative leg stiffness

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Fig. 17

Preliminary experimental results comparing relative leg stiffness against top forward speed

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Fig. 18

Final leg design: (left) illustration of mechanical stop, (right) photo of final assembly

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Fig. 15

Deflection path of leg for various stiffness settings




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