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Research Papers

Benchmark of the Compactness Potential of Adjustable Stiffness Mechanisms

[+] Author and Article Information
Marius Stücheli

Product Development Group Zurich,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: marius.stuecheli@alumni.ethz.ch

Marianne Schmid Daners

Product Development Group Zurich,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: marischm@ethz.ch

Mirko Meboldt

Professor
Product Development Group Zurich,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: meboldtm@ethz.ch

1Corresponding author.

Manuscript received December 20, 2016; final manuscript received May 7, 2017; published online August 8, 2017. Assoc. Editor: Marcia K. O'Malley.

J. Mechanisms Robotics 9(5), 051009 (Aug 08, 2017) (13 pages) Paper No: JMR-16-1382; doi: 10.1115/1.4037114 History: Received December 20, 2016; Revised May 07, 2017

The VariLeg is an exoskeleton allowing a paraplegic to walk. It was used for competing on an obstacle course at the first Cybathlon. It integrates an adjustable stiffness in the knee joint to improve the walking performance. However, the adjustable stiffness mechanism (ASM) of the VariLeg is bulky and heavy, which hampers the handling of the exoskeleton. Hence, the choice of an ASM concept that only needs small springs is essential. This study benchmarks six state-of-the-art ASMs regarding their needed energy storage capacity, thus their potential for a high compactness. The benchmark is performed with the requirements of the VariLeg and a second requirements set, which can be fulfilled by all six ASMs. The benchmark can be transferred to other requirements as well. It is based on models of the ASMs with their design parameters optimized for the given requirements set. The benchmark reveals large differences between the performances of the investigated ASM concepts of up to a factor of five in the energy storage capacity. This compactness benchmark is a useful design tool to choose a suitable mechanism to realize a compact implementation. More compact ASMs will improve the handling of assistive robots with a physically adjustable stiffness, such as the VariLeg, to support handicapped people in everyday life.

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References

Figures

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Fig. 1

VariLeg 2 lower-limb exoskeleton in use by a paraplegic pilot during the Cybathlon 2016 (Reproduced with permission from Alessandro Della Bella [3]. Copyright 2016 by ETH Zürich.)

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Fig. 2

Requirements set 1 in the torque-deflection space: output deflections must be possible up to either an output deflection of δmax or an output torque of τmax (limit L, solid lines). The output stiffness in the equilibrium point (0,0) must be adjustable from Kmin (dash-dotted slope) to Kmax (solid slope). The mechanism must allow for the cornerstone CS1=CS2=(δmax,τmax) to be reachable at a setpoint. Thus, the mechanisms with a progressive torque-deflection behavior must reach δmax with a torque τmax or lower (dotted line) while the mechanisms with a degressive behavior must reach τmax at a deflection δmax or smaller (dashed line).

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Fig. 3

Requirements set 2 in the torque-deflection space: output deflections must be possible up to either a torque τδ=c/δ or an output torque of τmax (limit L, solid lines). The output stiffness in the equilibrium point (0,0) must be adjustable from Kmin (dash-dotted slope) to Kmax (solid slope). The mechanism must allow for the cornerstones CS1 and CS2 and all points of L between them to be reached at some setpoints.

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Fig. 4

Sketch of the working principle of the DLR VS-Joint in cylindrical coordinates. On the left-hand side, gray: geometry with no spring pretension and no deflection, black: with pretension xα through a motor M and deflection δ. On the right-hand side, the force Fn of the cam on the roller split into the axial component Fs and the tangential component Ft.

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Fig. 5

(a) Implementation of the MACCEPA in the VariLeg 1. The equilibrium actuator sets an angle between the lever and the shank link. (b) Working principle of the MACCEPA with the mechanism undeflected and with the lowest stiffness setting (gray) and with an output deflection δ and a stiffness setting xα (black).

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Fig. 6

Sketch of the working principle of the AwAS in the undeflected state with the lowest stiffness setting (gray) and with an output deflection δ and a stiffness setting rα (black)

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Fig. 7

Sketches showing the working principle of the CompAct-VSA mechanism: (a) the geometry undeflected and with the lowest stiffness setting (gray) and with an output deflection δ and a stiffness setting xα (black) and (b) the forces acting on both sides of the lever: the spring force Fs is decomposed in a component in parallel and a component perpendicular to the lever and so is the opposite force FE′. The force FE is the component of FE′ exerted by the output port while the component FB is exerted by the bearing.

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Fig. 8

Sketches showing the working principle of the FSJ regarding the geometry (a) and the forces acting at the cam roller (b) in cylindrical coordinates. In (a), the gray elements show the mechanism in the minimum stiffness setting and in its equilibrium position (δ = 0). The black elements show the mechanism with the cams shifted against each other in the rotary direction by the adjustment actuator M about an angle α and the output port attached to the roller deflected by an angle δ.

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Fig. 9

(a) A picture of the core of the adjustable stiffness mechanism of the AIE Uno with bevel gears for symmetric pretension, two spring packages, and a shaft connecting bothsprings in the center. (b) A sketch of its working principle. Rotation angles are displayed in the horizontal direction. The adjustment actuator M pretensions the two progressive springs symmetrically.

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Fig. 10

Output stiffness-deflection behavior of the CompAct-VSA with pivot positions xα varying from 0.32 mm to 32 mm witha spring stiffness of ks=1.58×105 N/mm; the output stiffness scales linearly with ks. The deflection where the output stiffness becomes negative increases toward 0.42 rad for decreasing values of xα.

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Fig. 11

Output torque-deflection curves of the resulting design of the VS-Joint for varying setpoints xα (0 mm: dark to 22.6 mm: bright). The VS-Joint can withstand high torques with low stiffness settings.

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Fig. 12

Output torque-deflection curves of the resulting design of the MACCEPA for varying setpoints xα (0 mm: dark to 23.2 mm: bright). At low stiffness settings, the output stiffness increases quickly toward the maximum output stiffness.

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Fig. 13

Output torque-deflection curves of the resulting design of the AwAS for varying setpoints rα (25.3 mm: dark to 80 mm: bright). The torque-deflection curves are degressive. The performance envelope is close to a constant output work (hyperbola) with much higher torques than required at a high stiffness setting and much higher deflections than required at a low stiffness setting.

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Fig. 14

Output torque-deflection curves of the resulting design of the FSJ for varying setpoints α (4.27 rad: dark to 4.89 rad: bright)

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Fig. 15

Output torque-deflection curves of the resulting design of the stiffness part of the adjustable impedance element AIE Uno for varying setpoints α (0.67 rad: dark to 1.04 rad: bright). The performance envelope tightly fits the requirement envelope.

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Fig. 16

Output torque-deflection curves of the resulting design of the stiffness part of the CompAct-VSA for varying setpoints xα (4.2 mm: dark to 9.6 mm: bright). The performance envelope almost perfectly fits a constant output work requirement (hyperbola).

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Fig. 17

Internal energy-storage capacities Ucap of the compared mechanisms needed to fulfill the first (a) and the second (b) requirements set. Both the ranking and the relative quantities of the needed Ucap vary considerably between the two requirements sets.

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Fig. 18

Relative output work wr of the compared mechanisms to fulfill the first (a) and the second (b) requirements set. While wr is always 0.25 for the AwAS and the CompAct-VSA mechanisms, it is higher or lower for the other mechanisms, depending on the requirements set.

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Fig. 19

Performance envelopes of the six benchmarked adjustable stiffness mechanisms with the design parameters optimized for the second requirements set. The dotted lines show the torque-deflection curves at the minimum and the maximum stiffness setpoint. The black dashed line shows the requirement envelope.

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