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Abstract

In this paper, we propose a novel passive parallel continuum ankle exoskeleton that can provide assistive torque during ankle plantar flexion. Due to the flexible branches arranged in compliance with ankle motion and shape, the compact design can also offer some vertical support. The proposed parallel mechanism consists of two types of branches. The first type is a pre-bent flexible rod, mainly used to apply assistive force/torque during ankle plantar flexion. The second type of branch consists of a bounded sphere joint, flexible rod, and bounded sphere joint (BFB), which is mainly used for support. We formulate the kinetostatic model of the BFB branch as a series of parallelizable unconstrained optimization problems to ensure efficient solvability. After that, we derive the kinetostatic model of the proposed mechanism. After calibration, the wrench error of the kinetostatic model is 9.07%. Simulation analysis based on the calibrated model shows that the designed mechanism has high supporting stiffness and low rotational stiffness. The assistive torque caused by the nonlinear rotational stiffness in the sagittal plane is similar to that of passive clutch-like mechanisms. These properties can still be maintained when the joint center changes within a small range. Besides, a walking experiment was conducted, and the results show that the proposed design can reduce gastrocnemius activity.

References

1.
Zoss
,
A.
,
Kazerooni
,
H.
, and
Chu
,
A.
,
2006
, “
Biomechanical Design of the Berkeley Lower Extremity Exoskeleton (BLEEX)
,”
IEEE/ASME Trans. Mechatron.
,
11
(
2
), pp.
128
138
.
2.
Sankai
,
Y.
,
2010
, “
Hal: Hybrid Assistive Limb Based on Cybernics
,”
Springer Tracts in Advanced Robotics
,
Berlin, Heidelberg
,
Oct. 22
, pp.
25
34
.
3.
Schiele
,
A.
,
2009
, “
Ergonomics of Exoskeletons: Objective Performance Metrics
,”
World Haptics Conference 2009 (WHC 2009)
,
Salt Lake City, UT
,
Mar. 18
, IEEE, pp.
103
108
.
4.
Miao
,
Y.
,
Gao
,
F.
, and
Pan
,
D.
,
2013
, “
Mechanical Design of a Lower Extremity Exoskeleton With Hybrid Legs for Power Augmentation
,”
2013 International Conference on Intelligent Robotics and Applications (ICIRA)
,
Berlin, Heidelberg
,
Dec. 16
, pp.
132
142
.
5.
Wang
,
T.
,
Zhu
,
Y.
,
Zheng
,
T.
,
Sui
,
D.
,
Zhao
,
S.
, and
Zhao
,
J.
,
2020
, “
PALExo: A Parallel Actuated Lower Limb Exoskeleton for High-Load Carrying
,”
IEEE Access
,
8
, pp.
67250
67262
.
6.
Wang
,
X.
,
Guo
,
S.
,
Qu
,
B.
,
Song
,
M.
,
Wang
,
P.
, and
Liu
,
D.-X.
,
2022
, “
Design and Experimental Verification of a Parallel Hip Exoskeleton System for Full-Gait-Cycle Rehabilitation
,”
ASME J. Mech. Rob.
,
14
(
5
), p.
054504
.
7.
Asbeck
,
A. T.
,
Schmidt
,
K.
,
Galiana
,
I.
,
Wagner
,
D.
, and
Walsh
,
C. J.
,
2015
, “
Multi-joint Soft Exosuit for Gait Assistance
,”
2015 IEEE International Conference on Robotics and Automation (ICRA)
,
Seattle, WA
,
May 30
, IEEE, pp.
6197
6204
.
8.
Lee
,
Y.
,
Kim
,
Y.-J.
,
Lee
,
J.
,
Lee
,
M.
,
Choi
,
B.
,
Kim
,
J.
,
Park
,
Y. J.
, and
Choi
,
J.
,
2017
, “
Biomechanical Design of a Novel Flexible Exoskeleton for Lower Extremities
,”
IEEE/ASME Trans. Mechatron.
,
22
(
5
), pp.
2058
2069
.
9.
Lee
,
Y.
,
Lee
,
J.
,
Choi
,
B.
,
Lee
,
M.
,
Roh
,
S.-G.
,
Kim
,
K.
,
Seo
,
K.
,
Kim
,
Y.-J.
, and
Shim
,
Y.
,
2019
, “
Flexible Gait Enhancing Mechatronics System for Lower Limb Assistance (GEMS L-Type)
,”
IEEE/ASME Trans. Mechatron.
,
24
(
4
), pp.
1520
1531
.
10.
Ma
,
L.
,
Leng
,
Y.
,
Jiang
,
W.
,
Qian
,
Y.
, and
Fu
,
C.
,
2022
, “
Design an Underactuated Soft Exoskeleton to Sequentially Provide Knee Extension and Ankle Plantarflexion Assistance
,”
IEEE Rob. Autom. Lett.
,
7
(
1
), pp.
271
278
.
11.
Sanchez-Villamanan
,
M. D. C.
,
Gonzalez-Vargas
,
J.
,
Torricelli
,
D.
,
Moreno
,
J. C.
, and
Pons
,
J. L.
,
2019
, “
Compliant Lower Limb Exoskeletons: A Comprehensive Review on Mechanical Design Principles
,”
J. NeuroEng. Rehabil.
,
16
(
1
), p.
55
.
12.
Zhang
,
J.
,
Nie
,
P.
, and
Zhang
,
B.
,
2024
, “
A Variable Structure Passivity Control Method for Elastic Joint Robots Based on Cascaded High-Order State Estimation
,”
Sci. China Technol. Sci.
,
67
(
2
), pp.
395
407
.
13.
Kong
,
K.
,
Bae
,
J.
, and
Tomizuka
,
M.
,
2012
, “
A Compact Rotary Series Elastic Actuator for Human Assistive Systems
,”
IEEE/ASME Trans. Mechatron.
,
17
(
2
), pp.
288
297
.
14.
Walsh
,
C.
,
Paluska
,
D.
,
Pasch
,
K.
,
Grand
,
W.
,
Valiente
,
A.
, and
Herr
,
H.
,
2006
, “
Development of a Lightweight, Underactuated Exoskeleton for Load-Carrying Augmentation
,”
2006 IEEE International Conference on Robotics and Automation (ICRA)
,
Orlando, FL
,
May 15
, pp.
3485
3491
.
15.
Collins
,
S. H.
,
Wiggin
,
M. B.
, and
Sawicki
,
G. S.
,
2015
, “
Reducing the Energy Cost of Human Walking Using an Unpowered Exoskeleton
,”
Nature
,
522
(
7555
), pp.
212
215
.
16.
Chang
,
Y.
,
Wang
,
W.
, and
Fu
,
C.
,
2020
, “
A Lower Limb Exoskeleton Recycling Energy From Knee and Ankle Joints to Assist Push-Off
,”
ASME J. Mech. Rob.
,
12
(
5
), p.
051011
.
17.
Black
,
C. B.
,
Till
,
J.
, and
Rucker
,
D. C.
,
2018
, “
Parallel Continuum Robots: Modeling, Analysis, and Actuation-Based Force Sensing
,”
IEEE Trans. Rob.
,
34
(
1
), pp.
29
47
.
18.
Kang
,
Y.
,
Liang
,
Z.
,
Yan
,
T.
,
Duan
,
X.
,
Wang
,
H.
,
Seidelmann
,
J.
, and
Chen
,
G.
,
2024
, “
Analysis and Validation of a Flexible Limb/Cable Hybrid-Driven Parallel Continuum Manipulator
,”
ASME J. Mech. Rob.
,
16
(
6
), p.
061010
.
19.
Kulkarni
,
S.
, and
Shabana
,
A. A.
,
2019
, “
Spatial ANCF/CRBF Beam Elements
,”
Acta Mech.
,
230
(
3
), pp.
929
952
.
20.
Bretl
,
T.
, and
McCarthy
,
Z.
,
2014
, “
Quasi-static Manipulation of a Kirchhoff Elastic Rod Based on a Geometric Analysis of Equilibrium Configurations
,”
Int. J. Rob. Res.
,
33
(
1
), pp.
48
68
.
21.
Till
,
J.
,
Aloi
,
V.
, and
Rucker
,
C.
,
2019
, “
Real-Time Dynamics of Soft and Continuum Robots Based on Cosserat Rod Models
,”
Int. J. Rob. Res.
,
38
(
6
), pp.
723
746
.
22.
Chen
,
G.
,
Zhang
,
Z.
, and
Wang
,
H.
,
2018
, “
A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices
,”
ASME J. Mech. Rob.
,
10
(
3
), p.
031012
.
23.
Antman
,
S. S.
,
2005
,
Nonlinear Problems of Elasticity
(Vol. 107 of Applied Mathematical Sciences),
Springer-Verlag
,
New York
.
24.
Till
,
J.
, and
Rucker
,
D. C.
,
2017
, “
Elastic Stability of Cosserat Rods and Parallel Continuum Robots
,”
IEEE Trans. Rob.
,
33
(
3
), pp.
718
733
.
25.
Tummers
,
M.
,
Lebastard
,
V.
,
Boyer
,
F.
,
Troccaz
,
J.
,
Rosa
,
B.
, and
Chikhaoui
,
M. T.
,
2023–2006
, “
Cosserat Rod Modeling of Continuum Robots From Newtonian and Lagrangian Perspectives
,”
IEEE Trans. Rob.
,
39
(
3
), pp.
2360
2378
.
26.
Lamm
,
B. M.
,
Stasko
,
P. A.
,
Gesheff
,
M. G.
, and
Bhave
,
A.
,
2016
, “
Normal Foot and Ankle Radiographic Angles, Measurements, and Reference Points
,”
J. Foot Ankle Surg.
,
55
(
5
), pp.
991
998
.
27.
Briot
,
S.
, and
Boyer
,
F.
,
2023
, “
A Geometrically Exact Assumed Strain Modes Approach for the Geometrico- and Kinemato-static Modelings of Continuum Parallel Robots
,”
IEEE Trans. Rob.
,
39
(
2
), pp.
1527
1543
.
28.
Rogati
,
G.
,
Leardini
,
A.
,
Ortolani
,
M.
, and
Caravaggi
,
P.
,
2021
, “
Semi-automatic Measurements of Foot Morphological Parameters From 3d Plantar Foot Scans
,”
J. Foot Ankle Res.
,
14
(
1
), p.
18
.
29.
Timošenko
,
S.
, and
Goodier
,
J.
,
1970
,
Theory of Elasticity
,
McGraw-Hill
,
New York
.
30.
Murray
,
R. M.
,
Li
,
Z.
, and
Sastry
,
S.
,
1994
,
A Mathematical Introduction to Robot Manipulation
,
CRC Press
,
Boca Raton, FL
.
31.
Rucker
,
C.
,
2018
, “
Integrating Rotations Using Nonunit Quaternions
,”
IEEE Rob. Autom. Lett.
,
3
(
4
), pp.
2979
2986
.
32.
Siciliano
,
B.
,
Sciavicco
,
L.
,
Luigi
,
V.
, and
Oriolo
,
G.
,
2009
,
Robotics: Modelling, Planning and Control
(
Advanced Textbooks in Control and Signal Processing
),
Springer
,
London
.
33.
Hou
,
T.
,
Ding
,
Y.
, and
Zhu
,
X.
,
2024
, “
A Geometric Framework for Stiffness Mappings of Compliant Robotic Systems on the Special Euclidean Group
,”
IEEE Trans. Rob.
,
40
(
4
), pp.
2181
2200
.
34.
Müller
,
A.
,
2021
, “
Review of the Exponential and Cayley Map on SE(3) as Relevant for Lie Group Integration of the Generalized Poisson Equation and Flexible Multibody Systems
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
477
(
2253
), p.
20210303
.
35.
Boyd
,
S.
,
Vandenberghe
,
L.
, and
Faybusovich
,
F.
,
2006
,
Convex Optimization
,
Cambridge University Press
.
36.
Andersson
,
J. A. E.
,
Gillis
,
J.
,
Horn
,
G.
,
Rawlings
,
J. B.
, and
Diehl
,
M.
,
2019
, “
Casadi—A Software Framework for Nonlinear Optimization and Optimal Control
,”
Math. Program. Comput.
,
11
(
1
), pp.
1
36
.
37.
Smith
,
R.
,
Rattanaprasert
,
U.
, and
O’Dwyer
,
N.
,
2001
, “
Coordination of the Ankle Joint Complex During Walking
,”
Human Movem. Sci.
,
20
(
4–5
), pp.
447
460
.
38.
Kirtley
,
C.
,
2016
, CGA Normative Gait Database, http://www.clinicalgaitanalysis.com/data/
39.
Brockett
,
C. L.
, and
Chapman
,
G. J.
,
2016
, “
Biomechanics of the Ankle
,”
Orthopaed. Trauma
,
30
(
3
), pp.
232
238
.
40.
Tillman
,
B.
,
Fitts
,
D. J.
,
Woodson
,
W. E.
,
Rose-Sundholm
,
R.
, and
Tillman
,
P.
,
2016
,
Human Factors and Ergonomics Design Handbook
, 3rd ed.,
McGraw-Hill Education
,
New York
.
41.
Ding
,
Y.
,
Galiana
,
I.
,
Asbeck
,
A.
,
Quinlivan
,
B.
,
De Rossi
,
S. M. M.
, and
Walsh
,
C.
,
2014
, “
Multi-joint Actuation Platform for Lower Extremity Soft Exosuits
,”
2014 IEEE International Conference on Robotics and Automation (ICRA)
,
Hong Kong, China
,
May 31
, IEEE, pp.
1327
1334
.
42.
Weimer
,
J.
,
1993
,
Handbook of Ergonomic and Human Factors Tables
,
Prentice Hall
,
Englewood Cliffs, NJ
.
43.
Kim
,
S.
,
Son
,
J.
,
Jung
,
B.
, and
Kim
,
Y.
,
2013
, “
Metatarsophalangeal Joint Kinetics Innormal Walking
,”
World Congress on Medical Physic and Biomedical Engineering May 26–31, 2012, Beijing, China
, Vol.
39
,
M.
Long
, ed., Springer, Berlin, pp.
136
138
.
44.
Chen
,
B.
,
Shi
,
C.
,
Zheng
,
C.
,
Zi
,
B.
,
Zhao
,
P.
, and
Li
,
Y.
,
2023
, “
Development of Lower Limb Exoskeleton for Walking Assistance Using Energy Recycled From Human Knee Joint
,”
ASME J. Mech. Rob.
,
15
(
5
), p.
051007
.
45.
Caron
,
S.
,
Pham
,
Q.
, and
Nakamura
,
Y.
,
2015
, “
Stability of Surface Contacts for Humanoid Robots: Closed-Form Formulae of the Contact Wrench Cone for Rectangular Support Areas
,”
2015 IEEE International Conference on Robotics and Automation (ICRA)
,
Seattle, WA
,
May 26
, pp.
5107
5112
.
46.
Xu
,
S.
, and
Ding
,
Y.
,
2021
, “
Real-Time Recognition of Human Lower-Limb Locomotion Based on Exponential Coordinates of Relative Rotations
,”
Sci. China Technol. Sci.
,
64
(
7
), pp.
1423
1435
.
47.
Sawicki
,
G. S.
, and
Khan
,
N. S.
,
2016
, “
A Simple Model to Estimate Plantarflexor Muscle–Tendon Mechanics and Energetics During Walking With Elastic Ankle Exoskeletons
,”
IEEE Trans. Biomed. Eng.
,
63
(
5
), pp.
914
923
.
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