Daisuke Suzuki

Hiromichi Fujie

Kei Kimura

Kota Watanabe

Mineko Fujimiya

Satoshi Yamakawa

Takuma Kobayashi

Toshihiko Yamashita

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Copyright © 2013 by ASME 1 
INTRODUCTION 
Ankle sprains are common injuries in daily and athletic activities. 
An epidemiological report indicated that the incidence rate of ankle 
sprains treated in emergency departments in the USA is more than 2 
per 1000 persons a year, and the rate is estimated to be more than 
double as for ankle sprains in athletic activity [1]. Better understanding 
of ankle biomechanics is, therefore, important for the improvement of 
clinical outcome. Many investigators have performed in vitro and in 
vivo experiments to determine the mechanical roles of ankle structures 
such as range of motion, contribution of ankle ligaments to joint 
stability, joint instability due to ligament transection, and so on. In 
spite of these efforts, tensile forces in ankle ligaments in response to 
specific loading conditions still remains unclear because of a lack of 
experimental methodology. Meanwhile, the use of robotic technology 
for knee joint biomechanics study has been established by Fujie et al 
[2]. Using the technique, tensile forces in knee cruciate ligaments have 
been determined by Woo et al [3], Li et al [4], Fujie et al [5], and other 
groups, while ligament reconstruction technique has been evaluated by 
many investigators [for example 6-8]. Therefore, the objectives of the 
present study were to determine the ankle joint instability due to 
ligament transection and to determine the tensile forces in the anterior 
tarofibular ligament (ATFL) and calcaneofibular ligament (CFL) in 
response to anterior-posterior (AP) drawer force to the human 
cadaveric ankle joints. 
 
MATERIALS AND METHOD 
A 6-DOF robotic system consisting of a custom made 6-axis 
manipulator with a 6-DOF universal force/moment sensor (UFS) 
(Fig.1) [9] was used.  All the actuators attached to the axes of the 
manipulator were position control-based actuators.  In the original 
system, a LabView-based control program runs on a windows PC to 
control the displacement of, and force/moment applied to the 
cadaveric knee joints with respect to the knee joint coordinate system 
[10].  Kinematic and kinetic calculation in the program was modified 
to adapt to ankle joints since the joint coordinate system of the ankle 
[11] used in the present study is similar to that for the knee joint. 
Detailed information has been presented as regard with the 6-DOF 
real-time control in the robot system [12]. Briefly, it was assumed that 
the mass, stiffness and viscosity of an object to be controlled were 
described as [M], [S], and [C], respectively.  When the manipulator 
applies force/moment F to the ankle, the following equation is derived. 
 
[ ]
  
  
 [ ]   [ ]       (1) 
 
Note that the v represents the 6-DOF ankle joint velocity with respect 
to the joint coordinate system [10].  Under the assumption that the 
velocity change is small equation (1) can be finally rewritten in a 
discrete expression as follows, 
 
       [ ]
  (  [ ]  )  ([ ]    [ ]  [ ])     (2) 
 
where  t represents the iterative time of control, and [I] represents a 
unit matrix.  Based on the current velocity vn, the velocity in the next 
step vn+1 can be calculated from equation (2).  The parameters of [M], 
[K], and [C] were predetermined so that the mechanical response of 
the force control could be enhanced.  The procedure that includes 
sensing of force/moment and displacement at the ankle, calculation of 
v, as well as manipulator motion at v was repeated at a rate of 200 Hz.  
In the present study, human cadaveric ankle joints (n=2) were 
dissected down to the joint capsule and fixed to the developed system.  
The anterior-posterior (AP) drawer test was performed for the human 
 
THE USE OF A 6-DOF ROBOTIC SYSTEM FOR THE FUNCTIONAL ANALYSIS OF 
ANKLE JOINT LIGAMENTS 
 
Satoshi Yamakawa (1), Takuma Kobayashi (2), Kei Kimura (1), Daisuke Suzuki (3), 
Kota Watanabe (2), Mineko Fujimiya (3), Toshihiko Yamashita (2), Hiromichi Fujie (1,4) 
(1) Graduate School of System Design 
 Tokyo Metropolitan University 
Tokyo, Japan 
 
(3) Dept of Anatomy 
Sapporo Medical School 
Sapporo, Japan 
(2) Dept of Orthopedic Surgery 
Sapporo Medical School 
Sapporo, Japan 
 
(4) Research Institute for Science and Technology 
Kogakuin University 
Tokyo, Japan 
Proceedings of the ASME 2013 Summer Bioengineering Conference 
SBC2013 
June 26-29, 2013, Sunriver, Oregon, USA 
SBC2013-14460
Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 07/02/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use
Copyright © 2013 by ASME 2 
ankle joints at 10° of dorsal flexion, and at 15°and 30° of planter 
flexion, and neutral position.  During the AP test, the AP DOF was 
translated under the displacement control at a rate of 0.1 mm/s up to 
±60 N while all the DOFs except the AP and dorsal-planter(DP) DOFs 
were set under the force control with prescribed force/moment at zero. 
Six-DOF displacement and force/moment of the ankle joint were 
measured during the tests. After transection of the CFL, the AP test 
was performed for the CFL-transected ankle in a manner identical to 
the tests for intact ankle joint. This allowed to determine joint 
instability due to CFL transection. Subsequently, the intact ankle 
motions were reproduced to the CFL-transected ankle joint. This 
allowed to determine the tensile forces in the CFL in the intact state of 
the ankle joint. Joint instability due to transection of both the ATFL 
and CFL, and tensile forces in the ATFL in the intact state of the ankle 
joint were also determined in a manner identical to the tests for the 
CFL and ATFL-transected ankle joint. 
 
 
Fig.1 Six-DOF robotic system for the joint biomechanical tests for the 
ankle joint 
 
RESULTS 
An example of the relationship between AP force and AP 
displacement at 0 degree of dorsi-flexion in the AP test was indicated 
in Fig.2.  The AP laxity between ± 30 N of AP forces was 
approximately 8 mm in the intact ankle joint. Although the AP laxity 
remained unchanged in the CFL-transected ankle joint, the laxity 
tremendously increased to approximately 16 mm in the CFL and 
ATFL-transected ankle joint. Tensile forces in the CFL and ATFL in 
intact ankle joint were 15 N, and 55 N, respectively, in response to 60 
N of anterior force. With the increase of dorsi-flexion, tensile force in 
the CFL increased while that in the ATFL decreased (Fig.3). 
 
DISCUSSION AND SUMMARY 
The present study is the first one that quantitatively determined joint 
laxity to ligament transection and tensile forces in ankle ligaments. 
The joint loading tests have been successfully performed using the 6-
DOF robotic system developed in our laboratory. The system 
consisted of stiff body and structure, and allowed for fast control and 
easy programming.  Making use of these features, it was possible to 
simulate physiological ankle loadings and motions. 
Although the AP instability of the ankle joint was not affected by 
the transection of the CFL, it was tremendously increased by 
subsequent transection of the ATFL in planter-flexion. In addition, the 
tensile force in the ATFL was increased chose to 70 N, while the 
tensile force in the CFL was around 10 N at planter-flexion in 
response to 60 N of anterior force. These results suggested that the 
ATFL is a crucial structure for preventing from ankle sprains in 
planter-flexion, which indicated a good agreement with the clinical 
incidence of ankle ligament injuries. 
 
 
Fig.2 AP force-displacement curves of ligament-transected ankle 
joints at 0 degree of dorsi-flexion 
 
 
Fig.3 Tensile forces in the CFL and ATFL in response to 60 N of 
anterior force 
 
REFERENCES 
[1] Waterman BR, et al, Am J Bone Joint Surg., 92, pp. 2279–2284. 
2010 
[2] Fujie, H., et al., J. Biomech. Eng. (ASME), 115, pp. 211–217. 1993 
[3] Woo, S., et al., J. Biomech. Eng. (ASME), 30, pp. 431–439. 1997 
[4] Li, G., et al., J. Biomech. Eng. (ASME), 32, pp. 395–400. 1999 
[5] Fujie H., et al, J. Biomech. Eng. (ASME), 31, pp. 219–220. 1995 
[6] Muneta T., Arthroscopy, 15, pp. 618–624. 1999 
[7] Mae T., et al., Arthroscopy 17, pp. 708–716. 2001 
[8] Shino K., et al., Oper Tech Orthop 15, pp. 130–134. 2005 
[9] Fujie H., J. Biomech. Eng. (ASME), 126, pp. 54–61. 2004 
[10] Grood ES., J. Biomech. Eng. (ASME), 105, pp. 136–144. 1983 
[11] Wu G., J. Biomech. Eng. (ASME) 35, pp. 543-8. 2002 
[12]Fujie H., et al., SBC 2011 
 
ACKNOWLEDGMENT 
The present study was financially supported by the MEXT-
Supported Program for the Strategic Research Foundation at Private 
Universities 2008-2012 (BERC, Kogakuin University) Japan. 
 
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The Use of a 6-DOF Robotic System for the Functional Analysis of Ankle Joint Ligaments

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The Use of a 6-DOF Robotic System for the Functional Analysis of Ankle Joint Ligaments

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