Proceedings of the 2012 IEEE
International Conference on Robotics and Biomimetics
December 11-14, 2012, Guangzhou, China

Wearable dummy to simulate joint impairment:
Model for the discontinuous friction resistance due to arthritis
Shun Ishikawa, Shogo Okamoto, Yasuhiro Akiyama, Kaoru Isogai, Yoji Yamada and Susumu Hara
Abstract— Physical therapists master manual examination
techniques for testing impaired motor functions. We developed
a wearable robotic dummy joint to simulate disordered joint
resistances for supporting physical therapists to learn suchtechniques. A model to simulate discontinuous joint friction
resistances due to diseases such as osteoarthritis was developed.
Because such resistance originates from abnormal frictions ofbones and cartilages, we used a stick-slip model to simulate theresistances. The model was validated based on the introspectionof physical therapists. This study concludes that a discontinuous
friction model presents forces that are perceptually similar
to those typically caused by damaged or roughened joint
cartilages.

I. INTRODUCTION
The importance of physical therapy has been increasing
to rehabilitate for patient’s motor functions impaired due todisorders such as stroke and arthritis. Rehabilitations improve
the QOL of patients, and as a result of hastening the recovery,
the medical cost reduction is expected. Physical therapists
learn techniques called manual examinations. In these examinations, they move and palpate affected body parts. They,
then examine pains and neurological symptoms to understandthe pathology and the sites to be treated. As one of thesetechniques, physical therapists flex and extend patient’s joints
in order to classify the degrees of motor impairment andrecovery statuses based on the dynamic joint resistances,
limited ranges of joint motions, and patient’s complaints.
Physical therapists should understand various symptoms
by manual examinations and treat them appropriately. The
joint resistance patterns are highly dependent on patient’s
symptoms. Hence, the learners need to experience various
symptoms in order to master manual examination techniques.
However, they scarcely have chances to experience symptoms in training institutions. Even during internship trainings,
it is considered ethically problematic that learners without
qualification treat patients. Therefore, we develop a robotic
joint that simulates various symptoms in order to support
physical therapists to learn manual examinations.
Related research: Recently, some researchers havestarted to develop robotic systems that support the educationof physical therapists. Masutani et al. developed a robotic
leg that simulates impaired knee joints. They simulated alimited range of joint motion, a jackknife phenomenon, andarticular rigidity [1]. Kikuchi et al. controlled a robot’s knee
S. Ishikawa, S. Okamoto, Y. Akiyama, Y. Yamada and S. Hara are with
the Graduate School of Engineering, Nagoya University, Furo-cho, Chikusaku, Nagoya 464-8603, Japan.
K. Isogai is with the Faculty of Health and Medical Sciences, Hamamatsu
University, 1230, Miyakoda-cho Kita-ku, Hamamatsu 431-2102, Japan and
the Graduate School of Engineering, Nagoya University.

978-1-4673-2126-6/12/$31.00 © 2012 IEEE

joint using a MR crutch and a DC motor in order to achievea limited range of joint motion that typically generates large
forces [2]. Grow et al. compared and validated two models tosimulate spasticities of elbow joint [3]. Also, they suggested
that the robot is effective for training of the classificationof spasticities. In these studies, they treated human joints as
simply uniaxial joints and decreased the degrees of freedom
in robot joints. However, even single human joint has multiple degrees of freedom, which lead to the complex motionsof human joints. Takahashi et al. simulated the stretch andcontraction of a forearm accompanied with the extension andflexion of an upper limb using an oval cam in the robot
joint [4]. Oki Electric Industry Co. Ltd. proposed a robot
with six degrees of freedom for the trainings of physicaltherapists [5].
Osteoarthritis & crepitus: Thus far, symptoms such as
contracture, rigidity, limited range of joint motion and clonus
that are typical to paralysis, have been simulated. We focus
on discontinuous frictional joint resistances which are prominently seen in osteoarthritis (OA). OA is a chronic painfularthropathy characterized by disruption and potential loss ofjoint cartilage along with other joint changes [6]. Fig. 1
illustrates a typical osteoarthritic knee joint and healthy one.
Due to the erosion of cartilages as cushion, joint spaces
narrow. Bony spurs and malalignment are also observed
for these knee joints. OA is more common in women thanin men. Worldwide estimates are that 9.6% of men and
18.0% of women over 60-year old have symptomatic OA [7].
Diagnoses of OA are typically based on X-rays, clinical tests,
MRIs, and arthroscopes. Although the arthroscopy test may
be a more appropriate “gold standard” in the evaluation of
OA, a clinical test is practically beneficial for diagnosis of
OA or patients with less severe cartilage damages [8]. In
understanding the severity or recovery of damaged joints,
physical therapists check the symptoms such as early morning stiffness, joint pain, tenderness, synovial swelling, bonyenlargement, and crepitus [8] [9] [10]. Physical therapists
make use of crepitus as one of the criteria to classify OA in aclinical test. Crepitus is caused by the contacts of roughened
articular cartilages or tendons [6], and is typically defined ashearing of a grinding noise and/or palpable vibrations in the
joint, detected by the hand of the investigator rested on it [7].
It’s an important feature to indicate osteoarthritic lesions [7].
Crepitus indicates the state of the gliding surfaces. Fine
crepitus at a joint indicates minor roughening of the joint
surface. Coarse crepitus indicates considerable superficial
fragmentation of cartilage. For these two types of crepitus,
physical therapists feel vibratory resistance forces caused1409

Learner
Cuff

Flexionand Extension(a) Healthy person(b) OA patient

Link
Fig. 1.

Schematic diagram of knee joint

Healthy personby roughened surfaces [11]. As the most severe case, theintermittent creaking of bone against bone shows articularcartilage to have been wholly eroded [11]. Physical therapists
classify these states by the degree of crepitus.
Objective: In educational institutions, when the trainers
teach typical resistances of the impaired joints to theirstudents, they experience the trainer’s limbs that mimic
the resistances. However, such resistances simulated by thetrainers are limited. Crepitus is clearly one of the symptoms
that the trainers cannot accurately imitate. Therefore, a robot
joint that simulates the unique joint resistance of crepitus
is beneficial for learners of physical therapists. Thus far, amethod to effectively simulate the friction torques caused bycrepitus has not been known. It is difficult to build a suitemodel of complex impaired human joint and mechanismsthat cause crepitus. The objective of the present study is tosimulate crepitus using the model of discontinuous frictions
known as a stick-slip phenomena. Then, we apply it to
the wearable dummy joint described in the next section.
Furthermore, a physical therapist validates the simulated
crepitus.
II. WEARABLE DUMMY SIMULATING MOTORDISORDER
A. Technical problems of dummy robots for training ofmanual examination
There are some technical issues that should be considered for developing a robotic device for training physicaltherapists. First, fidelity to the joint resistance forces shouldbe achieved. It is required to simulate dynamic reaction
force patterns or large resistance forces caused by disorders.
Second, it is preferable that the robotic and human joints have
similar degrees of freedom of motion. For example, humanknee joint involves minor rotation and stretch and contraction
along the limb when it extends and flexes. Finally, humanlikelihood such as appearance, skin and conversation withpatients as if facing patients is necessary. To balance theseissues into a robotic device is required.
B. Concept of wearable dummy joint
Fig. 2 shows a conceptual diagram of the wearable dummy
joint worn on a knee joint of a healthy relaxed person that isFig. 2.

Motor and Encoder

Conceptual diagram of wearable dummy joint

typically a student. The dummy joint is simply constructedby one motor and two links. Each of the links is fixed to
his/her lower and femoral thighs through a brace called acuff. As well as educational sites, students practice examination techniques in a pair. One of them performs a patient, andthe other practices manual examinations. The learners grasp
the lower thigh side of a mock patient and flexes or extends
the knee. The mock patient is relaxed and does not exert any
voluntary movements. The motor generates resistance forces
to the lower thigh depending on the simulated symptoms andmotion of the dummy joint. The joint then, simulates the
behaviors of disordered knee joint. The trainee can practicemanual examinations in several postures as shown in Figs. 2
and 3.
The dummy joint neither has a rotational nor sliding
mechanism that human knee joints have. These mechanicaldifferences between the human and dummy knee joints areabsorbed into human fats or clothes. Hence, the trainee canexperience the minor rotations and slides that the human knee
joint inherently have. Furthermore, unlike previous dummy
robots, the trainee touches a real human leg. Human-tohuman communications are also maintained. One concern
is that this dummy does not present joint resistance forces
to trainees because of non rigid connections between cuffs
and a human leg. Especially, high-frequency forces tend
to be decayed by the wearer’s cloth and fat and are notdelivered to the learner’s hand. Hence, the wearable dummy
joint is limited to symptoms that implicate low-frequency
resistances. However, the approach is still applicable to many
symptoms with no high-frequency responses needed such as
contracture, clonus, spasticity.
C. Mock-up Dummy Joint for Knee Joint
Fig. 3 shows a prototype of the wearable dummy joint.
This dummy joint was fitted into a healthy femoral andlower thighs using cloth bands. A DC motor (RE35, Maxon,
stalling torque 949 mNm) and a gear box (1/86) were used.
The links were MC nylon. The motor was controlled by a1410

Upper thigh side

Motor

EncoderFig. 4.

Stick-slip model of rotary motion

Lower thigh side
Fig. 3.

−Tsmax ≤ T (t) ≤ Tsmax .

Wearable dummy joint simulating motor disordermicrocomputer by way of a motor driver with a PI current
controller. The microcomputer also received signals froman encoder installed on the motor. We compensated for the
kinetic friction force of the reduction gear that was measured
as approximately 0.5 Nm regardless of the rotary speed.
III. CREPITUS MODEL BASED ON STICK-SLIP
PHENOMENON
Crepitus is partly caused by the contact between bones
in the joint whose soft tissues such as cartilages are destroyed [7]. We propose to simulate the resistance forces
caused by crepitus using a stick-slip model because oneof the causes of crepitus is the discontinuous joint friction
forces. We modified Nakano’s stick-slip model of two objects
on a plane [12] to fit into a rotating body. Fig. 4 shows themodel of a stick-slip phenomenon between a rotary shaft andan imaginary object. An imaginary object attached to a rotaryspring contacts the shaft that rotates at angular velocity Ω (t).
They are subjected to the friction torque T (t). This T (t) ispresented to the learner. The coulomb friction is assumed as
the frictional properties. θ̇ (t) is the angular velocity of theimaginary object. Variables used in this model areJ: moment of inertia [kg · m2 ],θ (t) : displacement of the imaginary object [rad],θ̇ (t) : angular velocity of the imaginary object [rad/s],kr: constant of rotational spring [N/rad],Ω (t) : angular velocity of shaft [rad/s],
T (t) : friction torque [Nm],Tk: kinetic friction torque [Nm],Tsmax : maximum static friction torque [Nm].
A. Analytic Expression
The frictional model has two phases that are sticking andslipping phases. Fig. 5(a) shows the model of a sticking
phase. In the sticking phase, the imaginary object and theshaft rotate at the same angular velocity (Ω (t) − θ̇ (t) = 0).
The static friction torque between the object and shaft isequal to the torque that the learners generate and perceive.
Therefore,
T (t) = kr θ (t) ,
(1)

(2)

During the sticking phase, above T (t) is achieved by the
robotic dummy joint to the learner’s hand. Fig. 6 shows
the diagram of the stick-slip motion. A black line shows afriction torque between the imaginary object and shaft, and agray line shows an angular velocity of the imaginary object.
kr influences the period of sticking phase. Large kr values
decrease the period of sticking phase. Tsmax is a parameterthat determines the maximum resistance torque applied to
the learner.
Fig. 5(b) shows the model of a slipping phase. In theslipping phase, the angular velocity of the imaginary object
is different from that of the shaft (Ω (t) − θ̇ (t) ̸= 0). The
angular velocity of the imaginary object is always smaller
than that of the shaft. The kinetic friction torque occurs
between the imaginary object and shaft. This friction torqueis expressed as()
T (t) = sign Ω (t) − θ̇ (t) · Tk .
(3)
During the slipping phase, this friction torque is presented
by the dummy joint to the learner’s hand. Tk determines theminimum friction torque applied to the learner. The torquechanges between Tk and Tsmax as being the minimum andmaximum values, respectively.
Because of the difference between the maximum static
friction and kinetic friction torques, sticking and slipping
phases alternately transit, and the stick-slip motion continuously occurs. Here, we describe the conditions of the switch
between two phases. Fig. 7 shows a flow chart of the stickslip transitions.
The condition that stick-to-slip transition occurs is thatthe restoring torque of the spring plus the inertia of imaginary object exceed the maximum friction torque, which isexpressed byJ θ̈ (t) + kr θ (t) ≥ Tsmax .

(4)

Given that t0 is the time that slipping phase starts, the angularvelocity of the shaft isθ̇ (t0 ) = Ω (t0 ) .

(5)The displacement of the imaginary object at t0 is1411

θ (t0 ) =Tsmax − J θ̈ (t0 )
.
kr

(6)

startstick phase starts

yes(a) Sticking phaseFig. 5.

(b) Slipping phaser    smax

stick-to-slip transitionnostick phase continues

Two phase model of rotary motion

Friction torqueT (t )Tsmax

AΩ(t0 )0−A

Tk

Sticking
phase

Fig. 6.

Slipping
phase

Sticking
phasetAngular velocity of imaginary object

slip phase starts
θ&(t )

Schematic diagram of stick-slip motion

Because J and θ̈ (t0 ) are small, θ (t) is approximated as
θ (t0 ) ≃

Tsmax
.
kr

(7)

The condition that slip-to-stick transition occurs is that theangular velocity of the imaginary object during the slipping
phase reaches that of the shaft, which is described asθ̇ (t) ≥ Ω (t) .

(8)

Because the kinetic friction torque acts in the same direction
as the rotation of the shaft, equation of motion isJ θ̈ (t) + kr θ (t) = Tk .

(9)

Using the initial conditions described by (5) and (7), thevelocity of the imaginary object is calculated as,√√
Tsmax − Tkkrkrθ̇ (t) = − √sint + Ω (t0 ) cos
t
J
J
Jkr
)
(√
kr
Ω (t0 )
= A cost + arccos
,
(10)
J
A
√
2
(Tsmax − Tk )2
A =+ Ω (t0 ) .
(11)Jkr
When θ̇ (t) becomes equal to Ω (t0 ), slip-to-stick transition
occurs. According to (10), the ratio of kr to J affects theperiod of slipping phase. The period decreases as this ratio
increases.

yes   Ω ଴

slip-to-stick transition

Fig. 7.

noslip phase continues

Flow chart of stick-slip transition

B. Example of Simulated Crepitus
We implemented the crepitus model explained above into
the developed dummy joint. The parameters were J =0.01 kg · m2 ，kr = 400 N/rad，Tk = 0.2 Nm，Tsmax =0.4 Nm. These parameters were determined based on thesense of a physical therapist. Fig. 8 shows the example ofan angular velocity and presented torque that was measured
by a force sensor attached to the lower thigh side. In the
sticking phase, the presented torque increased and angularvelocity decreased. On the contrary, in the slipping phase, thepresented torque decreased and angular velocity increased.
The repetitive transitions between sticking and slipping phases successfully generated vibratory friction resistances. However, there are some discrepancies between theschematic diagrams of friction torque and phase transitions
shown in Fig. 6 and those observed in Fig. 8. Note that theangular velocities in both figures are not comparable because
the velocity in Fig. 6 is that of imaginary object whereas thevelocity in Fig. 8 is that of the robotic lower thigh.
First, in Fig. 6, during slipping phase, the presented torqueremains at constant value of kinetic friction Tk that was
0.2 Nm: however, it did not remain at constant in Fig. 8.
This was partly because the rapid force drop, that occurs on
the transition from sticking to slipping transition, was notachieved due to a limited response of motors. Furthermore,
the intervals between two sticking phases are short in Fig. 8that a successive sticking phase started before the generative
force converged to the constant kinetic friction torque.
Second, the simulated phases slightly differ from theapparent phases. As shown in Fig. 6, in the simulated model,
the point of state transition matches the peaks or beginningsof changes in friction torques. However, in Fig. 8, due to thelimited response of the actuator system again, the changes intorques ran after the phase shifts. Nonetheless, such temporalgap between the phases and friction torque changes does not1412

Stick

Slip

Stick

Slip

26
25

0.4
24
23
0.35
22

Angular velocity of lower thigh [deg/s]

Presented torque [Nm]0.45 StickFig. 10.

21

0.3
0

0.05

0.1

Joint motion of severe knee osteoarthritis

0.15Time [s]Fig. 8. Angular velocity and presented torque during simulating crepitus
at high angular velocity

Stick

Slip

Stick

Slip

Stick

12

0.35

11

0.3

10

0.25

Angular velocity of lower thigh [deg/s]

Presented torque [Nm]

0.4

9
0

0.05

0.1
Time [s]Fig. 9. Angular velocity and presented torque during simulating crepitus
at low angular velocity

deteriorate the quality sensations generated by the method
because the learners experience just friction torques but notphases.
Fig. 9 shows the example of an angular velocity of robotic
lower thigh and torque presented to the learner at low angularvelocity range. Characteristics similar to those observed inFig. 8 were also seen at low velocity ranges.
IV. EVALUATION
The wearable dummy joint that we developed will be used
for the education of physical therapist. Hence, the dummy
joint should simulate symptoms that the trainers regard as
typical. Based on this idea, we invited two physical therapists. From their introspection, we validated our model of
crepitus. There may be some disputes over the introspectionbased assessment due to the lack of quantitative evaluation.
One may claim that we should compare the resistance torques
between real patients and our model. However, patientsusually suffer from various symptoms along with crepitus,
which makes it virtually impossible to compare only crepitus.
Also, the data observed from patients include individual
differences. Rather than mimicking individual characteristics,
the dummy joint for the training of manual examination
should capture the typical symptoms common to a large
portion of patients. Experienced physical therapists understand such typical symptoms. Also, introspection will reveal
the latent flaws of the system, whereas rating tasks, which
also give us quantitative values, focus on specific terms. For
example, in such tasks, the assessors respond to questions
such as ”how similar is the magnitude of simulated resistanceforces to that of real symptom.” Such question provides us
with the ratings on specific terms, however it is unsuitable forthe early stage of the development, in which we still need
to identify the latent problems of the system. Hence, we
conducted the assessment based on introspection, expectingthat free descriptions would discover defects that we were
unaware of.
Also, one physical therapist mentioned the benefits ofwearable dummy joint as follows. The wearable dummy joint
enables the learners of physical therapy to experience theweight, warmth, and skin thickness of real human legs. Fromthese points, the wearable dummy joint is superior to therobotic dummy joints.
The physical therapists were in 50s and had long careers
in clinical experience. They evaluated that the simulated
resistances were perceptually similar to those of typicalcrepitus after experiencing the simulated crepitus for several
minutes. Especially grating sensations during the motion
were commended. Also, one physical therapist said that thefeel of leg by hands such as leg weight, thickness and warmth
is important as compared with no such feel. He evaluatedthat a dummy joint was more useful than a robot leg in that
respect. However, the following two problems were pointed.
The first problem was that the wearable dummy joint
did not exhibit the displacement along its lower thigh’s
longitudinal direction. As shown in Fig. 10, the bones ofsevere knee osteoarthritis are so roughened that the lower
thigh translates along its longitudinal direction when the knee
is passively flexed or extended by a physical therapist. Due tothe lack of the actuation along such direction, our prototype1413

of the dummy joint cannot essentially resolve this problem.
Even worth, as long as the healthy person wears the dummy
joint, it cannot present such abnormal motion. For example,
in the case of a knee joint with the torn collateral ligament,
the instabilized leg moves to the valgus and varus sides.
Of course, the leg of the healthy person does not move so.
Hence, in this aspect, the concept of wearable dummy has
limitations for certain symptoms involving abnormal joint
motions. However, it is potentially valid for early stages ofthe symptoms or those that do not cause the malalignmentof joints.
The second problem was about the lack of high-frequency
palpable vibrations. When physical therapists treat patientswith osteoarthritis, they typically hold the tibial part ofpatients. The skin on the tibial part is thin enough thatthe therapists experience high-frequency palpable vibrationsdelivered through bones. In the case of wearable dummy
joint, it delivers resistance forces to the users through a cuff.
The cuff was fastened to the wearer’s calf covered witha thicker skin. Such skin may have decayed the deliveryof high-frequency forces. Or, our crepitus model did not
implicate the frequency responses of human bones. The rolesof bones as frequency filter should have been considered.
This problem can be resolved by some frequency-shaping
techniques of force signals. This problem is not unique tothe wearable dummy joints. Robotic joints developed in theprevious related researches also include this problem because
their robots clearly have frequency responses different fromhumans. The previous researches did not face this problem
merely because they dealt with symptoms formed by only
low-frequency forces. However, in the case of the joint
rigidity or stiffness simulated by the wearable dummy joint,
such problem was not pointed because these symptoms arecomposed of only low-frequency forces. The assessors highly
valued the simulated stiffness.
V. CONCLUSION
We proposed a concept of wearable dummy joint underwhich a healthy person wears a robotic joint and it simulates
the resistances of disordered joints. This idea enables thetrainee of physical therapy to experience human-likelihood
including human knee’s inherent minor rotation or stretch
and contraction. Further, we developed a simulation model
to mimic the resistance forces of crepitus that is typicallydefined as a palpable vibration due to damaged cartilages
and bones. Given that crepitus has a connection with vibratory frictional rotation of joint, the model we developed
simulates the stick-slip phenomena of rotary motion. Fromthe introspection of physical therapists that experienced themodel implemented on the dummy joint, we conclude thatthe model is possible to present joint resistance forces thatare perceptually similar to those of typical crepitus. However,
we found that there are two technical problems for simulating
crepitus. These problems were that the wearable dummy
joint did not exhibit the displacement along its lower thigh’s
longitudinal direction and about the lack of high-frequency

palpable vibrations. In the future, it is necessary to solvethese problems.
R EFERENCES[1] Asahi Denshi Kenkyusho KK, Kujima Denki KK, Nittamokei corp.,
M. Yasuhiro, and N. Atsushi, Patient simulating robot for rehabilitation education and rehabilitation education method, JP. patent,
JP2006204832 (A), 2006-08-10.
[2] T. Kikuchi, K. Oda, S. Yamaguchi, and J. Furusho, “Leg-robot with
MR clutch to realize virtual spastic movements,” Journal of intelligent
material systems and structures, vol.21, pp.1523-1529, 2010.
[3] D. I. Grow, M. Wu, M. J. Locastro, S. K. Arora, A. J. Bastian,and A. M. Okamura, “Haptic simulation of elbow joint spasticity,”IEEE symposium on haptic interfaces for virtual environments andteleoperator systems, pp. 475–476, 2008.
[4] Y. Takahashi, T. Komeda, H. Koyama, S. Yamamoto, T. Arimatsu,
Y. Kawakami, K. Inoue, and Y. Ito, “Development of an upper limb
patient simulator for physical therapy exercise,” Proceedings of the2011 IEEE international conference on rehabilitation robotics, pp. 1–
4, 2011.
[5] Oki electric industry co. ltd., Robot for rehabilitation education, JP.
Patent, JP2008281926 (A), 2008-11-20.
[6] R. D. Altman, “Osteoarthritis (OA),” The Merck manual for healthcare professionals, http://www.merckmanuals.com/professional/
musculoskeletal and connective tissue disorders/joint disorders/
osteoarthritis oa.html#v906115, (accessed 2012-06-27).
[7] D. Schiphof, “Identifying Knee Osteoarthritis –Classification, earlyrecognition and imaging,” Erasmus University Rotterdam, 2012, p.
94, Ph.D. thesis.
[8] C. W. Wu, M. R. Morrell, E. Heinze, A. L. Concoff, S. J. Wollaston, E.
L. Arnold, R. Singh, C. Charles, M. Louise Skovrun, J. D. FitzGerald,
L. W. Moreland, and K. C. Kalunian, “Validation of American Collegeof Rheumatology Classification Criteria for Knee Oateoarthritis Using
Arthroscopically Defined Cartilage Damage Scores,” Seminars in
Arthritis and Rheumatism, pp. 197–201, 2005.
[9] A. Jones, N. Hopkinson, M. Pattrick, P. Berman, and M. Doherty,“Evaluation of a method for clinically assessing osteoarthritis of theknee,” Annals of rheumatic diseases, vol. 51, pp. 243–245, 1992.
[10] W. Zhang, M. Doherty, G. Peat, S. M. A. Bierma-Zeinstra, N. K.
Arden, B. Bresnihan, G. Herrero-Beaumont, S. Kirschner, B. F. Leeb,
L. S. Lohmander, B. Mazieres, K. Pavelka, L. Punzi, A. K. So,
T. Tuncer, I. Watt, and J. W. Bijlsma, “EULAR evidence-based
recommendations for the diagnosis of knee osteoarthritis,” Annals of
rheumatic diseases, vol. 69, pp. 483–489, 2010.
[11] J. Cyriax, “The joint is moved,” Textbook of orthopaedic medicine:vol. 1: diagnosis of soft tissue lesions. 7th ed., Bailliere Tindall, p. 73,
1978.
[12] K. Nakano and Y. Kikuchi, “Conditional expression for the occurrenceof stick-slip motion based on the coulomb friction model (part 1) –Formulation and approximation of conditional expression–,” Tribologist, vol. 51, part 2, pp. 131-139, 2006.

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