2019 19th International Conference on Control, Automation and Systems (ICCAS 2019)
Oct. 15∼18, 2019; ICC Jeju, Jeju, Korea

Effect of the relative rotation axis positionof the stretching machine and ankle
Yuma SHIRAISHI1 , Shogo OKAMOTO1 , Naomi YAMADA1,2
Koki INOUE1 , Yasuhiro AKIYAMA1 and Yoji YAMADA1
1

Graduate School of Engineering, Nagoya University, Nagoya, Japan
2
Aichi Medical College, Kiyosu, Japan

Abstract: At the onset of a stroke, paralysis of the lower leg typically causes a foot deformity called the foot drop.
Stretching is an effective technique for physical therapy. An automated stretching machine provides the option to incorporate long–term stretching at home. We have remodeled a commercial foot exerciser to function as a stretching machine
for ankle dorsiﬂexion [1]. It is believed that the rotation axis of such machines should be aligned with the biomechanicalaxis of the human body, which is the design principle our prototype is based on. However, there have been no studies thathave investigated the best position of the axis required to achieve effective stretching. In this study, we evaluated several
positions of the machine’s rotation axis in the sagittal plane with respect to the stretching effect and physical burden(safety). The force applied on the foot and ankle dorsiﬂexion angle were measured during the stretching experiments.
We computed the work involved in ankle dorsiﬂexion and the force not contributing to the dorsiﬂexion movement, which
served as indicators for the stretching effect and potential physical burden, respectively. It was found that the best positionof the machine’s rotation axis can be above the ankle.
Keywords: Foot deformity, Stretching machine, Rotation axis

1. INTRODUCTION
The paralysis of the lower leg after a stroke increases
the tone of the ankle’s plantar ﬂexors, and causes a footdeformity called the foot drop [2] (Fig. 1). The contact
area of the foot sole is decreased in the stance phase of
the gait, adversely affecting stability. Additionally, a trip
is induced in the swing phase of the gait with an increased
risk of having a fall [3], [4].
Stretching the affected muscles is an effective treatment for the foot drop [5], [6]. This causes a decrease in
the muscle and tendon stiffness, and increases the ankle
range of motion [7], [8], resulting in improved walking
ability. It has been reported that more than 40% of all paralyzed patients exhibit the above mentioned symptoms
even after three months after the onset of a stroke [9].
Thus, this indicates that long–term stretching is essential. However, it is difﬁcult for patients to engage the services of a physical therapist to help with stretching overan extended time period. There are also additional restrictions that have been introduced by medical insurancecompanies. Stretching machines can be useful for solving the above problem. The availability of at–home rehabilitation devices such as therapy bands and stretchingboards may still prove insufﬁcient as some patients may
have paralyzed body parts in addition to the lower limbs,
which makes the use of these devices difﬁcult.
Few studies on ankle stretching machines have beenreported to date. Zhang et al. developed a machine thatfacilitates ankle dorsiﬂexion for stretching using an electromagnetic motor [8], [10]. Yamada et al. developed
a machine for the three dimensional control of the footusing wire–driven mechanisms [11], [12]. This machine

Fig. 1 Foot drop: Foot deformation of the plantar ﬂexion
due to hypertonia of the plantar ﬂexor muscles.

achieves three–dimensional foot movement by independently pulling the lateral and medial wires using two
Mckibben–type pneumatic actuators.
However, despite various research studies, there is nocommercially available stretching machine due to problems such as effectiveness, safety, and usability. We havepreviously proposed safety concepts that should be incorporated when developing stretching machines. The safetymeasures and stretching function were implemented in
a commercial foot exerciser. Further, we veriﬁed anddemonstrated the effect of our prototype stretching machine in healthy young volunteers prior to tests in footdrop patients [1].
In this study, we discuss the position of the rotation
axis of the machine that achieves improvement in thestretching effect. In studies on ankle rehabilitation machines, the axis aligns along the ankle [8], [10], [13],[14]. However, to date this conclusion has not been quantitatively established. In the present study, we identify
parameters that represent the indices of the effect and investigate the position of the machine’s rotation axis basedon the deﬁned parameters. The results of our investigation are reported for the sagittal plane.

We acknowledge technical support from LAP Co., Ltd.

978-89-93215-18-2/19/$31.00 ⓒICROS

403

Fig. 3 The experimental setup. The force sensor was
mounted on the moving part of the machine where
the sensor and acrylic plate pushed the thenar and the
hypothenar. The height of the heel was changed in thesagittal and frontal planes as follows. The machine’s
rotation axes in cases 1 and 2 were 14 mm and 7 mmabove the ankle, respectively. The machine’s rotation
axis in case 3 was aligned along the ankle while incases 4–7, it was 7, 14, 21, and 28 mm below theankle, respectively.

Fig. 2 A prototype stretching machine for ankle dorsiﬂexion. Developed in [1].

2. PROTOTYPE MACHINE
The machine used in our study is based on a commercial foot exerciser (Relegs, LAP Co,. Ltd., Japan)that is originally not used for stretching. Fig. 2 shows
the stretching machine that was used, which contains a
remodeled chassis of the Relegs [1]. An air compressor (CP–12Si, Minato Electrical Co., Ltd., Japan) and anelectro–pneumatic regulator (ITV1030–312S, SMC Co.,
Ltd., Japan) were used to drive and control the machine.
The regulator was controlled by a micro–computer (mbed
LPC1768, Arm Holdings plc, UK). The pneumatic actuator (bellows) expanded along the longitudinal direction
when pressurized, causing the machine’s moving part torotate around the axis near the ankle. This movement
caused the dorsiﬂexion of the foot. The operation of
the machine was controlled by the user via an industrial
enabling switch (A4EG–BM2B041, OMRON Co., Ltd.,
Japan). The machine continued to operate and dorsiﬂex
the foot while the switch was constantly pushed. The operation stopped when the switch was released, and thefoot was returned to the initial relaxed position. The operational speed of the machine reduced as the foot was
dorsiﬂexed, with the rate of movement dropping to lessthan 2◦ /s. Other measures were also implemented to enable safe use of the machine in addition to the above detailed stretching functions.

ions were used in case 1. Cases 2 and 3 had one and two
cushions, respectively. The experimental conditions up tocase 7 were prepared in a similar manner. The machine’s
rotation axis aligned with the ankle in cases 2 or 3 for all
the participants.
The participants operated the machine to dorsiﬂex
their feet using the enabling switch. They then released
the switch when they felt that the plantar ﬂexors had
stretched to the desired extent. This trial was conducted
twice in a succession. Once the measurements were performed in the order of the cases 1–7, the reverse order ofthe cases 7–1 was executed. The above procedures reduced the effect of the measurement order on the results.
A total of four trials were conducted in each case.
3.4 Angle and Force Measurement
The ankle joint angle was measured by monitoring thedirection of gravity using two three–axis accelerometersattached to the foot and tibia. The sensors were attachedin the regions where there was no signiﬁcant deformationin the skin surface due to ankle movement. The angle inan upright position was 0◦ along with a positive dorsiﬂexion angle.
The force applied on the forefoot was measured usinga three–axis force sensor (USL08–H18–1KN–AP, TEC
GIHAN Co., Ltd., Japan). Fig. 3 shows that the sensor
maintained contact with the thenar and hypothenar of thefoot sole via an acrylic plate (7 mm × 25 mm × 3 mm).
The measured forces f0 = [fy0 fz 0 ]T were transformed
into a force that was tangential and perpendicular to thefoot sole. f1 = [fy1 fz 1 ]T shown in Fig. 4 (a) can becomputed using the following equation:

3. EXPERIMENT
3.1 Objectives
Experiments were conducted to measure the ankle
joint angle and force applied on the forefoot and to also
investigate the appropriate position of the machine’s rotation axis.
3.2 Participants
Five healthy volunteers participated in the experiments. They had no foot or leg injuries prior to commencing the experiments.
3.3 Procedures
Participants sat in a chair and experienced the stretching of the machine. The knee joint was fully extended bychanging its position relative to the stretching machine.
Fig. 3 shows that the position of the machine’s rotation
axis relative to the ankle was changed by placing a few
cushions (7 mm in thickness) below the heel. No cush-

f1 = Rx (ϕ)f0(1)

where, Rx (ϕ) is the coordinate transformation matrix
around the x axis, and ϕ is the angle between the footsole and the upper surface of the machine’s moving component (the acrylic board). The x axial forces fx 0 and fx 1
were not used as this study only focused on the movement404

Fig. 4 Force applied on the forefoot. (a) fy1 and fz 1 are
the forces that are tangential and perpendicular to thefoot sole, respectively. l is the length between the ankle and the point of force application. a and b are thelengths of the sides of the triangle with hypotenuse l .
(b) fdorsi is the force that contributes to ankle dorsiﬂexion and θdorsi is the ankle joint angle.
in the sagittal plane. Thus, the resultant force on the fore
foot can be expressed as:√(2)
f = fy1 2 + fz 1 2 .

Fig. 5 An example of the dorsiﬂexion angle ,and they– and z –axial forces applied on the foot. Top: The
dorsiﬂexion angle continued to increase till the footreached the end of the ankle motion range in all thecases. Middle: The changes in the y–axial force weredifferent for different positions of the rotation axis.
The force increased with changes in the dorsiﬂexion
angle in the depicted case. Bottom: The z –axial force
kept increasing during operation in all the cases andamongst all participants.

3.5 Force and Work for Ankle dorsiﬂexion Caluculations
The force contributing to and work associated withdorsiﬂexion were calculated from the measured ankle
joint angle and forces.
The force contributing to dorsiﬂexion is the component that is perpendicular to the line segment of length l ,as shown in Fig. 4 (b). This force can be calculated as:
fdorsi = fy1 sin θ + fz 1 cos θ(3)where, θ is the angle shown in Fig. 4 (a) that was calculated as:a
θ = arctan(4)busing the measured lengths a and b.
The work in the dorsiﬂexion angle θdorsi range of 10◦ –◦20 was calculated as:∫ 20
W =fdorsi · l d θdorsi .
(5)Fig. 6 shows the maximum values of the dorsiﬂexion
angle, the resultant force applied on the foot and force
contributing to dorsiﬂexion, and the work for ankle dorsiﬂexion seen in all the cases. The values corresponding to all the participants were normalized to the meanvalues in case 3, wherein the machine’s rotation axis approximately aligned with the ankle. The outliers in eachdataset were eliminated by Smirnov–Grubbs test for eachcase. The number of the of data outliers corresponding to
the dorsiﬂexion angle, resultant force, force contributing
to dorsiﬂexion, and work equaled 8, 4, 5 and 8 samples,
respectively, when a total of 140 samples from all the participants was considered.
Fig. 6 (a) shows that the maximum dorsiﬂexion angles did not signiﬁcantly vary between the different position levels of the machine’s rotational axis (p = 0.39).
Fig. 6 (b) shows that the maximum resultant force had nodependency on the position of the machine’s rotation axis
(p = 0.09). Fig. 6 (c) shows that the force contributing
to dorsiﬂexion decreased signiﬁcantly (p < 0.05) withan increase in the case number. On the other hand, thework increased signiﬁcantly with an increase in the casenumber (p < 0.001) as shown in Fig. 6 (d).

10

4. RESULTS
Fig. 5 shows an example of the changes in the ankle
dorsiﬂexion angle, and the y and z axial forces during
an operation. The illustrated results are from one participant in case 4. The foot was dorsiﬂexed and reached
the end of the range of ankle motion approximately 15
s after operating the machine. The dorsiﬂexion angle
was subsequently approximately stable, while the z axial force continued to increase during machine operation.
These trends did not depend on the position of the machine’s rotation axis and the individuals. The changes inthe y axial force were different in each of the cases under consideration. In the case shown in Fig. 5, the y axial
force increased with an increase in the dorsiﬂexion angle,
whereas it decreased after reaching its maximum value
in a few cases. The maximum values in all cases weredifferent for each individual or position of the machine’s
rotation axis.

5. DISCUSSION
The maximum dorsiﬂexion angle was expected to increase when the misalignment between the machine’s rotation axis and ankle reduced. However, the results in405

Fig. 6 Experimental results. The data values corresponding to each participant were normalized to that in case 3.
(a) Maximum dorsiﬂeixon angle. There was no dependence on the position of the machine’s rotation axis. (b) Resultant force applied on the foot. There was no dependence on the position of the machine’s rotation axis. (c) Forcecontributing to ankle dorsiﬂexion. This decreased as the machine’s rotation axis was moved below the ankle. (d) Work
for ankle dorsiﬂexion. This increased as the machine’s rotation axis was moved below the ankle.
Fig. 6 (a) show that the position of the machine’s rotation axis had a smaller effect on the stretching effect interms of the maximum dorsiﬂexion angle. Stretching is
generally performed to improve the range of joint motion.
However, in our study, the maximum dorsiﬂexion angle
was not used as an indicator of the stretching effect.
Figs. 6 (b) and (c) show that the resultant force applied on the forefoot remained constant, while the force
contributing to dorsiﬂexion reduced when the machine’s
rotation axis was above the ankle (case 1). The force
not contributing to dorsiﬂexion is perpentdicular to thatmaking a contribution, which was greater towards case
1. Further, the work for dorsiﬂexion was larger when themachine’s rotation axis was positioned above the ankle.
The force that did not contribute to dorsiﬂexion waslarge in cases where the work was also large. This can be
related to the efﬁciency of dorsiﬂexion as follows. Theinternal pressure in the talocrural joint rose and increased
the ankle stiffness when the force not contributing to dorsiﬂexion increased towards the ankle. An increase in theankle stiffness caused reduced efﬁciency and increased
the work.
Here, we describe the techniques adopted by the physical therapists. The foot is dorsiﬂexed by stretching theankle plantar ﬂexors. Simultaneously, the heel is held andpulled by some therapists along the downward directionof the lower leg’s longitudinal axis [15] (Fig. 7). These
techniques are performed to separate the talocrural joint
and improve the efﬁciency of ankle movement. Additionally, such methods are used to directly stretch the muscles

Fig. 7 An illustration of manual stretching. Physical therapists hold the heel and push the sole whenstretching the muscles. Some therapists tend to pull
the heel in the distal direction.

along the running direction, which terminate at the heel.
This ensures that the therapists not only dorsiﬂex the footbut also simultaneously incorporate techniques to reduce
the ankle stiffness. It is reasonable to speculate while theabove factors into consideration that the force not contributing to dorsiﬂexion increased the work for dorsiﬂexion in our experiments.
There is to date a belief that the alignment of the machine’s rotation axis with the ankle is safe and efﬁcient.
However, our study found that a misalignment between
them is not signiﬁcant in terms of the maximum dorsiﬂexion angle. Rather, there is an increase in the efﬁciency
and the force not contributing to dorsiﬂexion can be prevented from being generated when the machine’s rotation
axis is positioned above the ankle.

406

6. CONCLUSIONS

L. Q. Zhang, “Developing a wearable ankle rehabilitation robotic device for in–bed acute stroke rehabilitation,” IEEE Transaction on Neural Systems
and Rehabilitation Engineering, vol. 25, no. 6, pp.
589–596, 2016.
[11] N. Yamada, S. Okamoto, Y. Akiyama, K. Isogai,
and Y. Yamada, “Ankle stretching rehabilitation machine for equinovarus: Design and evaluation fromclinical aspects,” Proceedings of IEEE International
Conference on Systems, Man, and Cybernetics, pp.
1687–1692, 2017.
[12] T. Kimura, S. Okamoto, N. Yamada, Y. Akiyama,
K. Isogai, and Y. Yamada, “Ankle stretching rehabilitation machine for equinovarus: Automation ofeversion and ﬂexion control,” Proceedings of IEEE
International Conference on Systems, Man, and Cybernetics, pp. 2696–2700, 2017.
[13] N. Saga and N. Saito, “Rehabilitation instrument
for prevent contracture of ankle using the pneumatic balloon actutator,” Proceedings of Annual
International Conference on IEEE Engineering in
Medicine and Biology Society, pp. 4294–4297,
2008.
[14] H. Toda, T. Matsumoto, R. Tanizaki, and T. Imaeda,“Ankle joint pushing mechanism by stabilization of
ankle position using a brace structure,” Journal ofAdvanced Mechanical Design, Systems, and Manufacturing, vol. 10, no. 1, p. JAMDSM0013, 2016.
[15] N. Yamada, S. Okamoto, Y. Akiyama, K. Isogai,
K. Kawakami, and Y. Yamada, “Commonality andindividuality in manual stretching of physical therapists for equinovarus,” Proceedings of IEEE/SICE
International Sym posium on System Integration, pp.
495–460, 2014.

In this study, we investigated the rotation axis position of the stretching machine in the sagittal plane to improve the stretching effect. The force applied on the forefoot and ankle joint angles were measured to evaluate theeffect caused by the changes in the position of the machine’s rotation axis. There was an increase in the force
and work when the machine’s rotation axis was locatedbelow the ankle. The force can raise the internal pressurein the talocrural joint and increase ankle stiffness, thus,increasing the work. The results obtained in this study
are reasonable when taking the techniques used by physical therapists into consideration. It can thus be suggested
that placing the machine’s rotation axis above the ankle
can increase the machine’s stretching efﬁciency.

REFERENCES[1] Y. Shiraishi, S. Okamoto, N. Yamada, K. Inoue,
Y. Akiyama, and Y. Yamada, “Pneumatic–driven
ankle stretching machine,” Proceedings of IEEE
Global Conference on Life Sciences and Technologies, pp. 10–11, 2019.
[2] B. Singer, J. Dunne, and G. Allison, “Reﬂex andnon-reﬂex elements of hypertonia in triceps suraemuscles following acquired brain injury: implications for rehabilitation,” Disability and Rehabilitation, vol. 23, no. 17, pp. 749–757, 2001.
[3] A. Lamontagne, F. Malouin, and C. Richards, “Contributions of passive stiffness to ankle plantar ﬂexor
moment during gait after stroke,” Archives of Physical Medicine and Rehabilitation, vol. 81, no. 3, pp.
351–358, 2000.
[4] A. F. Thilmann, S. J. Fellows, and H. F. Ross,“Biomechanical changes at the ankle joint after
stroke,” Journal of Neurology, Neurosurgery & Psychiatry, vol. 54, no. 2, pp. 134–139, 1991.
[5] J. H. Carr and R. B. Shepherd, Neurological
Rehabilitation: Optimizing Motor Performance.
Churchill Livingstone, 1998.
[6] A. M. Mosely, “The effect of casting combined withstretching on passive ankle dorsiﬂexion in adults
with traumatic head induries,” Physical Therapy,
vol. 77, no. 3, pp. 240–247, 1997.
[7] C. I. Morse, O. R. Seynnes, C. N. Maganaris, and
D. A. Jones, “The acute effect of stretching on thepassive stiffness of the human gastrocnemius muscle tendon unit,” Journal of Physiology, vol. 10,
no. 1, pp. 97–106, 2008.
[8] G. Waldman, C. Y. Yang, Y. Ren, L. Liu, X. Guo,
R. L. Harvey, E. J. Roth, and L. Q. Zhang, “Effectsof robot-guided passive stretching and active movement training of ankle and mobility impairments
in stroke,” NeuroRehabilitation, vol. 32, no. 3, pp.
625–634, 2013.
[9] J. Wissel, A. Manack, and M. Brainin, “Toward an
epidemiology of poststroke spasticity,” Neurology,
vol. 80, pp. S13–19, 2013.
[10] Y. Ren, Y. N. Wu, C. Y. Yang, T. Xu, R. Harvey, and407