Orthosis with a controllable plantar height for fall prevention using acompact magnetorheological fluid brake
Kohei MORIMURA1, Rieko YAMAMOTO1.2, and Toshihiko SHIRAISHI1*
1) Graduate School of Environment and Information Sciences, Yokohama National University
79-7, Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan
2) Department of Rehabilitation Medicine, Keio University School of Medicine, 35 Shinanomachi, Shinjuku-ku,
Tokyo, 160-8582, Japan

E-mail: kmori554b.htoy@gmail.com (Kohei MORIMURA)
yamamoto-rieko-tz@ynu.jp (Rieko YAMAMOTO)
shira@ynu.ac.jp (Toshihiko SHIRAISHI)*Corresponding author

Abstract
In this study, a compact magnetorheological (MR) fluid brake embedded in an orthosis was designed and fabricatedto maintain plantar height for use in lateral fall prevention, and its performance and the fall prevention effect of the orthosis
were evaluated. The results of the brake design and fabrication indicated that the MR fluid brake has the advantage of being
compact, lightweight, and power-saving at 88.4 mm long, 128 g, using two AA batteries. Performance tests of the brakeindicated that it was able to generate sufficient force (125N) to maintain plantar height. Furthermore, through theassessments of lateral fall, the center of gravity and center of pressure inclination angle of a subject wearing the orthosis
without the MR brake was determined to be 4.0˚, as opposed to 4.4˚ with the MR fluid brake in the ON state. Therefore,
the moment of force acting on the subject to prevent fall was larger, making them more stable when the MR fluid brake
was in the ON state.

Keywords
Magnetorheological fluid, brake, controllable device, wearable device, fall prevention, plantar

1.

Introduction
In

recent years, hospital stays have shortened, and the number of people with disabilities living in thecommunity has been increasing. Living in a community requires necessary activities such as shopping , hospital visits,
etc., that require to walk on uneven surfaces, such as inclines and uneven surfaces outdoors, and on flat surfaces1indoors. The elderly, hemiplegic patients, and cerebellar ataxia, who often show a decreased lateral stability, areparticularly prone to losing their balance in the lateral direction during the stance phase on the affected side, leading
to lateral falls. According to a study that examined fall direction, 34% of falls in elderly were lateral (Cummings andNevitt, 1989).The higher risk of falling when walking on a lateral incline was found to be due to the increased activityof the peroneal muscles to maintain balance compared to walking on flat surface (Bavdek, Zdolsek, et al., 2018). The
other factor is that the distance of the outward center of gravity (COG) movement is significantly smaller in the groupthat has experienced falling than in the group without experience (Barak, Wagennar, et al., 2006). Pelvis acceleration
is significantly smaller in the elderly than in the young when walking on level and uneven grounds (Menz, Lord, etal., 2003); thus, the COG movement range is smaller in the elderly, leading to increased risk of lateral fall (Takai,
Miyano, et al., 2001). A lateral fall would likely cause femoral neck fractures, which are severe and would likely
require hospitalization. The risk of complications and mortality from immobility is high (WHO scientific group, 2003).
Lateral fall prevention is an essential factor for maintaining safe mobility in their community and associated daily
activity level that requires a specific solution. To this end, we consider herein a wearable device that can be used
unobtrusively in the user's living environment and daily life, preventing falls only when a risk occurs.
The COG–center of pressure (COP) inclination angle is used as an index to evaluate the effect of fall prevention.
Many studies have used the COG movement and the relative position of the COG to the COP to investigate thewalking stability (MacKinnon and Winter, 1993; Kaya, Kreb, et al., 1998). Examples include the COG momentum(Kaya, Kreb, et al., 1998) and the maximum horizontal distance between COG and COP (Krebs, Gillbody, et al.,
1993; Krebs, McGibbon, et al., 2001). However, these values may be affected by the subject's height (Berger, Trippel,
et al., 1992); thus, it is necessary to have a gait stability index that can eliminate the variation among subjects. The
angle between the line connecting COG and the COP and the vertical line passing through the COP (COG–COP
inclination angle) has been proposed as an index. This angle may be used to evaluate the risk of falling (Lee and Chou,
2006). We focus on insole therapy to investigate methods of fall prevention. The plantar orthosis used in insole therapy
is an orthotic device used to treat pain in osteoarthritis of the knee and big toe and prevent foot injuries in athletes.
The main effects of foot orthosis have been reported from various biomechanical perspectives, such as correcting thealignment of the lower limb and the whole body, eliminating pain by load distribution, and improving the shock
mitigation function during ground contact during walking (Kobayashi and Shimizu, 2014). When a plantar orthosis
provides plantar height to the lateral side of the foot, the COP moves laterally, and the COG–COP inclination angle
increases (Figure 1). In the case that a subject rotates with an angular velocity and the point where the combined forceof gravity and inertia acting on the COG is projected onto the floor is inside the base of support (BOS) (Figure 1 left),the moment of force to prevent fall does not act on the subject leading to instability and a fall . On the other hand, inthe case that a subject rotates with an angular velocity and the projected point described above exceeds the BOS limit
and is in the opposite side to the rotation by a planter orthosis (Figure 1 middle), the moment of force to prevent fall2

acts on the subject to provide stability. Therefore, although foot sole plates are not currently used to prevent falls, they
can be used for this purpose by controlling the plantar height.
A magnetorheological (MR) fluid brake, which is compact, light, and power-saving, but is able to generate alarge amount of force and is highly responsive, is used to control the plantar height only when there is a risk of falling.
The MR fluid is a fluid in which micron-sized magnetic particles are dispersed in the carrier fluid (Rabinow, 1948).
The yield shear stress changes in a few milliseconds depending on the external magnetic field. MR fluid has been
applied to devices such as dampers and engine mounts for vibration control by taking advantage of its force control
range and responsiveness (Shiraishi, Miida, et al., 2011; Shiraishi, Misaki, 2016; Phu, Choi, 2019; Phu, Choi, et al.,2014; Phu, Shah, et al., 2014). The MR fluid response to the magnetic field can be applied to a device to generate africtional force against an external force, which can be used as a braking force. This study aims to develop an orthosis
with a controllable plantar height to prevent fall of people with walking disabilities using a compact MR fluid brake.
First, we designed and fabricated a compact MR fluid brake that can maintain the plantar height. Next, we combined
it with footwear, a controller, batteries, and a sensor to develop an orthosis for fall prevention. Subsequently, the MR
fluid brake characteristics, including the component of the generated force and its magnitude and the response to theimpact load by a human walking, were examined to verify whether the MR fluid brake could act as a brake that cancontrol the plantar height. Finally, an experiment was conducted to evaluate the fall prevention effect of the orthosis.

Plantar height is provided.
Angularvelocity

COP moves laterally.
Moment offorce toprevent fall

COG

COP-COG inclination angle increases.
Point where force is projected onto afloor exceeds BOS limit.
Moment of force to prevent fall acts.

θ COG–COP
inclination
angle

θ

COP

MR fluid brake

PlantarheightFigure 1 Image of fall prevention with the MR fluid brake. The COP moves laterally, and the COG–COP
inclination angle increases by giving the plantar height. The COG–COP inclination angle is a gaitstability index.

2.

Orthosis with a controllable plantar height for fall prevention
2.1 Design of a compact magnetorheological fluid brake3

The MR fluid brake was designed to be compact and light, able to generate enough force to support body weight,
and is responsive enough to prevent falls. The MR fluid brake structure mainly consisted of a cylinder and a piston(Figure 2). An O-ring between the piston and the cylinder was unnecessary to reduce the sliding resistance. The
magnetic circuit spanned both the piston and the cylinder. A double-rod type, which did not require air to interpolate
the volume of the piston rod, was adopted to prevent air from entering the MR fluid and the which would prevent thedevice from acting as a brake. Although the mass that affects the walking speed and the muscle activity is 1.5 kg(Omuro, Shiba, et al., 2011), the maximum weight of the device should be approximately 300 g based on theexperience of physical therapists observing patients walking. The MR fluid brake stroke was set at 7 mm to allow a
margin for the Iritani plantar plate, which uses a 6 mm-thick arch pad (Iritani, 2017).
Figure 3 illustrates the design flow. The generated force of the MR fluid device, in which the pressure mode isdominant, was obtained by the product of the pressure-receiving area of the piston and the pressure difference before
and after the orifice. We determined the pressure difference and pressure-receiving area after determining the desiredwithstand load. To achieve a compact MR fluid brake, the pressure-receiving area must be small; therefore, thepressure difference must be increased. Since the channel height must be reduced to achieve a large pressure difference,
it was set as 0.5 mm as that is minimum setting from the general in the range of 0.5 to 2 mm (Nanthakumar andJancirani, 2019). The number of coil turns and piston outer diameter were determined by B–H curve of the MR fluid
and the experimentally-derived equation as described below, respectively.

Figure 2 Schematic diagram of the MR fluid brake.
4

Figure 3 Design process flowchart.

Withstand load
Equation (1) expresses the force F generated by the MR fluid brake.

𝐹𝐹 = 𝐹𝐹𝜏𝜏 + 𝐹𝐹𝜂𝜂 + 𝐹𝐹𝑓𝑓(1)

where, 𝐹𝐹𝜏𝜏 : force due to the yield stress of the MR fluid; 𝐹𝐹𝜂𝜂 : force due to viscosity as a Newtonian fluid; and 𝐹𝐹𝑓𝑓 : sliding
friction force by the seal material.

Of these forces, 𝐹𝐹𝜏𝜏 is the force that can be controlled by an external magnetic field, while 𝐹𝐹𝜂𝜂 and 𝐹𝐹𝑓𝑓 are theforces that occur, even when no magnetic field is applied. 𝐹𝐹𝜏𝜏 and 𝐹𝐹𝑓𝑓 act as the braking force. The MR fluid brake

was placed outside of the foot, and the stepping force was transmitted to the MR fluid brake using a load-bearing partbased on the principle of leverage. Based on the foot width and the MR fluid brake position, the distance from thecenter of rotation to the load-bearing target point was determined as 40 mm, and the distance to the MR fluid brakewas 90 mm (Figure 4).

5

We assumed that the entire body weight was applied to the load-bearing part. It is reported that the heaviest
average weight for men was 70.3 kg for 40 to 49 years old, while that for women was 55.2 kg for 50 to 59 years old(Statistic Bureau of Japan, 2016). Assuming that the target heaviest weight was 70.3 kg, the load applied to the MR
fluid brake can be calculated as follows:

70.3 [kg] × 9.8 [m⁄s 2 ] ×

40 [mm]= 306.1 [N]
90 [mm](2)

Assuming that the safety factor of disc brakes is 1.5 for reference (Naikwadi, 2017), the allowable load is as follows:

306.1 [N] × 1.5 = 459.1 [N](3)The influence of 𝐹𝐹𝜂𝜂 and 𝐹𝐹𝑓𝑓 was smaller than that of 𝐹𝐹𝜏𝜏 when the electric current was sufficiently large. Therefore,

the maximum controllable force of the MR fluid brake 𝐹𝐹𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏 was set as the allowable load, and 𝐹𝐹𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏 = 460 N.
PistonAmong the many components, the piston design is described because this part is the key to reducing the size andweight of the MR fluid brake. The material is structural carbon steel commonly used in DC electromagnets. Among
structural carbon steels, S10C was used because of its lower carbon content, which has been found to give better
magnetic properties (Ishiguro, Tsuboshima, et al., 1978). Considering the length of the MR fluid brake when placedoutside of the foot, the piston height ℎ𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 was determined as 12.5 mm. The cross-sectional area perpendicular tomagnetic fluxes I, II, and III should be designed to be the same to avoid magnetic saturation due to a local decreasein the cross-sectional area in a magnetic circuit (Figure 5). The piston outer diameter 𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑛𝑛 was determined using
the equation experimentally derived under the condition that cross-sectional areas I and II are the same.

6

Figure 5 Detailed view of the piston.

ℎ𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =22− 𝑑𝑑𝑟𝑟𝑟𝑟𝑟𝑟
𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
2𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐(4)

As a fundamental property of the MR fluid in the pressure mode, Equation (5) was experimentally derived for the
relation between the pressure difference before and after the orifice and the magnetic flux density (Shiraishi andMorishita, 2004).

Δ𝑝𝑝 = (6.89 × 103 ⁄𝑙𝑙𝑀𝑀𝑀𝑀 )𝐵𝐵2 + 𝑏𝑏

(5)

The value of b does not significantly change with the change of the channel height; hence, we set 𝑏𝑏 = 1.37 × 105 ,which is the value at 𝑙𝑙𝑀𝑀𝑀𝑀 = 0.5 mm. The force F generated by the MR fluid device, where the pressure mode isdominant, can be obtained from the product of the pressure-receiving area A of the piston and the pressure differenceΔp before and after the orifice. The pressure difference is divided into a term that depends on the magnetic flux density
generated in the MR fluid by applying an external magnetic field and a term that does not depend on the magnetic
flux density. The maximum force 𝐹𝐹𝜏𝜏𝜏𝜏𝜏𝜏𝜏𝜏 that can be controlled by the MR fluid brake is obtained by increasing thepressure difference to Δ𝑝𝑝𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 by an external magnetic field:𝐹𝐹𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 = Δ𝑝𝑝𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 𝐴𝐴(6)𝐹𝐹𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 is proportional to the channel length in the section where the magnetic field is applied; therefore, it can be

expressed as follows from Equations (5) and (6).

7𝐹𝐹𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚 = �

6.89 × 103 2
𝐵𝐵𝑚𝑚𝑚𝑚𝑚𝑚 + 𝑏𝑏� 𝐴𝐴 𝐿𝐿𝑑𝑑𝑑𝑑𝑑𝑑 ⁄𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒𝑙𝑙𝑀𝑀𝑀𝑀(7)

Equation (8) can be derived by solving for 𝑙𝑙𝑀𝑀𝑀𝑀 and substituting Equation (4).
2𝑙𝑙𝑀𝑀𝑀𝑀 = 6.89 × 103 𝐵𝐵𝑚𝑚𝑚𝑚𝑚𝑚
�−1

2𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒𝐹𝐹𝜏𝜏𝑚𝑚𝑚𝑚𝑚𝑚
− 𝑏𝑏�
2
2
2
2
𝜋𝜋𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 𝜋𝜋𝑑𝑑𝑟𝑟𝑟𝑟𝑟𝑟 𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐− 𝑑𝑑𝑟𝑟𝑟𝑟𝑟𝑟
4

−

4

(8)

𝐿𝐿𝑒𝑒𝑒𝑒𝑒𝑒 is the length of the flow path, where the magnetic field is applied in the characterization device (i.e., 20 mm)(Shiraishi and Morishita, 2004). The piston rod outer diameter 𝑑𝑑𝑟𝑟𝑟𝑟𝑟𝑟 was set to 5 mm for a small size. The dent forwinding the coil�𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 −𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 �2

was determined by considering the copper wire diameter and the number of coil layers.

If the coil winding dent is known, the inner diameter of the coil 𝑑𝑑𝑐𝑐𝑐𝑐𝑖𝑖𝑖𝑖 can be determined by the piston outer diameter

𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 ; therefore, Equation (8) becomes a relation between 𝑙𝑙𝑀𝑀𝑀𝑀 and 𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 when 𝐵𝐵𝑚𝑚𝑚𝑚𝑚𝑚 is determined. We set the

maximum operating magnetic flux density 𝐵𝐵𝑚𝑚𝑚𝑚𝑚𝑚 to 0.9 T. From the above, the channel height and piston volume arecalculated when the piston outer diameter is varied as a parameter. The smaller the piston outer diameter, the smaller

the piston volume, which leads to a smaller overall device; however, a smaller channel height is required to generate
the desired force. Assuming 𝑙𝑙𝑀𝑀𝑀𝑀 = 0.5 mm to prevent clogging, the piston outer diameter is set to 15.5 mm.
ResponsivenessAs a control method, when the MR fluid brake was incorporated into a fall prevention device, two AA batteries
were used to supply electric current to the MR fluid brake when the lateral inclination of the road exceeded a certain
angle. However, the self-inductance of the coil acted to cancel the current; thus, it took time for the current to rise.
The time constant 𝜏𝜏 was calculated to evaluate whether the device can prevent fall in time. The time constant can becalculated as the self-inductance L and resistance R from Equation (9).

𝜏𝜏 =

𝐿𝐿
𝑅𝑅

(9)

The self-inductance is obtained from the number of coil turns that satisfy the desired magnetic flux density andthe coil height obtained earlier. The time constant is 179 ms.
We then consider whether this time constant is sufficient to prevent falling. In this study, an electric current must
be applied when a lateral inclination of the walking path is detected by an accelerometer attached to the target foot8

before the next initial contact of the target foot. Considering the gait cycle from the initial ground contact of the target
foot (0%) to the next initial ground contact (100%), the lateral inclination should be detected at the foot flat phase(10%); the electric current should start to flow after the toe off (60%); and the MR fluid brake should prepare to
generate force against the external force by the next initial ground contact (100%) described in control low of Section
2.2 in detail (Figure 6). Since a walking cycle is approximately 1 s (Murray, Kory, et al., 1969), the time from thestart of the current flow to the response of the MR fluid must be within 400 ms or 40% of a walking cycle considering
applying the electric current at the toe off. Assuming that the sampling period of the sensor is 10 ms, the required
response time of the MR fluid is 400 ms–179 ms–10 ms = 211 ms. This MR fluid brake can be used to prevent fallbecause its response time is a few milliseconds.

Figure 6 Schematic diagram of walking cycle (Andrew, Arima, et al., 2018) adding inclination detection andcurrent outputting timing for the fall prevention control.

Parameter
We designed and fabricated an MR fluid brake that is compact, light, and power-saving, generates enough force
to support the body weight, and is responsive enough to prevent falls (Figure 7). Table 1 lists the parameters
determined in the design.

9Figure 7 Compact and light MR fluid brake (128 g).
Table 1 Parameters of the MR fluid brake.
Parameter

Value

Mass

128 g

Piston outer diameter (𝑑𝑑𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 )15.5 mm

Channel height (𝑙𝑙𝑀𝑀𝑀𝑀 )0.5 mmCylinder outer diameter (𝑑𝑑𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 )Coil height (ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 )20 mm
7.7 mmStroke7 mm

Number of coil turns (N)Time constant (𝜏𝜏)

80
179 ms

2.2 Orthosis development
The MR fluid brake was combined with sandals, a controller, batteries, and a sensor to develop a fall prevention
device (Figure 8). Sandals with a stiff sole were chosen such that the MR fluid brake effect on the plantar height canbe easily seen. As for the point where the adjustment to the plantar height is applied, the reaction when the plantar
height is given to the entire sole differs from person to person, which may make the gait unstable. Dynamic balanceis improved by supporting the cuboid bone (Takata, Takeda, et al., 2016); hence, the plantar height is given not to theentire sole, but to the vicinity of the tuberosity of the fifth metatarsal bone, including the cuboid bone. The MR fluid
brake was placed outside of the sandal, and the stepping force was transmitted to the MR fluid brake by using a loadbearing part based on the leverage principle. An inertial measurement unit (IMU, Umemoto LLC, REES-01) that
detects three-axis acceleration and three-axis angular velocity was used to measure the road inclination angle and10detect the ground contact. The sensor was controlled by a microcontroller (Arduino, Arduino Uno Rev3 A000066).
The controller and the IMU location were placed above the ankle so as not interfere with walking, if they were placed
as close to the ankle joint as possible. However, their mass was relatively light (approximately 40 g). The IMU wasused to determine the posture from the acceleration of the gravity component when the foot stopped moving
momentarily after the foot made contact with the ground; thus, we attached the sensor directly to the belt part of theinstep, which showed little relative motion with the foot. Two batteries were required: one to supply power to thecontroller and the other for the MR fluid brake. Both batteries were mounted on the lower leg. For the controller, wechose a battery that could continuously supply power, even at low currents without activating the protection function.
The MR fluid brake required 1.3 V; hence, we used two AA batteries of 1.5 V connected in series to provide sufficient
power. Since the voltage is 3 V and the resistance is 0.89 Ω, the input current is 3.4 A which is enough for the MR
fluid brake to act as a brake as described below.

Figure 8 Fall prevention orthosis using the MR fluid brake: (a) Overall view of the fall prevention orthosis using
MR fluid brake. (b) Enlarged view near the sandal. The MR fluid brake is placed outside of the sandal.
11

Control law
When the lateral inclination angle of the road exceeds 5˚ during walking, the switch is turned ON 0.5 seconds
after the angle exceeds 5˚ and turned OFF 1 second later so that the electric current flows at the next foot contact.
According to Road Structure Ordinance, the standard cross slope of a sidewalk is 2% (1.1˚) or less, but the slope
where a vehicle enters a sidewalk is 15% (8.5˚) or less (MLIT, 2003). The threshold was set at 5˚ considering fall
prevention when people with balance disorders walk on a slope greater than the standard cross slope. We used themagnitude of the acceleration of gravity distributed to each axis by the tilt of the IMU itself for lateral inclination
angle measurement. The orientation of the axes of the IMU attached to the sandal is shown in Figure 9. The
acceleration of each axis is 𝑎𝑎𝑥𝑥 , 𝑎𝑎𝑦𝑦 , or 𝑎𝑎𝑧𝑧 . The angular velocity around each axis is 𝜔𝜔𝑥𝑥 , 𝜔𝜔𝑦𝑦 , or 𝜔𝜔𝑧𝑧 . The lateralinclination angle is calculated from Equation (10).

𝜃𝜃𝑥𝑥 = tan−1

𝑎𝑎𝑦𝑦�𝑎𝑎𝑥𝑥2 + 𝑎𝑎𝑧𝑧2(10)

Figure 9 Axis of the IMU attached to a sandal. A positive roll angle indicates clockwise motion.

However, the values observed by the sensor are a mixture of those caused by the foot placed and those causedby the lateral inclination angle of the road. Therefore, to measure the lateral inclination angle, it is necessary torecognize the state of foot contact where the foot stops moving temporarily. In a preliminary experiment, the IMU
was attached to the toe, and acceleration and angular velocity were measured during walking. As a result, when the
difference between the composite acceleration a and the acceleration of gravity g is less than a certain small value ∆aand the composite angular velocity ω is less than a certain small value ∆ω for a certain period of time ∆t, the state isconsidered to be foot contact. In Equation (11), scon is a variable representing the foot contact state (1: foot contact, 0:
otherwise) in walking and depends on time t.

1, if |𝑎𝑎| − 𝑔𝑔 < ∆𝑎𝑎 and |𝜔𝜔| < ∆𝜔𝜔 during 𝑡𝑡 − ∆𝑡𝑡 ~ 𝑡𝑡
𝑠𝑠con = �0, otherwise
where , 𝑔𝑔 = 9.8 [m⁄s 2 ] , ∆𝑎𝑎 = 1.96 [m⁄s 2 ] , |𝜔𝜔| = �𝜔𝜔𝑥𝑥2 + 𝜔𝜔𝑦𝑦2 + 𝜔𝜔𝑧𝑧2 , ∆𝜔𝜔 = 25 [˚⁄s] , ∆𝑡𝑡 = 0.1 [s]
12

(11)

From the above, the control current I is expressed as Equation (12) in the case of a time in a walking cycle T.

𝐼𝐼 during 𝑡𝑡 + 𝑇𝑇⁄2 ~ 𝑡𝑡 + 3𝑇𝑇⁄2 , if 𝜃𝜃𝑥𝑥 > 5° and 𝑠𝑠con = 1
𝐼𝐼 = � 00, otherwise(12)

where 𝐼𝐼0 = 3.4 [A], 𝑇𝑇 = 1 [s].
We verified that the control law worked correctly by walking on a 10˚ inclined surface. A slope was placed in the middle
of a flat surface, and a subject wearing a fall prevention device walked along the path (Figure 10). After the right foot with
the MR fluid brake makes contacts with the ground on the slope, and when the MR fluid brake is released, it is set to 0 s.
The time when the current started to flow (tcurrent_ON), the time when the second step of the right foot made contact with theground (tinitial_contact), the time when the MR fluid brake was released on the second step of the right foot (trelease), and thetime when the current stopped (tcurrent_OFF) were measured. These trials were performed ten times. The sampling frequency
was 30 Hz. The results showed that the current started to flow between the MR fluid brake release of the first step of theright foot and the contact of the second step of the right foot, and the current stopped after the MR fluid brake release of
the second step of the right foot in all ten cases (Table 2). Therefore, it was confirmed that the control always operated
correctly.

13

Figure 10

The experimental setup for verification of sensor operation. (a) Schematic and (b)photograph.
Table 2 Checking the control of fall prevention device.

3.

Trial No.

t current_ON [s]t initial_contact [s]

1

0.2

0.67

1.24

2.44

2

0.17

0.6

1.23

2.4

3

0.27

0.6

1.24

2.4

4

0.2

0.6

1.23

2.4

5

0.2

0.6

1.27

2.4

6

0.23

0.6

1.23

2.4

7

0.2

0.6

1.27

2.4

8

0.23

0.57

1.2

2.37

9

0.2

0.6

1.23

2.4

10

0.24

0.57

1.2

2.37

Performance test of the MR fluid brake
3.1 Hysteresis loops for the MR fluid brake14

t release [s]t current_OFF [s]We verified that the generated force was small enough not to act as a brake during normal walking. We also
verified the frictional force necessary to act as a brake was dominant when there was a risk of falling and that thedevice performance was sufficient for use as a fall prevention device.

Methods
The MR fluid brake was fixed horizontally to the floor, and a spherical plain bearing was used at the connection
between the piston rod and the excitation part (Figure 11). The reason for installing this part was to prevent the MR
fluid brake from being damaged by excessive force when the direction of vibration and the MR fluid brake axis were
not aligned. A jig was used to prevent the excitation part from rotating during vibration, which would loosen the upper
lid and cause a leak of MR fluid. The piston displacement and the force generated by the MR fluid brake were
measured by a displacement sensor and a load cell attached to the hydraulic shaker and recorded by an oscilloscope.
A bipolar power supply was used as the power source to supply electric current to the coils in the MR fluid brake. A
hydraulic shaker was used to apply a sinusoidal forced displacement to the MR fluid brake, and the generated force
and the piston displacement were measured. The experimental conditions were amplitude of 2.5 mm, vibration
frequency of 1 Hz, and electric current of 0, 0.4, 0.8, 1.2, and 1.5 A.

15

Figure 11 The experimental setup for vibration test. (a) Schematic and (b) photograph.

Results and discussion
The hysteresis loops of the piston displacement and the generated force were almost rectangular representing thefrictional force required to act as a brake, with and the force increasing as the current increased (Figure 12). The
maximum force at 0 A was approximately 17 N, which was as small as expected. Compared to the MR fluid brakedeveloped in the previous study, which had a maximum force of approximately 180 N at 0 A (Morimura, Yamamoto,et al., 2019), the present design was confirmed to have a smaller initial resistance. In a preliminary experiment, wefabricated a slipper with an MR fluid brake that gives plantar height vicinity of the tuberosity of the fifth metatarsal
and examined the force applied to the MR fluid brake when a person applied a load. Assuming an average weight of
70.3 kg used in the design, approximately 69 N was applied to the MR fluid brake, therefore, the force of 17 N was
small enough not to act as a brake. The maximum force was approximately 125 N. Assuming that 69 N was applied
to the MR fluid brake from the preliminary experiment as before, 125 N was large enough to act as a brake.
In the MR fluid brake developed in the previous study, the force was not generated immediately after the piston
16

motion direction changed due to the effect of compressibility caused by air in the MR fluid (Morimura, Yamamoto,et al., 2019). On the other hand, the shape of the hysteresis loops was not perfectly rectangular in this experiment, but
the force rose immediately after the direction of motion changed. The displacement required for the force to rise wasapproximately 0.5 mm at 1.5 A, but this was not a problem because the plantar height commonly used in physicaltherapy is a few millimeters to 6 mm (Iritani, 2017), and the displacement of 0.5 mm is smaller than this height.
Therefore, it was confirmed that this device satisfied the performance requirements for a brake.

Figure 12 Vibration test results of MR fluid brake with an amplitude of 2.5 mm and a frequency of 1 Hz.

3.2 Response characteristics of the MR fluid brake to the impact load given by human walking
In an actual application, the MR fluid brake is attached to a shoe. A load is applied to the MR fluid brake every
time the shoe makes contact with the ground during walking. If there is a risk of falling, the piston is maintained
constantly against the load by the current from an external power source. The load applied by a human is not constant,but dynamic, including the impact load; hence, we applied load under the expected conditions of use to the MR fluid
brake and verified whether it operated as a brake when an electric current was applied. The piston was displaced
against external forces when no electric current was applied, such that the MR fluid brake did not give the plantar
height, except when there was a risk of falling.

Methods
The MR fluid brake was attached to a slipper and fixed to the ground to apply a load under actual use (Figure1713). The slipper height was adjusted so that the load-bearing part would be horizontal when the piston rod was most
retracted. The upper part of the slipper was removed such that the foot could contact the top of the slipper. When theslipper was stepped on with the foot, load was applied to the load-bearing part attached to the slipper. Subsequently,
load was applied to the MR fluid brake. The load-bearing part was large enough to give the plantar height at the
tuberosity of the fifth metatarsal. The load applied to the MR fluid brake and the piston displacement were measured
by a load cell and a laser displacement sensor, respectively, and recorded by an oscilloscope. Even if the piston rod is
extended by a maximum of 7 mm, the misalignment between the MR fluid brake axis and the vertical axis is so smallthat the experimental setup has sufficient precision to measure 99.8% of the original force. A bipolar power supply
was used to supply the electric current to the coils in the MR fluid brake. We started the experiment with the rightfoot one step behind, then swung the right foot forward and contacted the ground directly on the slipper. The
experiment was completed when the toes left the slipper. The load applied to the MR fluid brake and the piston
displacement were measured. The subject was a healthy person aging 23 years and weighing 55 kg. Two conditions
were tested: 0 A and 1.5 A current.

Figure 13

The experimental setup for measuring the MR fluid brake response when a person applies18

an impact load to the MR fluid brake. (a) Schematic diagram and (b) photograph. The
upper part of the slipper was removed on measuring it.

Results and discussion
The piston moved by approximately 2.5 mm when a human applied load at 0 A (Figure 14). In contrast, thepiston barely moved, even when a load was applied at 1.5 A (Figure 15). A 2.5 mm displacement when no electric
current was applied was smaller than a 7 mm stroke. This may be because the load applied to the MR fluid brake wassmaller than expected due to the plantar height being given only to a part of the sole. However, although thedisplacement without electric current was smaller than the stroke, the displacement was kept constant against the
impact load when the electric current was applied. The device acted as a brake when the electric current was applied.

Figure 14 Time series of the piston displacement and force applied to the MR fluid brake (0 A).

19

Figure 15 Time series of the piston displacement and force applied to the MR fluid brake (1.5 A).
4.

Evaluation test of the fall prevention effect of the orthosis
The COG–COP inclination angle on the frontal plane was measured when walking on a slope. The orthosis effecton preventing falls was evaluated from the minimum COG–COP inclination angle during the right-leg stance phasewith the attached MR fluid brake.
4.1 Methods
Four slopes with a low right side, whose angle was 10˚, were prepared. Three of the four slopes were placed
above the force plate (Figure 16). Eleven infrared markers were attached to the body, and the position of each marker
was measured by a high-precision 3D motion measurement system. The markers were attached to the top of the head,acromion process, buttocks, knee joint, ankle joint, and toes. The COG of each body segment part was determinedfrom the measurement results. The COG position was determined from each body part's mass ratio and center ofgravity (Nakamura, Nagasaki, et al., 2005). The COP position on the slope of the first step of the right foot of theslope was determined from the measurement results of the force plate (Figure 17(a)). Finally, the COG–COP
inclination angle was calculated from the COG and the COP on the slope (Figure 17(b)). The sampling frequency was
100 Hz for the 3D motion measurement system and 1000 Hz for the force plate.
The three conditions are as follows: 1) wearing a fall prevention device without the MR fluid brake, 2) with the
MR fluid brake attached and current OFF; and 3) current ON. The condition of the current ON corresponded to thecontrol of giving the plantar height when a risk of falling occurred.

20

Figure 16

The experimental setup for evaluation test of the fall prevention effect of the orthosis. (a)Schematic and (b) photograph. Lateral slopes are placed on the force plates. Eleven infraredmarkers are attached to each position on the body. The position of each marker is measured
by four cameras.

21

Figure 17 Analysis methods for the acquired data.
4.2 Results and discussion
The COG–COP inclination angle in the condition without the MR fluid brake, current OFF, and current ON was
4.0˚, 4.2˚, and 4.4˚ on average, respectively and they had some variation. There was a significant difference in theangle between current ON and the condition without the MR fluid brake (Figure 18). In a study that examined theeffect of the plantar height on fall prevention using a theoretical model that combined a self-righting doll and an
inverted pendulum, the COG–COP inclination angle with the MR fluid brake was larger than without it (Morimura,
Yamamoto, et al., 2020), which was consistent with the experiment results. In one of trials in the condition without
the MR fluid brake, the COG-COP inclination angle was 3.3˚ which was very close to the angle in the BOS limit ofthis subject estimated as 3.2˚ from the body measurement and the moment of force to prevent fall little acted on thesubject to be almost unstable as shown in Figure 1. On the other hand, the minimum value of trials in current ON was
4.1˚ far from the BOS limit angle of 3.2˚ and the moment of force to prevent fall acted on the subject to be stable. The
results indicate that the orthosis using a compact, light, and power-saving MR fluid brake is effective in preventing
lateral falls by increasing the COG–COP inclination angle by giving the plantar height when walking on a slope
simulating the falling risk.

22

Figure 18

Minimum value of the COG–COP inclination angle during contact of the first step of the rightfoot on the slope. The condition of the current ON corresponds to the control of giving theplantar height at the risk of falling.

5.

Conclusion
This study described the design and fabrication of a compact MR fluid brake capable of maintaining plantar
height for use in a lateral fall prevention orthosis, the development of an orthosis incorporating the MR fluid brake,
the performance evaluation of the MR fluid brake, and the evaluation of the fall prevention effect of the orthosis. The
MR fluid brake was compact, light, and power-saving, generates enough force to support the body weight, and is
responsive enough to prevent falls. The MR fluid brake is 88.4 mm long, has a cylinder outer diameter of 20 mm anda mass of 128 g, and operates on two AA batteries. The time constant was 179 ms, which is sufficient to prevent falls.
When the current was 1.5 A, the dominant generated force was the frictional force amounting to approximately 125
N, which is suitable for maintaining the plantar height. When the current was not applied, the force was approximately
17 N, and the MR fluid brake did not assist walking to improve the residual function during normal walking. In
addition, when the MR fluid brake was applied with an electric current, the piston position was maintained at aconstant level against the impact load applied by a human walking, indicating that the MR fluid brake is applicableas an actuator for the fall prevention device. When walking on a slope simulating the risk of falling while wearing thedeveloped orthosis, the COG–COP inclination angle of a subject in the condition without the MR fluid brake and with
the MR fluid brake in the ON state of current was 4.0˚ and 4.4˚, respectively, and the moment of force acting on thesubject to prevent fall was larger and the subject was more stable by the ON-state MR fluid brake.

Acknowledgments
The authors would like to thank Professor Haruhiko Sato and Mr. Hiroki Tanabe for technical assistance with theexperiments.
23

Funding
Part of this work was supported by “YNU Diversity Research Grant" under MEXT Funds for the Development of
Human Resources in Science and Technology, Japan, "Initiative for Realizing Diversity in the Research Environment(Collaboration Type).”Part of this work was supported by the Joint Research Promotion Program of the Research Institute of Environment
and Information Sciences, Yokohama National University, Japan, Joint Research Project “Type C”.

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