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  <front>
    <journal-meta><journal-id journal-id-type="publisher">MS</journal-id><journal-title-group>
    <journal-title>Mechanical Sciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">MS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Mech. Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">2191-916X</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/ms-14-429-2023</article-id><title-group><article-title>Wearable ankle assistance robot for a human walking with different loads</article-title><alt-title>Wearable ankle assistance robot for a human walking with different loads</alt-title>
      </title-group><?xmltex \runningtitle{Wearable ankle assistance robot for a human walking with different loads}?><?xmltex \runningauthor{J. Li et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name><surname>Li</surname><given-names>Junqiang</given-names></name>
          <email>lijunqiang@hebut.edu.cn</email>
        </contrib>
        <contrib contrib-type="author" corresp="no">
          <name><surname>Yang</surname><given-names>Kuan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no">
          <name><surname>Yang</surname><given-names>Dong</given-names></name>
          
        </contrib>
        <aff id="aff1"><institution>School of Mechanical Engineering, Hebei University of Technology, Tianjin, 300401, China</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Junqiang Li (lijunqiang@hebut.edu.cn)</corresp></author-notes><pub-date><day>11</day><month>October</month><year>2023</year></pub-date>
      
      <volume>14</volume>
      <issue>2</issue>
      <fpage>429</fpage><lpage>438</lpage>
      <history>
        <date date-type="received"><day>28</day><month>December</month><year>2022</year></date>
           <date date-type="rev-recd"><day>11</day><month>August</month><year>2023</year></date>
           <date date-type="accepted"><day>23</day><month>August</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 Junqiang Li et al.</copyright-statement>
        <copyright-year>2023</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023.html">This article is available from https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023.html</self-uri><self-uri xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023.pdf">The full text article is available as a PDF file from https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e92">To reduce energy consumption while a human is walking with
different loads, an active energy storage mechanism and a gait cycle
prediction method are proposed, and then a wearable ankle assistance robot
is developed. A motor, a clutch, and elastic rods are placed strategically in
the active energy storage mechanism to achieve energy storage and release.
During the period when the ankle does not generate torque, the clutch is
closed, and the elastic rods are driven by the motor to produce deformation
for energy storage. When the ankle generates torque, the motor is stopped
and the clutch is opened, and then energy is released. Assisted force is
transmitted to the human heel by a flexible transmission device to achieve
walking assistance. The deformation length of the elastic rods can be
changed to achieve assisted force adjustment for different loads. Based on
the hip angular displacement and heel pressure, the gait cycle can be
obtained with the proposed prediction method, and then assistance control
can be achieved. Consequently, the development of a wearable ankle
assistance robot is realized, a walking assistance experiment with different
loads is completed, and the net metabolic cost is used to indicate the
energy consumption. The experimental results show that the net metabolic
cost of the participants is reduced by averages of 5.30 %, 5.67 %, and
4.84 % with 0, 4, and 8 kg loads respectively. The reduced net
metabolic costs are compared with other research results; the reduced net
metabolic costs are close to the others, but the motor power in this work is
lower.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>National Natural Science Foundation of China</funding-source>
<award-id>U1813222</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e104">With progress in robotic research, robots are playing an increasingly
important role in military, industry, medicine, and daily life; robotics
provides new solutions to traditional problems (Qiao et al., 2022; Qi et
al., 2021). Walking with loads often occurs in the military (Mala et al.,
2015; Jones, 2005) and in daily life (Saelens et al., 2003). Compared with
walking without any load, walking with a load requires the consumption of
more energy (Browning et al., 2007; Hogan et al., 1998). Exoskeletons, such
as the Berkeley lower extremity exoskeleton (BLEEX) (Zoss et al., 2006) and
the Hybrid Assistive Limb (HAL) (Tsukahara et al., 2014), can be used to assist
humans in walking while carrying loads. However, this kind of exoskeleton
with several joints requires a complex control method and a greater energy
cost. In recent years, researchers have begun to focus on assisting single
or double lower limb joints with wearable devices (Kang et al., 2022; Han et al., 2020; Wang et al., 2020b).</p>
      <p id="d1e107">In the process of walking, the ankle provides approximately 35 % of the
mechanical work and accounts for 19 % of the metabolic cost (Gordon et
al., 2006; Sawicki and Ferris, 2009), so providing assisted force for the
ankle and reducing the activity of the leg muscles can reduce the energy
consumption of the human body (Wang et al., 2020a; Xie et al., 2021). In
view of such an important effect on the ankle, ankle assistance robots have
attracted the attention of researchers, and several excellent studies have
been proposed. The remainder of this article is organized as follows.
Section 2 introduces the related work of ankle assistance robot. Section 3
presents the design and working principle of the ankle assistance robot.
Section 4 introduces the control method of the robot. Section 5 carries out
experiments to verify the effectiveness of the ankle assistance robot.
Section 6 concludes this article.</p>
</sec>
<?pagebreak page430?><sec id="Ch1.S2">
  <label>2</label><title>Related work</title>
      <p id="d1e118">According to the operation mode, ankle assistance robots can be divided into
two categories: passive ankle assistance robots and active ankle assistance
robots. Passive ankle assistance robots have no power source or control
systems. They use components such as springs or artificial muscles to assist
ankle movement in the process of walking. In the flexible exoskeleton
developed by Park et al. (2014), four pneumatic artificial muscles
were used to simulate the structure of human muscles and ligaments to
provide power for the ankle. The passive ankle exoskeleton designed by
Collins et al. (2015) and Diller et al. (2016) had a light elastic
element that was parallel to the calf muscle, and a ratchet pawl mechanism
was used to achieve energy storage and release. As a result, the muscle
burden and energy consumption are reduced. The spring rate of the
exoskeleton was 180 Nm rad<inline-formula><mml:math id="M1" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, and the metabolic cost of walking flat on the
treadmill at a speed of 1.25 m s<inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> was reduced by <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.26</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.6</mml:mn></mml:mrow></mml:math></inline-formula> %. The
passive ankle assistance robot developed by Yandell et al. (2019)
was suitable for daily wear. It included a clutch on the sole and a linear
spring on the back of the shank. During walking, energy could be stored and
released in combination with the clutch and spring. The robot could adapt to
different walking speeds and did not limit the non-sagittal movement of
joints, and the average soleus activity was reduced by 5 %–17 % when the
robot was worn. Owing to the lack of a power source and control system, the
mechanical structure of the passive ankle assistance robot was simple, and
the weight was light.</p>
      <p id="d1e157">In contrast to passive ankle assistance robots, active ankle assistance
robots usually include a power source, one or more active actuators, and
sensing and control systems that monitor human gait information in real time
and control the assisted force in the process of walking. Galle et al. (2014) used pneumatic muscles as an actuator of the ankle-foot exoskeleton;
information on foot switches is used to impose a specific timing and
duration in which the pneumatic muscles are inflated. Under the condition of
walking on an inclined treadmill (15 %) at a speed of 1.1 m s<inline-formula><mml:math id="M4" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, the net
metabolic cost is reduced by <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mn mathvariant="normal">8.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">6.2</mml:mn></mml:mrow></mml:math></inline-formula> % when unloaded. When a load
of 22.5 kg is added, the net metabolic cost is reduced by <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mn mathvariant="normal">10.1</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">6.8</mml:mn></mml:mrow></mml:math></inline-formula> %.  Asbeck et al. (2015) developed a flexible exoskeleton for
walking assistance. The gait cycle was obtained by judging the heel landing
time using the plantar pressure sensor, and the motor displacement curve was
generated according to the gait cycle. Then the motor (power: 200 W) drove
the pulley cable to assist the ankle. Four subjects wearing the system and
carrying 23 kg on a treadmill at a speed of 1.25 m s<inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> reduced the average
optimal metabolic cost by 6.4 % and increased the metabolism by 9.3 %.
Two kinds of light ankle assistance robots named Alpha and Beta were
proposed by Witte et al. (2015). These robots had a power source and
a controller placed outside the body, and the tension was transmitted
through the Bowden cable. The assisted torque was calculated with the ankle
angle and gait phase information. Alpha used the tension sensor to measure
the tension of the Bowden cable, and Beta used four strain gauges to
directly measure the torque of the ankle mechanism. In the walking trials,
the peak average measured torque generated by Alpha and Beta was 80 and
87 Nm respectively.  Mooney and Herr (2016) and Mooney et al. (2014)
built an autonomous exoskeleton that used a DC motor (power: 200 W) to drive
the rope wound on a winch to provide mechanical power for an ankle, with an
inertial measurement unit (IMU) located in the front of the lower leg to
judge the gait phase of a human. The net metabolic cost of walking flat on a
treadmill at a speed of 1.4 m s<inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> with the exoskeleton was an 11 % <inline-formula><mml:math id="M9" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 4 % reduction compared to the cost of walking without the exoskeleton
under the condition of no load. For the subjects walking with a 23 kg load,
the net metabolic cost reduction was approximately 8 % <inline-formula><mml:math id="M10" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3 %. Wang et al. (2020) also used a flexible cable to transmit the assisted
force, and the ankle movements of plantar flexion and dorsal flexion were
driven by one motor. When a subject was wearing the exoskeleton with the
power on, the muscle activity of the soleus was reduced by 5.2 % compared
to the state without the exoskeleton. Shao et al. (2021) proposed a
load-adaptive actuator with variable stiffness to actuate ankle exoskeleton;
the ankle consumption can be reduced 0.23, <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.36</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M12" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.94</mml:mn></mml:mrow></mml:math></inline-formula>, and 1.63 J, with
0, 4, 12, and 20 kg loads respectively. Xie  et at. (2021) designed
and manufactured a lightweight flexible and wearable ankle-assisted robot. The Bowen cable is used as the transmission medium of power which is generated by a
motor (150 W), and the best net metabolic cost of eight experimenters wearing
this system for walking flat at a speed of 1 m s<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> on a treadmill was reduced
by 6.94 %, 5.23 %, 3.64 %, with 10 %, 20 %, and 30 % of the body
mass loads respectively.</p>
      <p id="d1e267">The passive ankle assistance robot stores energy through the change of the
ankle movement angular displacement during walking. This type of robot has
the advantages of having a simple structure and being lightweight, but the assisted
force provided by the robot is usually small and uncontrollable. The active
ankle assist robot has an actuator that can provide controllable assisted
force, but when a large assisted force is required (such as when the human
body is loaded), a higher power actuator and a larger capacity battery are
required. In this study, an ankle assistance method with active energy
storage is proposed, and an ankle assistance robot is developed that can
provide a large assisted force with a low-power motor and a simple control
method. The improvement achieved in this work will contribute to progressing
the development of ankle assistance robots and their applications to persons
who walk with loads.</p>
</sec>
<?pagebreak page431?><sec id="Ch1.S3">
  <label>3</label><title>Mechanism of wearable ankle assistance robot</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Active energy storage method</title>
      <p id="d1e285">In the process of walking, the torque of an ankle is concentrated at the end
of the supporting phase, with a short duration and a large peak value. When
people walk with a weight, the ankle load is further increased. The energy
storage and release of a passive ankle assist robot are realized by the
change of the ankle angular displacement during the support phase. Owing to
the lack of a power supply and motor, the structure of a passive ankle
assistance robot is simple, and the assisted force does not need to be
controlled in real time, but the assisted force provided by the robot is
small and unadjustable. An active ankle assistance robot has an actuator and
a control system, and the assisted force is controllable. However, the load
of a user will increase with a high-power motor and a high-capacity battery.
Combining the advantages of passive and active ankle assist robots, an
active energy storage method for ankle assistance is proposed. This method
is shown in Fig. 1.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e290">Active energy storage method.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f01.png"/>

        </fig>

      <p id="d1e299">According to the proposed method, an active energy storage mechanism is
designed. An electromagnetic clutch is driven by a motor with a synchronous
belt, the output of the electromagnetic clutch is connected with a reel, and
a Bowden cable is used to achieve flexible transmission and is wound on the
reel. One end of the elastic rod is fixed on the reel, and the other end
passes through the hole on the adjusting mount. The adjusting mount is
connected to the adjusting handle through threads. The adjusting mount can
be moved along the guide bar to adjust the deformation length of the elastic
rod (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> by rotating the adjusting handle. Then the assisted force can be
changed.</p>
      <p id="d1e313">The proposed active energy storage method works in two stages. When there is
no torque generated by the ankle, the electromagnetic clutch is closed. The
motor drives the elastic rod between the adjusting mount and the reel to
generate deformation, and then the energy storage is achieved. When the
ankle generates torque, the electromagnetic clutch is opened. Then the reel
is driven to rotate by the elastic rod in the energy storage mechanism, and
the assisted force on the user's heel is generated through the flexible
transmission device, thereby providing the assisted force for the ankle. The
output force (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is determined by multiple parameters such as the angular
displacement (<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the deformation length of the elastic rod (<inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the
diameter of the elastic rod (<inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the radius of the reel (<inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the elastic
modulus of the elastic rod (<inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and the number of elastic rods (<inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The
proposed active energy storage method has the following advantages:
<list list-type="custom"><list-item><label>(a)</label>
      <p id="d1e392">During walking, the ankle torque generation time is short. The active
energy storage method can store energy in the ankle's non-force-generation
stage in a gait cycle. Then the energy storage time is long. Therefore, a
small power motor can be used with a large reduction ratio gearbox to
provide larger assisted torque for the user.</p></list-item><list-item><label>(b)</label>
      <p id="d1e396">The deformation length of the elastic rod in the energy storage
mechanism can be adjusted according to the load of the user. Therefore, the
stored energy can be changed, and appropriate assisted forces can be provided
for different loads.</p></list-item><list-item><label>(c)</label>
      <p id="d1e400">According to the user gait cycle, the controller only needs to control
the motor to rotate at a certain angle and control the electromagnetic
clutch to open or close. The controller does not need to control the
assisted force in real time, so the control system is easy to develop.</p></list-item></list></p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Sketch of ankle assistance robot</title>
      <p id="d1e411">Based on the proposed active energy storage method, a wearable ankle
assistance robot is designed. A sketch of the robot is shown in Fig. 2. A
battery, motor, controller, and active energy storage mechanism are set at
the human waist. A Bowden cable is arranged along the outside of the thigh.
Two IMUs are arranged on the outside of each thigh, and pressure sensors are
arranged on the heels. The pressure sensors are combined with the two kinds
of sensing data to obtain the user's gait cycle information. One end of the
Bowden cable is connected to the energy storage mechanism, and the other end
is connected to the heel of the human body to achieve flexible transmission,
and the assisted force is transferred to the heel by the Bowden cable.
Because of the transmission loss and hysteresis of the Bowden cable (Veneman
et al., 2006), the assisted force (<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is less than the output force
(<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>). The relationship between the assisted force (<inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the output
force (<inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>) can be calculated with
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M26" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>f</mml:mi><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M27" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula> is the friction coefficient, and <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the wrap angle
between two ends.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e516">Sketch of wearable ankle assistance robot.</p></caption>
          <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f02.png"/>

        </fig>

      <?pagebreak page432?><p id="d1e525">Figure 3 shows the assisted force acting on the human heel. The changes in
the steel wire length of the Bowden cable and the assisted torque for the
ankle can be estimated with
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M29" display="block"><mml:mrow><mml:mfenced open="{" close=""><mml:mtable class="array" rowspacing="4.267913pt" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>l</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi mathvariant="normal">cos</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>l</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>l</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>-</mml:mo><mml:msqrt><mml:mrow><mml:msup><mml:mi>a</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>b</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>a</mml:mi><mml:mi>b</mml:mi><mml:mi mathvariant="normal">cos</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">α</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:msqrt></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>

            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M30" display="block"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mi>a</mml:mi><mml:mo>⋅</mml:mo><mml:mi mathvariant="normal">sin</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>l</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is the length of the steel wire, <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">α</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is the initial
angle between line <inline-formula><mml:math id="M33" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> and line <inline-formula><mml:math id="M34" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:math></inline-formula> is the change of the steel wire
length, and <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the assisted torque for the ankle. The change of the
steel wire length (<inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>l</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is used to calculate the angular displacement
(<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the active energy storage mechanism, and the assisted torque
(<inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is used to estimate the torque for the ankle that is generated by
the assisted force of the robot.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e779">Assisted force acting on the human heel.</p></caption>
          <?xmltex \igopts{width=142.26378pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f03.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Mechanical analysis of elastic rod</title>
      <p id="d1e796">The assisted force is generated by the deformation of the elastic rod. An
appropriate assisted force can be provided by designing the diameter and
length of the elastic rod appropriately. The cross-section of the elastic
rod is set to be circular and distributed along the reel uniformly. Figure 4
shows the deformation effect of the elastic rod during torque (with two
elastic rods).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e801">Elastic rod deformation.</p></caption>
          <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f04.png"/>

        </fig>

      <p id="d1e810">When the reel is driven by the motor to rotate from the balance position to
a certain angle, the contact point of the elastic rod and the reel is
transferred from point <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to point <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> in the circumferential
direction. The relationship between the displacement (<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and the
rotation angle (<inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> can be expressed by
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M44" display="block"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mi>R</mml:mi><mml:mi mathvariant="normal">sin</mml:mi><mml:mo>(</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M45" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> is the rotation radius of the elastic rod end.</p>
      <p id="d1e898">Owing to the structural characteristics of the energy storage mechanism, the
elastic rod only has bending deformation and no torsional deformation, so
the deformation of the elastic rod can be approximated as the bending of a
cantilever beam. With the rotation of the reel, a concentrated load opposite
to the rotation direction is applied to the elastic rod by the adjusting
mount. The cantilever beam bending model is shown in Fig. 5.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e903">Cantilever bending model.</p></caption>
          <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f05.png"/>

        </fig>

      <p id="d1e912">Because the deformation of the elastic rod is approximated as the bending of
the cantilever beam, the deflection value (<inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> can be calculated by
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M47" display="block"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>F</mml:mi><mml:msup><mml:mi>L</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi>E</mml:mi><mml:mi>I</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M48" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> is the concentrated load on the free end of the elastic rod, <inline-formula><mml:math id="M49" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> is the
effective bending length of the elastic rod, <inline-formula><mml:math id="M50" display="inline"><mml:mi>E</mml:mi></mml:math></inline-formula> is the elastic modulus of the
elastic rod, and <inline-formula><mml:math id="M51" display="inline"><mml:mi>I</mml:mi></mml:math></inline-formula> is the section moment of inertia of the elastic rod.</p>
      <?pagebreak page433?><p id="d1e989">According to Figs. 4 and 5, <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is equal to <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>w</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Then the force <inline-formula><mml:math id="M54" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>
acting on the end of the elastic rod can be obtained from Eqs. (<xref ref-type="disp-formula" rid="Ch1.E4"/>) and (<xref ref-type="disp-formula" rid="Ch1.E5"/>). The force <inline-formula><mml:math id="M55" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> can be described as
            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M56" display="block"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">6</mml:mn><mml:mi>E</mml:mi><mml:mi>I</mml:mi><mml:mi>R</mml:mi><mml:mi mathvariant="normal">sin</mml:mi><mml:mo>(</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mi>L</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The moment of inertia of a circular section can be calculated with
            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M57" display="block"><mml:mrow><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow><mml:mn mathvariant="normal">64</mml:mn></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M58" display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula> is the diameter of the elastic rod. <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that generates torque on
the reel is the component of the force <inline-formula><mml:math id="M60" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula> in the vertical radius, which can be
calculated with
            <disp-formula id="Ch1.E8" content-type="numbered"><label>8</label><mml:math id="M61" display="block"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mi>E</mml:mi><mml:mi>R</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msup><mml:mi mathvariant="normal">sin</mml:mi><mml:mo>(</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo><mml:mi>cos⁡</mml:mi><mml:mo>(</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn mathvariant="normal">32</mml:mn><mml:msup><mml:mi>L</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The torque generate by one elastic rod can be calculated with
            <disp-formula id="Ch1.E9" content-type="numbered"><label>9</label><mml:math id="M62" display="block"><mml:mrow><mml:mi>T</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mi>R</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Energy storage capacity analysis</title>
      <p id="d1e1214">Based on the working principle of the energy storage mechanism, the energy
storage capacity of the energy storage mechanism is analyzed, which can
provide a basis for the energy storage control and assisted force adjustment
of the robot.</p>
      <p id="d1e1217">By comparing the performance parameters such as the elastic modulus and
tensile strength, beryllium copper is selected as the material of the
elastic rod. The elastic modulus (<inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:mi>E</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and yield strength of beryllium copper
(<inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are 128 GPa and 1035 MPa respectively. During energy
storage, the elastic rod is bent and deformed, and the maximum bending
stress can be calculated with
            <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M65" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>M</mml:mi><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>Z</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the bending section coefficient of the circular section rod,
and <inline-formula><mml:math id="M67" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> is the bending moment of the elastic rod at the adjusting mount.
<inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M69" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> can be calculated with
            <disp-formula id="Ch1.E11" content-type="numbered"><label>11</label><mml:math id="M70" display="block"><mml:mrow><mml:mfenced open="{" close=""><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msub><mml:mi>W</mml:mi><mml:mi>Z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow><mml:mn mathvariant="normal">32</mml:mn></mml:mfrac></mml:mstyle></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mi>M</mml:mi><mml:mo>=</mml:mo><mml:mi>F</mml:mi><mml:mi>L</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>
          Then the maximum bending stress is
            <disp-formula id="Ch1.E12" content-type="numbered"><label>12</label><mml:math id="M71" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">32</mml:mn><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">32</mml:mn><mml:mi>F</mml:mi><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          Considering the safety of the energy storage mechanism, it is necessary to
ensure that the elastic rod meets the requirements of the allowable load
stress during use, and Eq. (<xref ref-type="disp-formula" rid="Ch1.E13"/>) should be satisfied in the design.
            <disp-formula id="Ch1.E13" content-type="numbered"><label>13</label><mml:math id="M72" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">max</mml:mi></mml:msub><mml:mo>≤</mml:mo><mml:mo>[</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:math></disp-formula>
          The allowable tensile stress of an elastic rod is the yield strength
<inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> divided by the safety factor <inline-formula><mml:math id="M74" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>, then
            <disp-formula id="Ch1.E14" content-type="numbered"><label>14</label><mml:math id="M75" display="block"><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">32</mml:mn><mml:mi>F</mml:mi><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:msup><mml:mi>d</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>≤</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mi>n</mml:mi></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          With Eqs. (<xref ref-type="disp-formula" rid="Ch1.E8"/>) and (<xref ref-type="disp-formula" rid="Ch1.E14"/>), the minimum length of the selected elastic rod
can be calculated with
            <disp-formula id="Ch1.E15" content-type="numbered"><label>15</label><mml:math id="M76" display="block"><mml:mrow><mml:mi>L</mml:mi><mml:mo>≥</mml:mo><mml:msqrt><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi>n</mml:mi><mml:mi>E</mml:mi><mml:mi>R</mml:mi><mml:mi>d</mml:mi><mml:mi mathvariant="normal">sin</mml:mi><mml:mo>(</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:msqrt><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          It can be known from Eq. (<xref ref-type="disp-formula" rid="Ch1.E15"/>) that after the parameters of the elastic
rod are determined, the minimum selected length is only related to the
rotation angle (<inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the reel. A circular section elastic rod with
a diameter of 2 mm is selected, and the safety factor <inline-formula><mml:math id="M78" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula> is set to 1.5.
Considering factors such as the volume and the installation of the active
energy storage mechanism, the distance <inline-formula><mml:math id="M79" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> from the contact point of the
elastic rod to the center of the reel is set to 15 mm. The rotation angle of
the reel is calculated based on the structure of the flexible transmission
device and the range of the ankle movement. Then, with Eq. (<xref ref-type="disp-formula" rid="Ch1.E15"/>), the
minimum length of the elastic rod can be calculated, which should not be
less than 64.75 mm. The adjustment range of the elastic rod is set to 65–80 mm.</p>
      <?pagebreak page434?><p id="d1e1552">According to the force requirements of the ankle joint and the structure of
the energy storage mechanism, the number of elastic rods (<inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is set to 10.
The torque generated by all elastic rods can be calculated with
            <disp-formula id="Ch1.E16" content-type="numbered"><label>16</label><mml:math id="M81" display="block"><mml:mrow><mml:msup><mml:mi>T</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:mi>N</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          The winding radius <inline-formula><mml:math id="M82" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> of the wire is 12.5 mm (the <inline-formula><mml:math id="M83" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> is shown in Fig. 6), and
the output force (<inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> generated by the torque <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msup><mml:mi>T</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> acting on the Bowdoin line can
be calculated with Eq. (<xref ref-type="disp-formula" rid="Ch1.E17"/>):
            <disp-formula id="Ch1.E17" content-type="numbered"><label>17</label><mml:math id="M86" display="block"><mml:mrow><mml:msup><mml:mi>F</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mi>T</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mi>r</mml:mi></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>
          According to the adjustment range of the elastic rod and the rotation angle
of the reel, the relationship between the maximum output force and the
deformation length of the elastic rod can be obtained from Eqs. (<xref ref-type="disp-formula" rid="Ch1.E16"/>) and
(<xref ref-type="disp-formula" rid="Ch1.E17"/>). The result is shown in Fig. 10. The output force of the designed
active energy storage mechanism decreases monotonically with the increase in
the deformation length of the elastic rod, an approximately linear
relationship, so it is convenient for the adjustment of the output force.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1657">Reel construction.</p></caption>
          <?xmltex \igopts{width=142.26378pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f06.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Control method of the robot</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Moment of assistance</title>
      <p id="d1e1682">To realize the power-assisted function, it is necessary to obtain the
moments when the ankle generates force and when the robot provides assisted
force. Much information can be used for robot decision making (Qiao et
al., 2022; Qi et al., 2021), but it is difficult to obtain the moment of assistance
directly, so a method is proposed to detect the gait cycle by combining the
information on the hip joint angle and the plantar pressure. Then the moment of assistance can be calculated.</p>
      <p id="d1e1685">An IMU is placed on the outside of the thigh to obtain the hip angle
information during walking. When the human body is standing, the thigh is
perpendicular to the ground, and the hip joint angle at this time is defined
as 0<inline-formula><mml:math id="M87" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. The angle is positive when flexed, and the angle is
negative when extended. The human gait cycle is shown in Fig. 7. According
to the literature (Dai and Tang, 1982), the minimum value of the hip angle
appears at 53.8 % of the gait cycle during walking, and then the angle
increases until 84.6 % of the gait cycle.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e1699">Gait cycle analysis.</p></caption>
          <?xmltex \igopts{width=184.942913pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f07.png"/>

        </fig>

      <p id="d1e1709">During walking, the gait cycles are different, but the ratios between the
hip flexion times and the gait cycles are approximately equal. Therefore,
the hip flexion time and the ratio can be used to predict the gait cycle.
The ankle does positive work between 40 % and 60 % of the gait cycle
(Collins et al., 2005), and the peak value of the ankle torque during
walking is at about 50.1 % of the gait cycle (Tang and Dai, 1986), so the
starting time of the assistance should between 40 % and 50.1 % of the
gait cycle. In this study, the starting time of the assistance is set at
43 % of the gait cycle (during the experiment, testers feel comfortable at
this moment). Based on the characteristics of human walking, the pressure
sensor is used to obtain the heel landing time as the start time of a gait
cycle. The IMU is used to obtain the angular displacement of the hip. After
the hip movement peak time is detected, the hip flexion time is obtained by
subtracting the trough time. At the same time, the gait cycle time is
obtained by using the difference between the two peak times. Then the ratio
is obtained with the flexion time divided by the cycle time. The predicted
gait cycle can be obtained using the flexion time of the previous gait cycle
divided by the average ratio of the previous three gait cycles. The starting
time of the power assistance can be calculated with
            <disp-formula id="Ch1.E18" content-type="numbered"><label>18</label><mml:math id="M88" display="block"><mml:mrow><mml:mfenced close="" open="{"><mml:mtable class="array" columnalign="left"><mml:mtr><mml:mtd><mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">3</mml:mn></mml:mfrac></mml:mstyle></mml:mstyle><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:munderover><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">peak</mml:mi><mml:mi>i</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">trough</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">peak</mml:mi><mml:mi>i</mml:mi></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">peak</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>T</mml:mi><mml:mi mathvariant="normal">pre</mml:mi><mml:mi>k</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">peak</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup><mml:mo>-</mml:mo><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">trough</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mstyle></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">assist</mml:mi><mml:mi>k</mml:mi></mml:msubsup><mml:mo>=</mml:mo><mml:msubsup><mml:mi>t</mml:mi><mml:mi mathvariant="normal">zero</mml:mi><mml:mi>k</mml:mi></mml:msubsup><mml:mo>+</mml:mo><mml:mn mathvariant="normal">0.43</mml:mn><mml:msubsup><mml:mi>T</mml:mi><mml:mi mathvariant="normal">pre</mml:mi><mml:mi>k</mml:mi></mml:msubsup><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mfenced></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M89" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula> is the current gait number, <italic>k-1</italic> is the last gait number, <inline-formula><mml:math id="M90" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> is the
predicted ratio, <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">pre</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the predicted gait cycle, <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">peak</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the peak
time of the hip, <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">trough</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the trough time of the hip, <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">zero</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the
start time of the gait, and <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi mathvariant="normal">assist</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the moment when the robot begins
to provide assisted force. The proposed assistance moment calculation method
has the following advantages:
<list list-type="custom"><list-item><label>(a)</label>
      <p id="d1e1970">The gait cycle is predicted using the hip angular displacement, whose
shape is similar to a sinusoidal curve, with only one maximum and one
minimum value in a gait cycle, so the prediction result is more stable and
accurate.</p></list-item><list-item><label>(b)</label>
      <p id="d1e1974">Using the pressure information of both heels and the angular
displacement of the hips, the human states of walking and standing can be
estimated accurately, so the incorrect operation of the robot can be
avoided.</p></list-item></list></p>
</sec>
<?pagebreak page435?><sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Control method</title>
      <p id="d1e1985">The robot control system is made up primarily of a controller, an IMU, a
pressure sensor, a DC motor, and an electromagnetic clutch. The robot
controlling principle is shown in Fig. 8. First, the gait information is
collected by the IMU and the pressure sensor and is then transmitted to the
controller. Second, the assistance time is calculated by the controller with
the heel pressure information and the hip joint angular displacement. Third,
the control command is sent to the DC servo motor driver and the
electromagnetic clutch to coordinate the motor and clutch.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e1990">Diagram of the robot control system.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f08.png"/>

        </fig>

      <p id="d1e1999">The same control method is applied to the left leg and the right leg of the
user. The start time of the energy storage is when the leg is in the swing
phase and the angular displacement of the hip joint is 0<inline-formula><mml:math id="M96" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>. After
the energy storage start time is obtained, the electromagnetic clutch is
closed by the controller. At the same time, the motor is controlled to
rotate for energy storage, and the motor stops after rotating to the preset
angle.</p>
      <p id="d1e2012">After the start time of the gait cycle is obtained according to the heel
pressure information, the starting time of assistance is calculated with Eq. (<xref ref-type="disp-formula" rid="Ch1.E18"/>). When
the power assistance time occurs, the electromagnetic clutch is opened, and
the energy storage mechanism drives the human ankle movement through the
flexible transmission mechanism to achieve walking assistance.</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Experiment</title>
<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Test of energy storage mechanism output force</title>
      <p id="d1e2034">An experimental platform is built to obtain the maximum output force of the
energy storage mechanism. This platform is shown in Fig. 9. The energy
storage mechanism is connected to the dynamic torque sensor, and a servo
motor is used to drive the energy storage mechanism to rotate. The maximum
output force is calculated with the test torque divided by the winding
radius <inline-formula><mml:math id="M97" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> of the wire. The result is shown in Fig. 10. The test results and
calculation results have similar trend. But the tested output forces are
slightly greater than calculated values, with an approximately constant
difference. This may be for several reasons, such as the difference
between the calculated parameters and the actual parameters of elastic rods
and other parts, the axiality error between the torque sensor and the energy
storage mechanism, and friction. The output force supplied by the robot
should reference the test result. With the output force, the assisted force
for the user can be calculated with Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e2048">Experimental platform for the output force test.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f09.jpg"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e2059">Maximum output force test result.</p></caption>
          <?xmltex \igopts{width=170.716535pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f10.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e2071">Ankle assistance robot.</p></caption>
          <?xmltex \igopts{width=227.622047pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f11.jpg"/>

        </fig>

</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><title>Walking assistance experiment</title>
      <p id="d1e2088">The prototype of the wearable ankle assistance robot is shown in Fig. 11.
According to the maximum torque required by the energy storage mechanism, a
90 W DC servo motor (RE35 Maxon) and an electromagnetic clutch (HB-YC-42,
Shenzhen Haibosi Technology Co., Ltd) are selected, and the reduction ratio
of the gearbox is <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:mn mathvariant="normal">26</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>. An NI myRIO-1900 (from NI Inc.) is used as the
controller for the robot. The active energy storage mechanism and the
controller are placed at the user's back and waist, and the mobile power
supply is arranged behind the controller. The IMUs (BWT901CL, WitMotion
ShenZhen Co., Ltd) are fixed in place by a flexible bandage. The pressure
sensors (FSR 402, SparkFun Electronics Inc.) are placed in the heels of the
shoes. The cardiopulmonary function tester (K4b2, Cosmed Inc.) is used to
measure the metabolic cost of the user. The walking<?pagebreak page436?> frequency of a healthy
person is about 0.8 Hz; when loaded with weight, the walking frequency maybe
lower. The control cycle was set to be 40 ms, which means the control
frequency is 25 Hz.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e2106">Participant information.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3">Age</oasis:entry>
         <oasis:entry colname="col4">Height</oasis:entry>
         <oasis:entry colname="col5">Body</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Participant</oasis:entry>
         <oasis:entry colname="col2">Gender</oasis:entry>
         <oasis:entry colname="col3">(years)</oasis:entry>
         <oasis:entry colname="col4">(m)</oasis:entry>
         <oasis:entry colname="col5">mass (kg)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">P1</oasis:entry>
         <oasis:entry colname="col2">M</oasis:entry>
         <oasis:entry colname="col3">24</oasis:entry>
         <oasis:entry colname="col4">1.73</oasis:entry>
         <oasis:entry colname="col5">65</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">P2</oasis:entry>
         <oasis:entry colname="col2">M</oasis:entry>
         <oasis:entry colname="col3">26</oasis:entry>
         <oasis:entry colname="col4">1.81</oasis:entry>
         <oasis:entry colname="col5">73</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">P3</oasis:entry>
         <oasis:entry colname="col2">F</oasis:entry>
         <oasis:entry colname="col3">26</oasis:entry>
         <oasis:entry colname="col4">1.65</oasis:entry>
         <oasis:entry colname="col5">50</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><?xmltex \gdef\@currentlabel{1}?></table-wrap>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e2222">Load and assisted force.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="3">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Load</oasis:entry>
         <oasis:entry colname="col2">Assisted</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(kg)</oasis:entry>
         <oasis:entry colname="col2">force (N)</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">0</oasis:entry>
         <oasis:entry colname="col2">75</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4</oasis:entry>
         <oasis:entry colname="col2">95</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">8</oasis:entry>
         <oasis:entry colname="col2">115</oasis:entry>
         <oasis:entry colname="col3"/>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><?xmltex \gdef\@currentlabel{2}?></table-wrap>

      <p id="d1e2298">During the experiment, participants walk on a treadmill, and the metabolic
costs of the participants in three states are measured: the resting state,
walking without the assisted robot, and walking with the assisted robot. The
net metabolic cost is obtained by subtracting the resting state metabolic
cost from the walking metabolic cost, which is used to indicate the energy
expenditure during walking. The assistance effect of the robot is evaluated
by comparing the net metabolic costs of wearing and not wearing the robot.
The data unit of the cardiopulmonary function tester is calories per second  (cal s<inline-formula><mml:math id="M99" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) in this
study, and the unit of the metabolic cost is watts per kilogram (W kg<inline-formula><mml:math id="M100" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>); the
value conversion can be realized by the following equation:
            <disp-formula id="Ch1.E19" content-type="numbered"><label>19</label><mml:math id="M101" display="block"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">4.184</mml:mn><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the value (in W kg<inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of the metabolic
cost, <inline-formula><mml:math id="M104" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> is the value (in cal s<inline-formula><mml:math id="M105" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) collected by the cardiopulmonary
function tester, and <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the body weight (in kg) of the
participant.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12"><?xmltex \currentcnt{12}?><?xmltex \def\figurename{Figure}?><label>Figure 12</label><caption><p id="d1e2412">Walking on the treadmill with robot and load.</p></caption>
          <?xmltex \igopts{width=213.395669pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f12.jpg"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13"><?xmltex \currentcnt{13}?><?xmltex \def\figurename{Figure}?><label>Figure 13</label><caption><p id="d1e2423">Net metabolic cost without robot assistance and with robot
assistance under different loads. <bold>(a)</bold> Load: 0 kg. <bold>(b)</bold> Load: 4 kg. <bold>(c)</bold> Load: 8 kg.</p></caption>
          <?xmltex \igopts{width=241.848425pt}?><graphic xlink:href="https://ms.copernicus.org/articles/14/429/2023/ms-14-429-2023-f13.png"/>

        </fig>

      <p id="d1e2441">Three participants participate in the experiment, and the information on
the participants is shown in Table 1. Different assisted forces are supplied
to participants with different loads. Because the accurate calculation of
the assisted force is difficult, the output force of the energy storage
mechanism is taken as a reference. The load and the assisted force are shown
in Table 2.</p>
      <p id="d1e2444">In each experiment, participants walk for 6 min at a speed of 4.5 km h<inline-formula><mml:math id="M107" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
(Fig. 12), and the net metabolic cost data of the last 2 min were
analyzed. The net metabolic costs of the three participants are shown in
Fig. 13.</p>
      <p id="d1e2460">It can be observed from Fig. 13 that the average net metabolic cost is
reduced by 5.30 % when the participants have no load, and the maximum
reduction is 5.53 %. When a 4 kg load is carried by the participants, the
average net metabolic cost is reduced by 5.67 %, and the maximum reduction
is 6.11 %. When an 8 kg load is carried by the participants, the average
net metabolic cost is reduced by 4.84 %, and the maximum reduction is 
5.61 %.</p>
      <?pagebreak page437?><p id="d1e2463">The test result shows that the net metabolic costs of all the participants
under different loads are reduced. This means that the developed wearable
ankle assistance robot can reduce the energy consumption of the human body
by providing assisted force for the ankle. The net metabolic cost reductions
when the participants are under loads are close to the reductions in the
case without loads. This indicates that the robot's function of adjusting
the assisted force for different loads is effective.</p>
      <p id="d1e2466">Although the expected functions are realized, there are still some problems
that need to be improved. For example, the weight of the developed robot is
about 5.3 kg, and participants feel heavier after wearing it. Some energy is
consumed by the friction that is generated in the process of the Bowden
cable working. The robot is inconvenient to wear and take off. About
2 min is needed to wear it or take it off by a participant without the help of others.
These problems impact the assistance effect of the robot and will be
improved in future study.</p>
</sec>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e2478">Based on the proposed active energy storage ankle assistance method, an
active energy storage mechanism is designed and developed that achieves the
function of energy storage using a small power motor with a larger reduction
ratio gearbox. By adjusting the deformation length of the elastic rods, the
energy storage capacity of the energy storage mechanism can be changed,
thereby providing an adjustable assisted force for the user.</p>
      <p id="d1e2481">With the information on the IMU, the information on the pressure sensor,
and human gait cycle characteristics, the moment of assisting the ankle can
be obtained. According to the assistance time and the start time of the
energy storage, the movement of the motor and the electromagnetic clutch can
be controlled accurately with the controller. Then the functions of storage
and release of energy can be realized, and the assisted force can be
provided by the robot for the user.</p>
      <p id="d1e2484">A wearable ankle assistance robot with the function of active energy storage
is developed, and a walking assistance experiment is carried out. The
experimental results show that the net metabolic cost of the participants is
reduced by averages of 5.30 %, 5.67 %, and 4.84 % with 0, 4, and
8 kg loads respectively. The results show that with different loads, the
robot can reduce participant energy consumption, and the assisted walking
function is achieved.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2491">All data included in this study are available upon request by contact with the corresponding author.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2497">Conceptualization, JL and DY; investigation, KY; methodology, JL; project administration, JL; resources, DY; software, KY;
validation, JL; writing (original draft preparation), KY;
writing (review and editing), JL and KY. All authors have read and
agreed to the published version of the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2503">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2509">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2515">The authors would like to thank Shijie Guo for his valuable insight and advice. The authors would also like to thank Jingyuan Qi, Liang Zhao, and Lei Zhao for their help with the testing of human subjects.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2520">This research has been supported by the National Natural Science Foundation of China (grant no. U1813222).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2526">This paper was edited by Zi Bin and reviewed by six anonymous referees.</p>
  </notes><ref-list>
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