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<section id="hardware">
<h1>Hardware<a class="headerlink" href="#hardware" title="Link to this heading">#</a></h1>
<p>A 3D-rendering of the table can be seen <a class="reference internal" href="#fig-3drendering"><span class="std std-ref">below</span></a>.
The basic hardware components of the shaking table are an aluminum
frame, linear rails, linear bearings, the plate, the motor with its
driver and the driving assembly, as well as the necessary electrical
components. Each component is described in this section and some details
on their functionality are given. Since different choices can be made
for each part we also give some comments about possible variants.</p>
<figure class="align-default" id="fig-3drendering">
<img alt="_images/3dtable_annotations.png" src="_images/3dtable_annotations.png" />
<figcaption>
<p><span class="caption-text">3D rendering of the table CAD files.</span><a class="headerlink" href="#fig-3drendering" title="Link to this image">#</a></p>
</figcaption>
</figure>
<p>A technical drawing with dimensions is shown <a class="reference internal" href="#fig-techdraw"><span class="std std-ref">below</span></a>.
The mass of the table is <span class="math notranslate nohighlight">\({6.80}\, \text{kg}\)</span>. Its footprint is about
<span class="math notranslate nohighlight">\({400}\, \text{mm}\times {500}\, \text{mm}\)</span> and it takes one person about
one hour to fully assemble it. <a class="reference internal" href="#tab-partsandcosts"><span class="std std-ref">This table</span></a> gives a list
of hardware components and the associated costs. Tested properties obtained with Namazu
are:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\label{eq:PhysProp}
\begin{split}
\text{Tested payload:} \hspace{1cm} &{2}\, \text{kg},\\
\text{Maximum acceleration with payload:} \hspace{1cm} &2\, g,\\
\text{Maximum speed with payload:} \hspace{1cm}&{0.4}\, {\text{m/s}}.
\end{split}\end{split}\]</div>
<figure class="align-default" id="fig-techdraw">
<img alt="_images/technicalDrawing.png" src="_images/technicalDrawing.png" />
<figcaption>
<p><span class="caption-text">Technical drawing of the table, dimensions in millimeters.</span><a class="headerlink" href="#fig-techdraw" title="Link to this image">#</a></p>
</figcaption>
</figure>
<div class="docutils container" id="tab-partsandcosts">
<div class="pst-scrollable-table-container"><table class="table" id="id3">
<caption><span class="caption-text">Costs of shaking table hardware (in 2022-2023, Germany), note that the costs are highly dependent on availability of the components. The cable and tools used for assembly are not mentioned here.</span><a class="headerlink" href="#id3" title="Link to this table">#</a></caption>
<thead>
<tr class="row-odd"><th class="head"><p>Nr.</p></th>
<th class="head"><p>Hardware</p></th>
<th class="head"><p>Description</p></th>
<th class="head"><p>Price</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>1</p></td>
<td><p>Frame</p></td>
<td><p>30x30 I-Type aluminium
extrusions (4x 400 mm,
2x 300 mm, 4x 70 mm)</p></td>
<td><p>21.64€</p></td>
</tr>
<tr class="row-odd"><td><p>2</p></td>
<td><p>Linear rails</p></td>
<td><p>igus drylin W,
WS16_0.4M</p></td>
<td><p>31.74€</p></td>
</tr>
<tr class="row-even"><td><p>3</p></td>
<td><p>Linear bearings</p></td>
<td><p>igus drylin W,
WJ2000UME-01-16</p></td>
<td><p>41.48€</p></td>
</tr>
<tr class="row-odd"><td><p>4</p></td>
<td><p>Plate</p></td>
<td><p>300x300x4 aluminium
plate</p></td>
<td><p>42.69€</p></td>
</tr>
<tr class="row-even"><td><p>5</p></td>
<td><p>Motor</p></td>
<td><p>NEMA23 (ACT
23HS8430D8P1)</p></td>
<td><p>21.60€</p></td>
</tr>
<tr class="row-odd"><td><p>6</p></td>
<td><p>Driver</p></td>
<td><p>ACT DM542</p></td>
<td><p>33.10€</p></td>
</tr>
<tr class="row-even"><td><p>7</p></td>
<td><p>Gears</p></td>
<td><p>GT-2, 20 teeth gear and
idler</p></td>
<td><p>5.00€</p></td>
</tr>
<tr class="row-odd"><td><p>8</p></td>
<td><p>Belt</p></td>
<td><p>GT-2, 1m</p></td>
<td><p>4.99€</p></td>
</tr>
<tr class="row-even"><td><p>9</p></td>
<td><p>Power supply</p></td>
<td><p>PEAKTECH 6227</p></td>
<td><p>123.17€</p></td>
</tr>
<tr class="row-odd"><td><p>10</p></td>
<td><p>Microcontroller</p></td>
<td><p>NodeMCU ESP32-WROOM32</p></td>
<td><p>11.49€</p></td>
</tr>
<tr class="row-even"><td><ul class="simple">
<li></li>
</ul>
</td>
<td><p>Misc.</p></td>
<td><p>Attachment plates,
screws, nuts, etc.
(price is an estimate)</p></td>
<td><p>60.00€</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td><p>Total:</p></td>
<td><p>396.90€</p></td>
</tr>
</tbody>
</table>
</div>
</div>
<section id="frame-and-rails">
<h2>Frame and rails<a class="headerlink" href="#frame-and-rails" title="Link to this heading">#</a></h2>
<p>The frame is made up of standard <span class="math notranslate nohighlight">\({30}\, \text{mm} \times {30}\, \text{mm}\)</span> I-Type aluminum extrusions. They make assembly and disassembly of the table very practical, and allow for flexibility in the design, since hardware components can be mounted anywhere the user desires. The plate is designed with different mounting holes for mounting a large variety of mock-up specimens. The plate is attached to the frame by two low-maintenance friction bearings and rails (igus drylinW). The frame has to be fixed to some object with high mass to avoid vibrations of the surroundings, e.g., it can be bolted to a rigid high-mass table.</p>
</section>
<section id="motor-and-driver">
<h2>Motor and driver<a class="headerlink" href="#motor-and-driver" title="Link to this heading">#</a></h2>
<p>The displacement is applied to the plate by a bipolar stepper motor through a belt-gear system. Bipolar stepper motors are made up of two sets of coils. By switching the current through the coils and, therefore, the polarity of the induced magnetic fields, the motor is forced to turn by one step. The motor driver is a specialized electronic circuit, which handles the necessary operations for the electrical current output to realize this careful switching. It acts as an interface between the controller and the motor.</p>
<p>Under ideal circumstances, the position of a stepper motor is known at all times, and a feedback loop is not needed. The setup is thus cost-effective and overall simple. In addition, the driver is able to perform so-called microsteps which enable the motor to be set to positions that do not correspond to full steps. This is achieved by interpolating the coil current. Using microsteps enhances the resolution of the motor without changing the hardware components. It also increases the versatility of the setup.</p>
<p>An important characteristic of the table is the number of steps
<span class="math notranslate nohighlight">\(n_{/disp}\)</span> that the motor performs for a given displacement,
often taken as the number of steps per millimeter. This characteristic
depends on the motor, the microstep setting and the hardware, i.e. the
driving components. It can be calculated from the number of steps the
motor performs per revolution and the displacement of the plate during
one revolution of the motor as follows</p>
<div class="math notranslate nohighlight">
\[n_{/disp} = \dfrac{\text{number of steps per motor revolution}}{\text{plate displacement per motor revolution}} .
% \text{steps per mm} = \frac{\text{steps per revolution}}{\text{mm per revolution}},
\label{eq:StepsPerMM}\]</div>
<p>The current setup uses a NEMA23 motor, where the coils are
<span class="math notranslate nohighlight">\(1.8^{\circ}\)</span> apart. The DM542-driver is set to a microstep
setting of 32 microsteps between two coils, so 6,400 . The belt
comprises a tooth every 2 mm, and the GT2 gear has 20 teeth in total, so
the belt moves by <span class="math notranslate nohighlight">\(40\)</span> . Therefore, the resolution of the Namazu
setup with the features detailed here is <span class="math notranslate nohighlight">\(n_{/disp}=160\)</span> steps per
millimeter; one microstep corresponds to a displacement of
<span class="math notranslate nohighlight">\({0.0063}\, \text{mm}\)</span>. This feature is directly set via a serial
command to the motor without the need to reprogram the controller.</p>
<p>For stepper motors, a trade-off has to be accepted between speed and
available torque. More microsteps per revolution decrease the available
torque and also slightly decrease the accuracy, since the driver needs
to interpolate the coil current between two full steps. Indeed, with
high speeds the driver has less time to switch the coil current between
steps and the inertia of the payload and the table assembly can perturb
the control. If the motor torque is not adequate for the applied loads,
it can result in loss of steps and therefore loss of accuracy.
Nevertheless, there are many different sizes of motors available with
torque ratings ranging from as low as a few <span class="math notranslate nohighlight">\(\text{Ncm}\)</span> (e.g.
NEMA 11) to large motors capable of achieving a few tens of
<span class="math notranslate nohighlight">\(\text{Nm}\)</span> (e.g. NEMA 42). A similar comment can be made about
the microstep setting. Another remedy is planetary gearboxes with
different ratios available for various motors. The planetary gearboxes
increase the resolution without the need for microsteps. The drawback is
that the gearboxes usually introduce some backlash, and the ratios are
not adjustable.</p>
</section>
<section id="microcontroller">
<h2>Microcontroller<a class="headerlink" href="#microcontroller" title="Link to this heading">#</a></h2>
<p>The microcontroller is the core element of the Namazu control
structure. It is the interfacing element between the hardware (driver)
and software, which sets the motor velocity and rotation direction as
well as storing, starting and stopping of an experiment. A desired
displacement signal can be uploaded to the controller via the serial
interface. Once the experiment is started, the controller pulses the
<code class="docutils literal notranslate"><span class="pre">STEP</span></code>-pin of the motor driver at a certain frequency that depends on
the desired speed, which in turn is dependent on the desired
displacement. These calculations are performed by the microcontroller
and stored before the experiment. For each <code class="docutils literal notranslate"><span class="pre">STEP</span></code>-pulse the motor
turns by one step, i.e. changing the frequency of the pulse allows for
the definition of arbitrary signals, which is the core functionality of
Namazu.</p>
<p>The compatibility of the microcontroller with the free real-time
operating system (FreeRTOS) and the Arduino framework is mandatory to
use the provided program. Further, we recommend a high-resolution
hardware timer for the microcontroller such that the motor is controlled
with high precision. The chosen microcontroller is an ESP32 devkit
module. The processors’ clock rate of <span class="math notranslate nohighlight">\(250\, \text{MHz}\)</span>
empowers us to update the motors’ velocity and direction of rotation up
to <span class="math notranslate nohighlight">\(200\)</span> times per second. Moreover, the ESP32 provides a second
core that can handle interrupts and provide a control interface, without
interfering with the motor’s update rate. Thereby, we isolate the
experiment from interfacing operations and improve the repeatability of
experiments.</p>
</section>
<section id="variants">
<h2>Variants<a class="headerlink" href="#variants" title="Link to this heading">#</a></h2>
<p>The Namazu shaking table that is presented here comprises various
pieces, which could be upgraded/downgraded independently depending on
the user’s budget and research needs. This makes the shaking-table
tunable. Indeed, it can be personalized to fit desired accuracy or
operational conditions. Some variants are exposed in
<a class="reference external" href="#tab:Namazuvariants">2</a>. Note that variations in the hardware make
it necessary to recalculate the steps per mm setting for the motor, as
this property depends on the physical properties of the table as well as
the microstep settings in the driver. As an example, changing the belt
and gear assembly of the current setup to a <span class="math notranslate nohighlight">\(1610\)</span> ball screw
assembly (<span class="math notranslate nohighlight">\(1610\)</span> referring to a screw diameter of
<span class="math notranslate nohighlight">\({16}\, \text{mm}\)</span> and a screw lead of <span class="math notranslate nohighlight">\({10}\, \text{mm}\)</span>) means that
the belt, and so the table, is moved by <span class="math notranslate nohighlight">\({10}\, \text{mm}\)</span> per
revolution of the motor. Together with the <span class="math notranslate nohighlight">\(200\)</span> steps per
revolution of the motor this leads to a resolution of the shaking table
of <span class="math notranslate nohighlight">\(n_{/disp}\)</span> equal to <span class="math notranslate nohighlight">\(20\)</span> steps per <span class="math notranslate nohighlight">\(\text{mm}\)</span>.</p>
<p>Most limitations on payload capacity, acceleration, and speed are only
given by the hardware components. Here, tests have shown that the
Namazu table with current components performs well with physical
properties given in <a class="reference external" href="#eq:PhysProp">[eq:PhysProp]</a>. The tested payload
is <span class="math notranslate nohighlight">\({2}\, \text{kg}\)</span>. This small payload can fit some research
projects. Besides, for teaching purposes, we find that using the table
in combination with 3D-printed structures offers a versatile and
low-cost solution to give students some experience with designing and
testing parts. Indeed, 3D-printed structures, when printed with
materials such as polylactic acid (PLA) or thermoplastic polyurethane
(TPU), are cheep and lightweight. Therefore, a low-torque motor as
introduced here can achieve already satisfying accuracy, with low cost
hardware and simple handling of the Namazu framework. As a reference,
the payload limitations on the SARSAR shaking table <a class="footnote-reference brackets" href="#footcite-damci2019development" id="id1" role="doc-noteref"><span class="fn-bracket">[</span>1<span class="fn-bracket">]</span></a> are given as
<span class="math notranslate nohighlight">\({200}\, \text{kg}\)</span> capacity while also using a (more capable) stepper
motor and a ball screw instead of the belt gear driving system.</p>
<div class="center docutils container">
<div class="docutils container" id="tab-namazuvariants">
<div class="pst-scrollable-table-container"><table class="table" id="id4">
<caption><span class="caption-text">Possible hardware variants.</span><a class="headerlink" href="#id4" title="Link to this table">#</a></caption>
<tbody>
<tr class="row-odd"><td><p><strong>Original piece</strong></p></td>
<td><p><strong>Upgraded piece</strong></p></td>
<td><p><strong>Advantage</strong></p></td>
</tr>
<tr class="row-even"><td></td>
<td></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>Belt & gear assembly</p></td>
<td><p>Trapezoidal screw</p></td>
<td><p>Higher accuracy and
payload
capabilities, more
rigid construction
due to no flexible
parts, no
inaccuracies due to
belt slipping</p></td>
</tr>
<tr class="row-even"><td></td>
<td><p>Ball screw</p></td>
<td><p>Even higher accuracy
and payload
capabilities,
smoother operation
than trapezoidal
screws, no
inaccuracies due to
belt slipping</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>Friction bearings</p></td>
<td><p>Roller bearings
(SBR16UU etc.)</p></td>
<td><p>Higher payload
capabilities</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>Frame</p></td>
<td><p>Pre-built linear
positioning table</p></td>
<td><p>Higher manufacturing
accuracy, multiple
variants available</p></td>
</tr>
<tr class="row-odd"><td></td>
<td></td>
<td></td>
</tr>
<tr class="row-even"><td><p>NEMA23 motor, DM542
driver</p></td>
<td><p>NEMA34 motor, DM860T
driver</p></td>
<td><p>Higher torque,
higher payload</p></td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
<p>The table can also be tuned to decrease the cost. A motor with a lower
torque such as the NEMA17 motor could be employed. These motors are very
common since they are a standard parts used in 3D printers. There exists
a wide variety of motor and driver combinations, thus we can not provide
a comprehensive list. <a class="reference external" href="#tab:PartsAndCosts">1</a> shows that the highest
cost in the setup comes from the power supply. We use here an adjustable
power supply. It could be changed by a fixed voltage power supply to
save cost.</p>
<section id="hardware-interface">
<span id="hwinterface"></span><h3><strong>Hardware interface</strong><a class="headerlink" href="#hardware-interface" title="Link to this heading">#</a></h3>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>These functionalities are currently under development and should be used with caution.</p>
</div>
<p>We implemented an option to connect buttons and limit switches to the table. The buttons can be used to enhance the functionality as they provide a direct way of starting and stopping the experiments, as well as moving the table to a desired position and centering the table in the middle position. The limit switches provide an additional safety mechanism and are also necessary to center the table.</p>
</section>
<section id="references">
<h3>References<a class="headerlink" href="#references" title="Link to this heading">#</a></h3>
<div class="docutils container" id="id2">
<aside class="footnote-list brackets">
<aside class="footnote brackets" id="footcite-damci2019development" role="doc-footnote">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">1</a><span class="fn-bracket">]</span></span>
<p>E Damcı and Çagla Şekerci. Development of a low-cost single-axis shake table based on arduino. <em>Experimental Techniques</em>, 43(2):179–198, 2019.</p>
</aside>
</aside>
</div>
</section>
</section>
</section>
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