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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Testing - Speedster Team Finger</title>
<link rel="icon" type="image/x-icon" href="static/images/Speedster Finger.jpg">
<link rel="stylesheet" href="static/css/bulma.min.css">
<link rel="stylesheet" href="static/css/index.css">
<link rel="preload" href="static/css/fontawesome.all.min.css" as="style" onload="this.onload=null;this.rel='stylesheet'">
<link href="https://fonts.googleapis.com/css2?family=Inter:wght@400;500;600;700;800&display=swap" rel="stylesheet">
<script defer src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<script defer src="static/js/fontawesome.all.min.js"></script>
<style>
/* ── sticky nav ── */
.test-nav {
position: sticky;
top: 0;
z-index: 30;
background: rgba(255,255,255,.96);
backdrop-filter: blur(6px);
padding: .75rem 0;
border-bottom: 1px solid #e8e0f0;
}
/* ── section dividers ── */
.test-section {
padding-top: 3rem;
padding-bottom: 2rem;
border-top: 1px solid #ede8f5;
}
.test-section:first-of-type { border-top: none; }
.anchor-offset { scroll-margin-top: 70px; }
/* ── section heading ── */
.section-title {
font-size: 1.4rem;
font-weight: 700;
color: #2e1a56;
letter-spacing: -0.01em;
margin-bottom: 1.25rem;
display: flex;
align-items: center;
gap: 0.6rem;
}
.title-num {
display: inline-flex;
align-items: center;
justify-content: center;
width: 32px;
height: 32px;
border-radius: 50%;
background: #4E2A84;
color: #fff;
font-size: 0.85rem;
font-weight: 700;
flex-shrink: 0;
}
/* ── metric pills ── */
.metric-row {
display: flex;
flex-wrap: wrap;
gap: 8px;
justify-content: center;
margin-bottom: 1.5rem;
}
.metric-pill {
display: inline-flex;
align-items: center;
border-radius: 999px;
overflow: hidden;
font-size: 13px;
font-weight: 500;
border: 1px solid #cfc0ed;
}
.metric-pill .pill-label {
background: #f0ecfa;
color: #4E2A84;
padding: 5px 11px;
}
.metric-pill .pill-value {
background: #4E2A84;
color: #fff;
padding: 5px 12px;
}
/* ── tables ── */
.test-table-wrap {
border-radius: 12px;
overflow: hidden;
box-shadow: 0 2px 12px rgba(78,42,132,0.10);
margin-bottom: 1.5rem;
}
.test-table {
width: 100%;
border-collapse: collapse;
font-size: 14px;
}
.test-table thead th {
background: #4E2A84;
color: #fff;
padding: 11px 15px;
font-weight: 600;
border: none;
white-space: nowrap;
}
.test-table tbody td {
padding: 10px 15px;
border: none;
border-bottom: 1px solid rgba(78,42,132,0.07);
vertical-align: middle;
color: #2c2040;
}
.test-table tbody tr:last-child td { border-bottom: none; }
.test-table tbody tr:nth-child(even) td { background: #f8f5fd; }
.test-table tbody tr:hover td { background: #ede8f8; }
/* ── figure captions ── */
.fig-caption {
font-size: 0.97rem;
color: #5a4e70;
margin-top: 0.65rem;
line-height: 1.6;
font-style: italic;
}
/* ── body text ── */
.test-section .content p {
font-size: 1.05rem;
line-height: 1.75;
}
/* ── note boxes ── */
.test-note {
display: flex;
gap: 10px;
align-items: flex-start;
background: #f0ecfa;
border-left: 4px solid #4E2A84;
border-radius: 0 10px 10px 0;
padding: 14px 16px;
font-size: 0.97rem;
color: #3a2060;
margin-top: 1.5rem;
line-height: 1.65;
}
.test-note .note-icon {
color: #4E2A84;
flex-shrink: 0;
margin-top: 2px;
}
.test-note code {
background: #ddd5f5;
color: #2e1a56;
padding: 1px 5px;
border-radius: 4px;
font-size: 0.9rem;
}
/* ── figure images ── */
.test-figure {
border-radius: 10px;
overflow: hidden;
background: #faf9fd;
border: 1px solid #ede8f5;
position: relative;
cursor: zoom-in;
transition: box-shadow 0.2s ease, transform 0.15s ease;
}
.test-figure:hover {
box-shadow: 0 6px 24px rgba(78,42,132,0.18);
transform: translateY(-1px);
}
.test-figure img { display: block; width: 100%; }
.test-figure::after {
content: "🔍 click to enlarge";
position: absolute;
bottom: 8px;
right: 10px;
background: rgba(20, 10, 40, 0.88);
color: #fff;
font-size: 0.82rem;
font-weight: 600;
font-style: normal;
padding: 4px 10px;
border-radius: 999px;
opacity: 0;
transition: opacity 0.2s ease;
pointer-events: none;
font-family: Inter, sans-serif;
letter-spacing: 0.01em;
}
.test-figure:hover::after { opacity: 1; }
/* ── lightbox ── */
#lightbox {
display: none;
position: fixed;
inset: 0;
z-index: 9999;
background: rgba(18, 10, 35, 0.88);
backdrop-filter: blur(8px);
align-items: center;
justify-content: center;
padding: 24px;
cursor: zoom-out;
}
#lightbox.is-open { display: flex; }
#lightbox-img {
max-width: min(92vw, 1200px);
max-height: 88vh;
border-radius: 10px;
box-shadow: 0 24px 80px rgba(0,0,0,0.6);
object-fit: contain;
cursor: default;
animation: lb-in 0.2s ease;
}
@keyframes lb-in {
from { opacity: 0; transform: scale(0.93); }
to { opacity: 1; transform: scale(1); }
}
#lightbox-caption {
position: absolute;
bottom: 20px;
left: 50%;
transform: translateX(-50%);
color: rgba(255,255,255,0.85);
font-size: 0.88rem;
font-style: italic;
text-align: center;
max-width: 720px;
pointer-events: none;
line-height: 1.5;
}
#lightbox-close {
position: absolute;
top: 16px;
right: 20px;
background: rgba(255,255,255,0.12);
border: none;
color: #fff;
font-size: 1.4rem;
width: 38px;
height: 38px;
border-radius: 50%;
cursor: pointer;
display: flex;
align-items: center;
justify-content: center;
transition: background 0.15s;
}
#lightbox-close:hover { background: rgba(255,255,255,0.25); }
</style>
</head>
<body>
<!-- Lightbox -->
<div id="lightbox" role="dialog" aria-modal="true" aria-label="Enlarged image">
<button id="lightbox-close" aria-label="Close">×</button>
<img id="lightbox-img" src="" alt="">
<p id="lightbox-caption"></p>
</div>
<!-- Header -->
<section class="hero">
<div class="hero-body pb-0">
<div class="container is-max-desktop">
<div class="columns is-centered">
<div class="column has-text-centered">
<h1 class="title is-1 publication-title">Speedster Team Finger</h1>
<p class="is-size-5 has-text-grey">Northwestern University · RDS Course Final Demonstration</p>
</div>
</div>
</div>
</div>
</section>
<!-- Navigation -->
<section class="section py-2">
<div class="container is-max-desktop">
<div class="columns is-centered">
<div class="column has-text-centered">
<a href="index.html" class="button is-rounded is-medium mx-2" style="background-color:#4E2A84;color:white;border:none;">
<span class="icon"><i class="fas fa-home"></i></span>
<span>Home</span>
</a>
<a href="bom.html" class="button is-rounded is-medium mx-2" style="background-color:#4E2A84;color:white;border:none;">
<span class="icon"><i class="fas fa-list"></i></span>
<span>Bill of Materials</span>
</a>
<a href="schematics.html" class="button is-rounded is-medium mx-2" style="background-color:#4E2A84;color:white;border:none;">
<span class="icon"><i class="fas fa-drafting-compass"></i></span>
<span>Schematics</span>
</a>
<a href="testing.html" class="button is-rounded is-medium mx-2" style="background-color:#4E2A84;color:white;border:none;">
<span class="icon"><i class="fas fa-flask"></i></span>
<span>Testing</span>
</a>
<a href="https://github.com/NU-RDS/Speedster-Codebase" target="_blank" class="button is-rounded is-medium mx-2" style="background-color:#4E2A84;color:white;border:none;">
<span class="icon"><i class="fab fa-github"></i></span>
<span>Code</span>
</a>
</div>
</div>
</div>
</section>
<!-- Page Title Banner -->
<section class="hero is-primary mt-4">
<div class="hero-body">
<div class="container is-max-desktop has-text-centered">
<h2 class="title is-1 mb-4">Testing</h2>
<p class="subtitle is-4 has-text-white mt-4">Characterization test results for the Speedster finger</p>
</div>
</div>
</section>
<!-- Jump-to-test nav -->
<div class="test-nav">
<div class="container is-max-desktop has-text-centered">
<div class="dropdown is-hoverable">
<div class="dropdown-trigger">
<button class="button is-rounded is-medium" style="background:#4E2A84;color:#fff;border:none;" aria-haspopup="true" aria-controls="test-menu">
<span class="icon"><i class="fas fa-flask"></i></span>
<span>Jump to Test</span>
<span class="icon is-small"><i class="fas fa-angle-down"></i></span>
</button>
</div>
<div class="dropdown-menu" id="test-menu" role="menu">
<div class="dropdown-content has-text-left">
<a href="#impedance" class="dropdown-item">1 · Fingertip Impedance</a>
<a href="#trajectory" class="dropdown-item">2 · Trajectory Tracking</a>
<a href="#position" class="dropdown-item">3 · Sinusoidal Position Control</a>
<a href="#velocity" class="dropdown-item">4 · Velocity Control Bandwidth</a>
<a href="#cycle" class="dropdown-item">5 · Finger Cycle Time</a>
<a href="#steppos" class="dropdown-item">6 · Step Position Control</a>
<a href="#forcestep" class="dropdown-item">7 · Step Force Control</a>
</div>
</div>
</div>
</div>
</div>
<!-- Main Content -->
<section class="section pt-5">
<div class="container is-max-desktop publication-body">
<p class="has-text-centered has-text-grey mb-6" style="font-size:1rem;">
Seven characterization tests of the 3-DOF tendon-driven finger. Each result is processed from
raw test data; figures and headline metrics are shown below.
</p>
<!-- ══════════ 1 · FINGERTIP IMPEDANCE ══════════ -->
<div class="test-section anchor-offset" id="impedance">
<h2 class="section-title">
<span class="title-num">1</span>
Fingertip Impedance
</h2>
<div class="metric-row">
<span class="metric-pill"><span class="pill-label">Stiffness</span><span class="pill-value">1.4–2.2 kN/m</span></span>
<span class="metric-pill"><span class="pill-label">Mass</span><span class="pill-value">40–89 g</span></span>
</div>
<div class="content has-text-justified" style="color:#3a3050;">
<p>Equivalent mechanical impedance of the fingertip, measured across three finger configurations.
The extended pose is the most compliant and lightly damped; the retracted pose is the stiffest;
the middle pose is the most damped.</p>
</div>
<div class="columns is-centered">
<div class="column is-three-quarters">
<div class="test-table-wrap">
<table class="test-table">
<thead>
<tr>
<th>Configuration</th><th>Mass (g)</th><th>Damping (N·s/m)</th><th>Stiffness (N/m)</th><th>Mean coh.</th>
</tr>
</thead>
<tbody>
<tr><td>1 : Extended</td><td>49.3</td><td>1.49</td><td>1424</td><td>0.95</td></tr>
<tr><td>2 : Retracted</td><td>39.7</td><td>7.39</td><td>2234</td><td>0.88</td></tr>
<tr><td>3 : Mid</td><td>89.1</td><td>16.23</td><td>2070</td><td>0.65</td></tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="columns mt-5">
<div class="column">
<div class="test-figure" data-caption="Config 1 — extended.">
<img src="static/images/testing/impedance_extended.png" alt="Config 1 fit">
</div>
<p class="fig-caption has-text-centered">Config 1 | Extended.</p>
</div>
<div class="column">
<div class="test-figure" data-caption="Config 2 — retracted.">
<img src="static/images/testing/impedance_retracted.png" alt="Config 2 fit">
</div>
<p class="fig-caption has-text-centered">Config 2 | Retracted.</p>
</div>
<div class="column">
<div class="test-figure" data-caption="Config 3 — mid.">
<img src="static/images/testing/impedance_middle.png" alt="Config 3 fit">
</div>
<p class="fig-caption has-text-centered">Config 3 | Middle</p>
</div>
</div>
</div>
<!-- ══════════ 2 · TRAJECTORY TRACKING ══════════ -->
<div class="test-section anchor-offset" id="trajectory">
<h2 class="section-title">
<span class="title-num">2</span>
Trajectory Tracking
</h2>
<div class="metric-row">
<span class="metric-pill"><span class="pill-label">Average RMS Error</span><span class="pill-value">7.352 mm</span></span>
<span class="metric-pill"><span class="pill-label">Average Mean Error</span><span class="pill-value">6.591 mm</span></span>
<span class="metric-pill"><span class="pill-label">Average Max Error</span><span class="pill-value">12.573 mm</span></span>
</div>
<div class="video" style="display:flex; flex-direction:column; align-items:center; justify-content:center;">
<div style="width:100%; max-width:800px; margin:0 auto; border-radius:12px; overflow:hidden; box-shadow:0 8px 32px rgba(78,42,132,0.18);">
<div style="position:relative; aspect-ratio:16/9;">
<iframe style="position:absolute; top:0; left:0; width:100%; height:100%; border:none;"
src="https://www.youtube.com/embed/9s27Xjp0ZQc?si=UtnszTUuHPwZIWpe"
title="Lissajous Test"
referrerpolicy="strict-origin-when-cross-origin"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share"
allowfullscreen></iframe>
</div>
</div>
<p style="max-width:800px; text-align:center; margin-top:10px; font-size:14px; color:#666;">
Video of the Lissajous trajectory we attempted to track.
</p>
</div>
<div class="columns is-centered">
<div class="column is-three-quarters">
<div class="test-table-wrap">
<table class="test-table">
<thead>
<tr>
<th>Trial</th><th>Mean Error(mm)</th><th>RMS Error(mm)</th><th>Max Error(mm)</th>
</tr>
</thead>
<tbody>
<tr><td>1</td><td>5.919</td><td>6.789</td><td>11.829</td></tr>
<tr><td>2</td><td>6.164</td><td>6.982</td><td>12.045</td></tr>
<tr><td>3</td><td>7.463</td><td>8.076</td><td>12.573</td></tr>
<tr><td>4</td><td>6.817</td><td>7.491</td><td>12.323</td></tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="content has-text-justified" style="color:#3a3050;">
<p>The fingertip traces a 1:2 Lissajous figure in the flexion plane while a marker is tracked
by camera. From the figure it can be seen that the finger tip does not fully track the desired trajectory, with an average max error of 12.573mm,
however, the result is very repeatable.</p>
</div>
<div class="test-figure" data-caption="Lassajous Trajectory Tracking">
<img src="static/images/testing/lassajous_out.png" alt="Lassajous Trajectory Tracking">
</div>
</div>
<!-- ══════════ 3 · SINUSOIDAL POSITION CONTROL ══════════ -->
<div class="test-section anchor-offset" id="position">
<h2 class="section-title">
<span class="title-num">3</span>
Sinusoidal Position Control
</h2>
<div class="metric-row">
<span class="metric-pill"><span class="pill-label">DC gain</span><span class="pill-value">1.29 (+2.22 dB)</span></span>
<span class="metric-pill"><span class="pill-label">−3 dB BW</span><span class="pill-value">3.15 Hz</span></span>
</div>
<div class="content has-text-justified" style="color:#3a3050;">
<p>The finger reached its -3dB bandwidth at a frequency of 3.15Hz, meaning that it was able to achieve a linear response up this frequency. The system begins
to experience attenuation after this point, with a significant magniutde drop off at around 7Hz. There also looks to be a resonant peak around 8Hz, however,
it is difficult to make a conclusive claim about this, as the coherence drops below 0.6 at frequencies greater than 6Hz. Low coherence is also present in the low
frequency range, indicating that the chirp signal was not long enough to get a meaningful reading. The last indicator of our systems performance is the phase delay,
which can be seen to be near zero between 1 and 5 Hz, indicating that minimal phase lag was present at these frequencies. The lack of coherence at higher frequencies
makes the phase response unreliable from this reading.
</p>
</div>
<div class="video" style="display:flex; flex-direction:column; align-items:center; justify-content:center;">
<div style="width:100%; max-width:800px; margin:0 auto; border-radius:12px; overflow:hidden; box-shadow:0 8px 32px rgba(78,42,132,0.18);">
<div style="position:relative; aspect-ratio:16/9;">
<iframe style="position:absolute; top:0; left:0; width:100%; height:100%; border:none;"
src="https://www.youtube.com/embed/LtvgRochfXE?si=3lrWFA3bX2FksK_C"
title="Position Chirp Test"
referrerpolicy="strict-origin-when-cross-origin"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share"
allowfullscreen></iframe>
</div>
</div>
<p style="max-width:800px; text-align:center; margin-top:10px; font-size:14px; color:#666;">
Video of the position chirp test we ran to obtain the data for this test.
</p>
</div>
<div class="test-figure" data-caption="Position Chirp Bode Plot">
<img src="static/images/testing/position_chirp_bode.jpg" alt="Position Chirp Bode Plot">
</div>
<p class="fig-caption has-text-centered">Bode plot of position chirp from 0.1 to 30 Hz.</p>
<div class="test-figure" data-caption="Time series of a the position chirp from 0.1 to 30 Hz.">
<img src="static/images/testing/finger_tip_joint_angle.png" alt="Time series of chirp">
</div>
<p class="fig-caption has-text-centered">Time series of the position chirp from 0.1 to 30 Hz.</p>
</div>
<!-- ══════════ 4 · VELOCITY CONTROL BANDWIDTH ══════════ -->
<div class="test-section anchor-offset" id="velocity">
<h2 class="section-title">
<span class="title-num">4</span>
Velocity Control Bandwidth
</h2>
<div class="content has-text-justified" style="color:#3a3050;">
<p>The -3dB bandwidth for the velocity control is 2.5Hz which is slightly lower than the 3.15Hz result for the postion controller. There
seems to be some attenuation present in the system, however, the range between 3 to 10 Hz seems to be somewhat consistent. The phase
delay seems to be very large, and in general behaves very inconsistently. This is further supported by the fact that the coherence throughout the
analysis is below 0.8, only showing a good coherence between 7 and 8 Hz. The most likely reason for this is noise accumulation in the derivation of the
velocity values, as we first obtain the position values of the fingertip from a video stream, which we then use to differentiate with Savitsky Golay. This process
causes any noise to stack which is felt strongly when converting to the frequency domain.
</p>
</div>
<div class="video" style="display:flex; flex-direction:column; align-items:center; justify-content:center;">
<div style="width:100%; max-width:800px; margin:0 auto; border-radius:12px; overflow:hidden; box-shadow:0 8px 32px rgba(78,42,132,0.18);">
<div style="position:relative; aspect-ratio:16/9;">
<iframe style="position:absolute; top:0; left:0; width:100%; height:100%; border:none;"
src="https://www.youtube.com/embed/kEPaQY82J-U?si=DLOizE5mkw0Ku4vn"
title="Velocity Chirp Test"
referrerpolicy="strict-origin-when-cross-origin"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share"
allowfullscreen></iframe>
</div>
</div>
<p style="max-width:800px; text-align:center; margin-top:10px; font-size:14px; color:#666;">
Video of the velocity chirp test we ran to obtain the data for this test.
</p>
</div>
<div class="test-figure" data-caption="Velocity Chirp Bode Plot">
<img src="static/images/testing/velocity_chirp_bode.png" alt="Velocity Chirp Bode Plot">
</div>
<p class="fig-caption has-text-centered">Bode plot of velocity chirp from 0.1 to 30 Hz.</p>
<div class="test-figure" data-caption="Time series of a the velocity chirp from 0.1 to 30 Hz.">
<img src="static/images/testing/velocity.png" alt="Time series of the velocity chirp">
</div>
<p class="fig-caption has-text-centered">Time series of the velocity chirp from 0.1 to 30 Hz.</p>
</div>
<!-- ══════════ 5 · FINGER CYCLE TIME ══════════ -->
<div class="test-section anchor-offset" id="cycle">
<h2 class="section-title">
<span class="title-num">5</span>
Finger Cycle Time
</h2>
<div class="metric-row">
<span class="metric-pill"><span class="pill-label">Max Cycle Frequency</span><span class="pill-value">3.45 Hz</span></span>
<span class="metric-pill"><span class="pill-label">Range of Motion</span><span class="pill-value">88.8°</span></span>
</div>
<div class="content has-text-justified" style="color:#3a3050;">
<p>Time to complete one full extension–flexion cycle through the entire range of motion, driven
by a 3.5 Hz square wave. The finger tracks essentially perfectly: mean cycle time 0.290 s
(3.45 Hz, within 1.5% of command) over 10 cycles, with the full ~89° MCP range reached every cycle.</p>
</div>
<div class="columns is-centered">
<div class="column is-three-quarters">
<div class="test-table-wrap">
<table class="test-table">
<tbody>
<tr><td>Average cycle time (10 cycles)</td><td>0.290 s (σ 0.19 ms)</td></tr>
<tr><td>MCP range of motion</td><td>88.8° (0.4° → 89.2°)</td></tr>
<tr><td>Peak acceleration</td><td>+30,935 °/s² (+540 rad/s²)</td></tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="test-figure" data-caption="Full run — actual vs commanded MCP angle, 10-cycle analysis window shaded.">
<img src="static/images/testing/cyc_overview.png" alt="Cycle time overview">
</div>
<p class="fig-caption has-text-centered">Full run — actual vs commanded MCP angle, 10-cycle analysis window shaded.</p>
<div class="test-figure mt-4" data-caption="The 10 analysed cycles with detected boundaries.">
<img src="static/images/testing/cyc_zoom.png" alt="Ten cycles">
</div>
<p class="fig-caption has-text-centered">The 10 analysed cycles with detected boundaries.</p>
</div>
<!-- ══════════ 6 · STEP POSITION CONTROL ══════════ -->
<div class="test-section anchor-offset" id="steppos">
<h2 class="section-title">
<span class="title-num">6</span>
Step Position Control
</h2>
<div class="metric-row">
<span class="metric-pill"><span class="pill-label">Settling (2%)</span><span class="pill-value">92 ms</span></span>
<span class="metric-pill"><span class="pill-label">Overshoot</span><span class="pill-value">0.11%</span></span>
<span class="metric-pill"><span class="pill-label">Steady-State Err</span><span class="pill-value">0.19°</span></span>
</div>
<div class="content has-text-justified" style="color:#3a3050;">
<p>Step response tracking a 1 Hz square-wave position reference against a spring environment.
The controller settles all 27 steps within the 0.5s half-period, with fast rise and essentially no overshoot.</p>
</div>
<div class="video" style="display:flex; flex-direction:column; align-items:center; justify-content:center;">
<div style="width:100%; max-width:800px; margin:0 auto; border-radius:12px; overflow:hidden; box-shadow:0 8px 32px rgba(78,42,132,0.18);">
<div style="position:relative; aspect-ratio:16/9;">
<iframe style="position:absolute; top:0; left:0; width:100%; height:100%; border:none;"
src="https://www.youtube.com/embed/OtefZUolBTg?si=0OZvI-V91jLRrc7U"
title="Spring Linear Move"
referrerpolicy="strict-origin-when-cross-origin"
allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share"
allowfullscreen></iframe>
</div>
</div>
<p style="max-width:800px; text-align:center; margin-top:10px; font-size:14px; color:#666;">
Video of the finger following a step position referenced again a spring.
</p>
</div>
<div class="columns is-centered">
<div class="column is-three-quarters">
<div class="test-table-wrap">
<table class="test-table">
<thead>
<tr><th>Metric</th><th>Rising</th><th>Falling</th><th>All</th></tr>
</thead>
<tbody>
<tr><td>Settling time (2%)</td><td>94.3 ms</td><td>90.0 ms</td><td>92.2 ms</td></tr>
<tr><td>Rise/fall (10–90%)</td><td>45.2 ms</td><td>41.2 ms</td><td>43.3 ms</td></tr>
<tr><td>Overshoot</td><td>0.13%</td><td>0.09%</td><td>0.11%</td></tr>
<tr><td>Steady-state error</td><td>0.29°</td><td>0.07°</td><td>0.19°</td></tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="test-figure" data-caption="Square-wave command and measured pip/dip response.">
<img src="static/images/testing/step_overlay.png" alt="Step response full run">
</div>
<p class="fig-caption has-text-centered">Square-wave command and measured pip/dip response.</p>
<div class="columns mt-5">
<div class="column">
<div class="test-figure" data-caption="All steps time-aligned and overlaid.">
<img src="static/images/testing/step_overlaid.png" alt="Steps overlaid">
</div>
<p class="fig-caption has-text-centered">All steps time-aligned and overlaid.</p>
</div>
<div class="column">
<div class="test-figure" data-caption="Representative step annotated with metrics.">
<img src="static/images/testing/step_representative.png" alt="Representative step">
</div>
<p class="fig-caption has-text-centered">Representative step annotated with metrics.</p>
</div>
</div>
</div>
<!-- ══════════ 7 · STEP FORCE CONTROL ══════════ -->
<div class="test-section anchor-offset" id="forcestep">
<h2 class="section-title">
<span class="title-num">7</span>
Step Force Control
</h2>
<div class="metric-row">
<span class="metric-pill"><span class="pill-label">Settling</span><span class="pill-value">0.2–0.3 s</span></span>
<span class="metric-pill"><span class="pill-label">Rise Time</span><span class="pill-value">35–70 ms</span></span>
<span class="metric-pill"><span class="pill-label">Overshoot</span><span class="pill-value">2–3%</span></span>
</div>
<div class="content has-text-justified" style="color:#3a3050;">
<p>Force step response tracking a square-wave force reference (alternating every ~1 s) at
several force ranges, measured with a stationary load cell.
Tests ran from force intervals starting at a low range of 1 N and stepping to 3 N, 10 N, 15 N, and 20 N.
The high force range response is very fast and settles in ~0.2–0.3 s, whereas the low force range is fast but never fully settles.</p>
</div>
<div class="columns is-centered">
<div class="column">
<div class="test-table-wrap">
<table class="test-table">
<thead>
<tr>
<th>Level</th><th>Achieved lo/hi (N)</th><th>Step (N)</th><th>Settle (ms)</th><th>Rise/fall (ms)</th><th>Overshoot (%)</th>
</tr>
</thead>
<tbody>
<tr><td>3 N</td><td>4.5 / 5.1</td><td>0.6</td><td>842 ± 109</td><td>14 ± 16</td><td>11.9 ± 2.7</td></tr>
<tr><td>10 N</td><td>5.2 / 13.2</td><td>8.0</td><td>210 ± 266</td><td>36 ± 9</td><td>2.8 ± 0.7</td></tr>
<tr><td>15 N</td><td>3.1 / 16.6</td><td>13.6</td><td>374 ± 357</td><td>75 ± 108</td><td>3.3 ± 3.3</td></tr>
<tr><td>20 N</td><td>4.5 / 25.4</td><td>20.9</td><td>288 ± 352</td><td>66 ± 27</td><td>2.0 ± 2.2</td></tr>
</tbody>
</table>
</div>
</div>
</div>
<div class="test-figure" data-caption="Measured load-cell force at each force level.">
<img src="static/images/testing/force_overview.png" alt="Force square waves">
</div>
<p class="fig-caption has-text-centered">Measured load-cell force at each force level.</p>
<div class="test-figure mt-4" data-caption="Rising steps time-aligned and overlaid.">
<img src="static/images/testing/force_steps.png" alt="Force steps overlaid">
</div>
<p class="fig-caption has-text-centered">Rising steps time-aligned and overlaid.</p>
</div>
</div>
</section>
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