Add AC/BC RTCP programs and 3D machine manager
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# 五轴机床与 RTCP 教学课件
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新增完整教材：[五轴RTCP与工件坐标：初学者完整讲义（72页A4）](../rtcp-beginners/五轴RTCP与工件坐标-初学者完整讲义.pdf)。系统补充原点/方向、G54配准、G代码逐字/逐行和真实关节计算。下方31页文件保留作投影概要；详细学习优先使用[完整版索引](../rtcp-beginners/README.md)。
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已交付：[五轴机床与RTCP-教学课件.pdf](五轴机床与RTCP-教学课件.pdf)，31 页、16:9 横向、中文可选择文本、目录书签。建议 60–90 分钟，适合投影或分两次授课。
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可编辑/离线阅读源稿：[course.html](course.html)。原理图和机床截图在 `assets/`，各页目录在 [outline.json](outline.json)。整个目录可离线使用；PDF 内的官方资料链接需要联网。
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## 核心理解
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- 五轴通常是 XYZ 加 AC 或 BC，本课以刀具侧 XYZ、工件侧 A/B→C 的双转台桁架为例，不把六个字母都当成五个轴。
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- 非 RTCP 的“独立”指不自动做旋转姿态引起的 XYZ 几何补偿，不代表不能同步插补，也不代表刀具与工件的相对位置不会改变。
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- G 代码的数值需要经过单位、绝对/增量、工件偏置、刀具补偿等解释；不能不加条件地等同于真实编码器反馈。
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- RTCP 根据目标位置、角度和机床几何换算关节位置。工件坐标方向随转台改变，但导轨方向并未旋转；旋转中心、轴间偏置及刀长也参与计算。
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- “刀尖跟随”是相对工件的目标关系。保持同一编程点时，刀尖可在机床空间移动；切换模式时则应保持物理关节，允许坐标数值重新解释。
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## 课程组织
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| 页码 | 内容 |
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| --- | --- |
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| 1–5 | 对原始表述的修正、轴名、两条机械链、AC/BC 桁架模型 |
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| 6–7 | 编程点、关节指令、实际反馈；G54/G90/G91 等影响 |
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| 8–13 | 非RTCP/RTCP点追踪、C轴算例、工件方向与AC/BC倾转 |
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| 14–17 | 旋转中心、偏置、父子顺序、刀长、相对刀轴方向 |
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| 18–21 | 联动情形、中间轨迹、模式切换、TCP/倾斜平面/刀补区别 |
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| 22–26 | G代码对照、浏览器实验、参数编辑、限位与常见误解 |
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| 27–28 | 五道课堂练习及答案 |
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| 29–31 | 公式推导、本项目完整参数式、课时安排和资料依据 |
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## 验证与来源
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- [numeric-evidence.json](numeric-evidence.json)：实际加载仓库 WASM，12 个姿态逆解及正解回代、方向增量、切换模式、圆弧与弦线比较；附 WASM SHA256。
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- [verification/layout.json](verification/layout.json)：31 页逐页边界、图片加载与页面错误检查。
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- [verification/acceptance.json](verification/acceptance.json)：PDF 页数、文本/字体、书签、文件哈希及数值验证汇总。
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- 原理示意图由 Matplotlib 绘制；机床图片来自本项目原创 GLB 渲染，没有使用许可不明的网络机床图片。
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- 已核对 [LinuxCNC 五轴运动学](https://linuxcnc.org/docs/html/motion/5-axis-kinematics.html)、[Switchkins](https://linuxcnc.org/docs/html/motion/switchkins.html)、[CNC Machine Overview](https://linuxcnc.org/docs/html/gcode/machining-center.html)，以及本地 `trtfuncs.c`、`control.c`、`428remap.ngc` 和 `429remap.ngc`。
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本课主要数值例子使用零旋转中心/偏置/刀长差，以分离概念；第20页模式切换使用真实BC示例参数。图的正向变换采用本项目原生AC/BC约定，不据此决定真实电机接线正负。M428/M429 是本项目重映射，不是跨控制器通用标准。内容为仿真教学，不替代真实机床标定与操作规程。
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## 重新生成
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不修改应用源码、上游或已有本地改动。Matplotlib/PyPDF 仅安装在临时目录，没有新增项目依赖。
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```bash
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node scripts/generate_rtcp_teaching_data.mjs
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PYTHONPATH=/tmp/rtcp-course-deps python3 scripts/generate_rtcp_teaching_figures.py
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# 仅重新截图模型时需要 http://127.0.0.1:5174/ 开发服务；已有资产可直接复用。
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PLAYWRIGHT_MODULE=/home/mes006/.npm/_npx/e41f203b7505f1fb/node_modules/playwright/index.mjs node scripts/capture_rtcp_teaching_models.mjs
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python3 scripts/generate_rtcp_teaching_html.py
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PLAYWRIGHT_MODULE=/home/mes006/.npm/_npx/e41f203b7505f1fb/node_modules/playwright/index.mjs node scripts/render_rtcp_teaching_pdf.mjs
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PYTHONPATH=/tmp/rtcp-course-deps python3 scripts/verify_rtcp_teaching_pdf.py
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```
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换环境需准备 Python Matplotlib/PyPDF、Chrome、Playwright 及 Noto Sans CJK 字体；已交付的 PDF 不依赖这些工具。
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<!doctype html><html lang="zh-CN"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><title>五轴机床与 RTCP：从各轴独立到刀尖跟随</title><style>
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</style></head><body><section class="slide cover" data-page="1">
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<div class="chapter">教学课件 · 2026.09</div><h1>五轴机床与 RTCP</h1>
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<div class="body"><div class="cover-grid"><div><p class="subtitle">从“各轴独立”到“刀尖跟随”</p><p>看懂两个坐标系、一棵结构树、<br>一条运动学计算链。</p><div class="rule"></div><p class="small">适用对象：数控入门、五轴调试与仿真教学<br>主线机型：XYZAC / XYZBC 双转台桁架机床<br>建议课时：60–90 分钟，可拆成两讲</p><p class="badge">原理图解 + 数值演算 + 浏览器实验 + 练习答案</p></div><figure class="cover-model"><img src="assets/machine-bc.png" alt="原创 BC 桁架模型：XYZ 移动刀具，B–C 转动工件"><figcaption>原创 BC 桁架模型：XYZ 移动刀具，B–C 转动工件</figcaption></figure></div></div>
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<div class="takeaway">核心问题：程序中的 XYZ，究竟是在告诉谁“去哪里”？</div>
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<footer class="footer"><span class="source">图：本项目原创 GLB 模型；数值：LinuxCNC WASM 实算。</span><span class="page-number">01 / 31</span></footer>
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</section><section class="slide " data-page="2">
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<div class="chapter">01 · 先统一理解</div><h1>你的两点理解，怎样说得更准确？</h1>
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<div class="body"><div class="cols"><div><h3>① 非 RTCP：直接轴映射</h3><p>在本课的双转台结构中，XYZ 带动刀具，A/C 或 B/C 带动工件。</p><p><b>只改变旋转轴指令，不自动触发 XYZ 的刀尖保持补偿。</b>但多个轴仍可在同一段 G 代码中协调插补。</p><p class="small">“独立”描述几何映射，不是运动时间完全无关。</p></div><div><h3>② RTCP：保持刀尖相对工件的轨迹</h3><p>控制器根据编程点、转台角度、旋转中心和标定参数，计算实际关节位置。</p><p><b>工件坐标方向随转台变换，XYZ 关节按需联动。</b>计算还包括平移与偏置，不能只旋转方向箭头。</p><p class="small">“跟随”是相对工件满足目标关系，不是世界坐标中的刀尖永远不动。</p></div></div></div>
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<div class="takeaway">课程约定：先用零工件偏置、零刀长差的简化模型讲清原理，再加入实际参数。</div>
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<footer class="footer"><span class="source">[S1][S2]；结合本项目 AC/BC 模型。</span><span class="page-number">02 / 31</span></footer>
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</section><section class="slide " data-page="3">
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<div class="chapter">01 · 结构与轴名</div><h1>五轴 = 三个直线轴 + 两个旋转轴</h1>
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<div class="body"><table class=""><thead><tr><th>名称</th><th>通常的轴线含义</th><th>本课中的执行机构</th></tr></thead><tbody><tr><td>X / Y / Z</td><td>沿三个正交方向平移</td><td>刀具侧的直线滑台、滑枕</td></tr><tr><td>A</td><td>绕 X 方向的轴线转动</td><td>AC 机床的外层倾转轴</td></tr><tr><td>B</td><td>绕 Y 方向的轴线转动</td><td>BC 机床的外层倾转轴</td></tr><tr><td>C</td><td>绕 Z 方向的轴线转动</td><td>装在倾转台上的内层旋转轴</td></tr></tbody></table><div class="pair"><p><b>AC 型：</b>X、Y、Z、A、C</p><p><b>BC 型：</b>X、Y、Z、B、C</p></div><p class="small">XYZABC 六个独立轴同时配置，通常应称六轴。A/B/C 是旋转轴的通用名称，本课不是三只转台轴同时工作。C 的轴线会被父级 A/B 倾转，倾转后不再固定平行于机床 Z。</p></div>
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<div class="takeaway">从正方向看懂箭头前，先确认观察视角、父级坐标系和机床正负号约定。</div>
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<footer class="footer"><span class="source">[S3] 轴命名；图中数值采用本项目原生变换约定。</span><span class="page-number">03 / 31</span></footer>
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</section><section class="slide " data-page="4">
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<div class="chapter">01 · 机械拓扑</div><h1>两条运动链，共用一个底座</h1>
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<div class="body"><figure class="wide-diagram"><img src="assets/hierarchy.png" alt="本课桁架结构：X 带动整个横梁，Y 带动滑座，Z 带动滑枕与刀具。"><figcaption>本课桁架结构：X 带动整个横梁，Y 带动滑座，Z 带动滑枕与刀具。</figcaption></figure><div class="cols tight"><p><b class="blue">刀具分支</b><br>底座 → X → Y → Z<br>运动从父节点传给所有子节点。</p><p><b class="teal">工件分支</b><br>底座 → A/B → C → 工件<br>A/B 转动时，C 的轴线也随之倾斜。</p></div></div>
|
||||
<div class="takeaway">这是一种五轴结构，不是所有五轴机床的通用拓扑；摆头、头台混合型需要不同模型。</div>
|
||||
<footer class="footer"><span class="source">本项目 trt-xyz-gantry/1；旧标准型在 Z 下另有固定主轴箱节点。</span><span class="page-number">04 / 31</span></footer>
|
||||
</section><section class="slide " data-page="5">
|
||||
<div class="chapter">01 · 真实模型</div><h1>AC 与 BC：外层倾转轴不同</h1>
|
||||
<div class="body"><div class="cols model-pair"><figure class=""><img src="assets/machine-ac.png" alt="AC 桁架：A 绕 X，内层 C 随 A 倾转"><figcaption>AC 桁架：A 绕 X，内层 C 随 A 倾转</figcaption></figure><figure class=""><img src="assets/machine-bc.png" alt="BC 桁架：B 绕 Y，内层 C 随 B 倾转"><figcaption>BC 桁架：B 绕 Y，内层 C 随 B 倾转</figcaption></figure></div><p class="small">两者都能实现刀尖相对工件的五轴轨迹，但同一角度数值对应的空间姿态不同；不能只把程序里的 A 字母换成 B，就认为加工姿态完全相同。</p></div>
|
||||
<div class="takeaway">先识别“哪根轴装在哪根轴上”，再选择运动学模型。</div>
|
||||
<footer class="footer"><span class="source">图：原创可下载 GLB；不是制造商的标定尺寸图。</span><span class="page-number">05 / 31</span></footer>
|
||||
</section><section class="slide " data-page="6">
|
||||
<div class="chapter">02 · 三种位置</div><h1>不要把“程序点、关节位置、实际反馈”混为一谈</h1>
|
||||
<div class="body"><table class=""><thead><tr><th>量</th><th>回答的问题</th><th>典型表示</th></tr></thead><tbody><tr><td>编程位置 p</td><td>刀尖相对所用编程参考系要到哪里？</td><td>(X, Y, Z)，加 A/C 或 B/C</td></tr><tr><td>关节指令 q</td><td>各执行轴需要到哪个位置？</td><td>(J0, J1, J2, J3, J4)</td></tr><tr><td>实际反馈 q_actual</td><td>编码器报告电机/机械轴在哪里？</td><td>真实设备中可能存在跟随误差</td></tr><tr><td>三维刀尖位置 r</td><td>把关节和模型组合后，刀尖在场景哪里？</td><td>显示坐标，不是独立运动控制源</td></tr></tbody></table><p class="small">理想仿真中“关节指令 = 关节反馈”常成立，但真实机床两者仍须区分。RTCP 的运动学把 p 转成 q；模型再把 q 投影成画面。</p></div>
|
||||
<div class="takeaway">“实际位置”一词要说明是在说编程坐标、关节指令，还是编码器反馈。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">06 / 31</span></footer>
|
||||
</section><section class="slide " data-page="7">
|
||||
<div class="chapter">02 · G 代码含义</div><h1>非 RTCP 时，G 代码也不总等于机械绝对位置</h1>
|
||||
<div class="body"><div class="flow"><span>程序字值</span><i>→</i><span>单位 / G90–G91</span><i>→</i><span>工件零点 / 补偿</span><i>→</i><span>运动学</span><i>→</i><span>关节指令</span></div><table class=""><thead><tr><th>因素</th><th>为什么不能直接等同</th></tr></thead><tbody><tr><td>G90 与 G91</td><td>G90 通常给绝对目标；G91 给相对增量，X10 不一定是到 X=10。</td></tr><tr><td>G54 等工件坐标系</td><td>工件零点可能偏离机床零点；程序 X10 可能对应机床 X30。</td></tr><tr><td>G92、刀长等补偿</td><td>控制器还需处理偏置和刀具参考点。</td></tr><tr><td>Identity 直接映射</td><td>在完成以上处理后，所选坐标与关节才按配置直接对应。</td></tr></tbody></table><p class="small">简化例：G54 原点位于机床 (20,30,0)，无其他偏置/补偿，程序点 (10,0,5) 对应机床点 (30,30,5)。</p></div>
|
||||
<div class="takeaway">只有把偏置、单位、增量方式、刀具基准都约定好，才能说“程序值直接对应轴位置”。</div>
|
||||
<footer class="footer"><span class="source">[S2][S3]；本页示例为无旋转的 Identity 情形。</span><span class="page-number">07 / 31</span></footer>
|
||||
</section><section class="slide " data-page="8">
|
||||
<div class="chapter">03 · 非 RTCP</div><h1>只转 C，工件点会离开刀尖</h1>
|
||||
<div class="body"><figure class="large-diagram"><img src="assets/identity-no-follow.png" alt="俯视图：蓝色为固定机床坐标；绿色为工件；红色为刀尖。Z 保持 20 mm。"><figcaption>俯视图：蓝色为固定机床坐标；绿色为工件；红色为刀尖。Z 保持 20 mm。</figcaption></figure><p>起点刀尖对准转台上半径 100 mm 的标记点。只命令 C 从 0° 转到 90°，<b>XYZ 关节不补偿</b>，标记点转到另一处，刀尖仍在原来的机床位置。</p></div>
|
||||
<div class="takeaway">轴可以独立驱动，不代表“刀具与工件的相对位置”不受其他轴影响。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">08 / 31</span></footer>
|
||||
</section><section class="slide " data-page="9">
|
||||
<div class="chapter">03 · RTCP</div><h1>同样只改变角度，刀尖跟住工件点</h1>
|
||||
<div class="body"><figure class="large-diagram"><img src="assets/tcp-follow.png" alt="同一个工件局部点 p=(100,0,20)，C=0° 与 C=90°；旋转中心和偏置取零。"><figcaption>同一个工件局部点 p=(100,0,20)，C=0° 与 C=90°；旋转中心和偏置取零。</figcaption></figure><p>保持编程点 p 不变，只改变 C。控制器计算所需 XYZ 关节，让刀尖到达标记点的新机床位置。<b>点在工件坐标中不变，在机床坐标中沿圆弧移动。</b></p></div>
|
||||
<div class="takeaway">判断“跟随”的参考系是工件，而不是屏幕或机床底座。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">09 / 31</span></footer>
|
||||
</section><section class="slide " data-page="10">
|
||||
<div class="chapter">03 · 数值算例 1</div><h1>C 转 90°：同一编程点，不同关节位置</h1>
|
||||
<div class="body"><p class="intro">零偏置、零刀长差，p = (100, 0, 20) mm；A/B = 0°。</p><table class=""><thead><tr><th>C 角度</th><th>RTCP 编程 XYZ</th><th>RTCP 所需关节 XYZ</th><th>非 RTCP：只转 C 的关节 XYZ</th></tr></thead><tbody><tr><td>0°</td><td>(100, 0, 20)</td><td>(100.000, 0.000, 20.000)</td><td>(100, 0, 20)</td></tr><tr><td>45°</td><td>(100, 0, 20)</td><td>(70.711, 70.711, 20.000)</td><td>(100, 0, 20)</td></tr><tr><td>90°</td><td>(100, 0, 20)</td><td>(0.000, 100.000, 20.000)</td><td>(100, 0, 20)</td></tr></tbody></table><div class="equation">q<sub>x</sub> = 100 cos C q<sub>y</sub> = 100 sin C q<sub>z</sub> = 20</div><p class="small">C=90° 时，XYZ 关节目标是 (0,100,20)。这不是控制器偷偷修改了程序点，而是同一点在另一参考系中的正确位置。</p></div>
|
||||
<div class="takeaway">RTCP：程序坐标可以不变，执行轴位置必须按姿态变化。</div>
|
||||
<footer class="footer"><span class="source">numeric-evidence.json；原生 WASM IK/FK 双向核对，显示保留3位小数。</span><span class="page-number">10 / 31</span></footer>
|
||||
</section><section class="slide " data-page="11">
|
||||
<div class="chapter">04 · 坐标方向</div><h1>C = 45° 时，“沿工件 X 走”意味着什么？</h1>
|
||||
<div class="body"><div class="cols image-right"><div><p>蓝色 X<sub>M</sub>、Y<sub>M</sub> 是机床固定方向；绿色 X<sub>W</sub>、Y<sub>W</sub> 随工件转动。</p><p>姿态保持 C=45°，编程增量：</p><div class="equation">Δp<sub>W</sub> = (10, 0, 0)</div><p>对应的机床直线轴增量：</p><div class="equation">Δq = (7.071, 7.071, 0)</div><p class="small">不是机床 X 导轨真的旋转了，而是 X、Y 导轨合成出所需空间运动方向。</p></div><figure class=""><img src="assets/rotated-direction.png" alt="图中工件原点为便于观看作了平移；增量不受原点平移影响。"><figcaption>图中工件原点为便于观看作了平移；增量不受原点平移影响。</figcaption></figure></div></div>
|
||||
<div class="takeaway">你的“XYZ 方向随旋转改变”可理解为工件基向量在机床坐标中的方向改变。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">11 / 31</span></footer>
|
||||
</section><section class="slide " data-page="12">
|
||||
<div class="chapter">04 · 数值算例 2</div><h1>BC 倾转后，沿工件 X 会同时改变机床 X、Y、Z</h1>
|
||||
<div class="body"><div class="cols image-right"><div><p>采用本课的正向变换约定：</p><div class="equation small-eq">R = R<sub>Y</sub>(B) · R<sub>Z</sub>(C)</div><p>当 B=30°、C=45° 时：</p><div class="equation small-eq">X<sub>W</sub> 在 M 中的方向<br>(0.6124, 0.7071, −0.3536)</div><p>所以沿 X<sub>W</sub> 前进 10 mm：</p><p class="number">Δq ≈ (6.124, 7.071, −3.536) mm</p><p class="small">倾斜后的坐标方向并不与任何一根直线导轨重合，需要三根直线轴合成。</p></div><figure class=""><img src="assets/bc-frame.png" alt="B=30°、C=45°；红点为工件点 p=(100,0,20) 的机床位置。"><figcaption>B=30°、C=45°；红点为工件点 p=(100,0,20) 的机床位置。</figcaption></figure></div></div>
|
||||
<div class="takeaway">RTCP 中“沿工件 X”不是“只让 X 电机动”。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">12 / 31</span></footer>
|
||||
</section><section class="slide " data-page="13">
|
||||
<div class="chapter">04 · AC 与 BC 对照</div><h1>同样的 30° / 45°，不是同一个姿态</h1>
|
||||
<div class="body"><p class="intro">仍取 p=(100,0,20) mm，所有旋转中心、偏置和刀长差为零。</p><table class=""><thead><tr><th>结构</th><th>父级倾转 × 子级旋转</th><th>倾转30°、C45°时的关节XYZ</th></tr></thead><tbody><tr><td>AC</td><td>R<sub>X</sub>(A) · R<sub>Z</sub>(C)</td><td>(70.711, 51.237, 52.676)</td></tr><tr><td>BC</td><td>R<sub>Y</sub>(B) · R<sub>Z</sub>(C)</td><td>(71.237, 70.711, -18.035)</td></tr></tbody></table><div class="cols"><div><h3>AC：绕 X 倾转</h3><p>C 先改变平面位置，A 再把局部 Y/Z 方向倾斜。</p></div><div><h3>BC：绕 Y 倾转</h3><p>C 先改变平面位置，B 再把局部 X/Z 方向倾斜。</p></div></div><p class="small">矩阵从右向左作用于列向量；这是坐标转换次序，不是要求 G 代码先运动 C 再运动 A/B。插补时两轴可以同时运动。</p></div>
|
||||
<div class="takeaway">运动学类型选错，即使每个轴都会动，刀尖也不会沿正确的相对轨迹走。</div>
|
||||
<footer class="footer"><span class="source">numeric-evidence.json；零偏置原生 WASM 结果。</span><span class="page-number">13 / 31</span></footer>
|
||||
</section><section class="slide " data-page="14">
|
||||
<div class="chapter">05 · 为什么还需要几何参数</div><h1>同样转 90°，绕不同的中心会到不同的位置</h1>
|
||||
<div class="body"><figure class="large-diagram"><img src="assets/pivot-offset.png" alt="二维俯视例：起点相同，旋转角度相同，仅旋转中心不同。"><figcaption>二维俯视例：起点相同，旋转角度相同，仅旋转中心不同。</figcaption></figure><div class="equation">p<sub>M</sub> = O + R · (p − O)</div><p class="small">计算顺序：先减去旋转中心 → 旋转 → 再加回中心。不能只计算 R·p，否则相当于错误地绕坐标零点转。</p></div>
|
||||
<div class="takeaway">RTCP 不只是“方向变换”，还包括“绕哪里转”的平移关系。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">14 / 31</span></footer>
|
||||
</section><section class="slide " data-page="15">
|
||||
<div class="chapter">05 · 轴间偏置与变换顺序</div><h1>C 轴装在倾转轴上：父子关系不能交换</h1>
|
||||
<div class="body"><div class="cols"><div><h3>先看几何，再写方程</h3><p><b>P：</b>C 轴零位参考点。<br><b>D：</b>倾转轴与 C 轴之间的偏置。<br><b>T=P+D：</b>倾转轴参考位置。</p><p>C 旋转后的点还要随 A/B 倾转；偏置也必须放在正确的父子层级中。</p></div><div><h3>URDF / GLB 里的对应关系</h3><table class="compact"><thead><tr><th>节点</th><th>本项目零位 origin</th></tr></thead><tbody><tr><td>A/B，父节点为底座</td><td>P + D</td></tr><tr><td>C，父节点为 A/B</td><td>−D</td></tr><tr><td>work，父节点为 C</td><td>−P</td></tr></tbody></table></div></div><div class="equation small-eq">q<sub>XYZ</sub> = P + D + R<sub>tilt</sub> [ R<sub>C</sub> (p − P) − D ] （刀长差为零）</div><p class="small">这是本项目 AC/BC TRT 约定。更一般的机床使用完整的刚体变换链；不能把这三个参数关系硬套到摆头机床。长度在运行配置中为 mm，URDF 为 m。</p></div>
|
||||
<div class="takeaway">R<sub>tilt</sub>R<sub>C</sub> 通常不等于 R<sub>C</sub>R<sub>tilt</sub>；机械安装顺序决定计算顺序。</div>
|
||||
<footer class="footer"><span class="source">本地 trtfuncs.c；本项目 URDF profile / D11 / D12。</span><span class="page-number">15 / 31</span></footer>
|
||||
</section><section class="slide " data-page="16">
|
||||
<div class="chapter">05 · 刀长与受控点</div><h1>控制的是刀尖，不只是主轴箱</h1>
|
||||
<div class="body"><figure class="large-diagram"><img src="assets/tool-length.png" alt="侧视示意：同一主轴参考位置，刀长不同会产生不同刀尖位置。"><figcaption>侧视示意：同一主轴参考位置，刀长不同会产生不同刀尖位置。</figcaption></figure><p>刀长改变时，为保持同一个刀尖目标，需要重新计算主轴参考点的位置。必须明确刀具长度的测量基准、正负号、刀补状态，以及模型上“tool”节点代表哪里。</p><p class="small">教学主算例采用刀长差为零。本项目原生 TRT 使用相对于 master tool 的 tool-offset 约定，不能把它直接当作任意模型网格的总长度。</p></div>
|
||||
<div class="takeaway">同一组关节位置 + 不同刀具标定，不一定得到同一个刀尖位置。</div>
|
||||
<footer class="footer"><span class="source">[S1][S3]；实际使用以机床和控制器的刀具标定约定为准。</span><span class="page-number">16 / 31</span></footer>
|
||||
</section><section class="slide " data-page="17">
|
||||
<div class="chapter">06 · 姿态的物理意义</div><h1>双转台没有转动主轴，却改变了相对刀轴方向</h1>
|
||||
<div class="body"><figure class="large-diagram"><img src="assets/orientation.png" alt="侧视：主轴在机床中保持竖直，工件随转台倾斜，二者的相对夹角改变。"><figcaption>侧视：主轴在机床中保持竖直，工件随转台倾斜，二者的相对夹角改变。</figcaption></figure><p>在本课双转台机床中，刀轴在机床坐标里的方向固定；工件转动后，<b>刀轴在工件坐标里的方向改变</b>。RTCP 根据指定角度协调刀尖位置，不会自动推断曲面法向。</p></div>
|
||||
<div class="takeaway">RTCP 不是“自动让刀轴垂直于任意曲面”；姿态仍由程序、CAM 或操作者给定。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">17 / 31</span></footer>
|
||||
</section><section class="slide " data-page="18">
|
||||
<div class="chapter">06 · 三种常见联动情形</div><h1>分清“保持点”“沿方向走”“同时改变位置和姿态”</h1>
|
||||
<div class="body"><table class=""><thead><tr><th>输入变化</th><th>RTCP 应做什么</th><th>观察重点</th></tr></thead><tbody><tr><td>XYZ 不变；A/B、C 改变</td><td>让刀尖保持同一工件编程点；XYZ关节可能联动。</td><td>刀尖与工件标记点不分离。</td></tr><tr><td>角度不变；XYZ 改变</td><td>沿当前工件参考系定义的方向移动。</td><td>机床多轴合成编程方向。</td></tr><tr><td>XYZ 与角度同时改变</td><td>执行变化的编程轨迹，同时维持角度对应的几何关系。</td><td>全过程相对轨迹正确，不只看终点。</td></tr><tr><td>XYZ 不变；点恰在 C 轴线上；只转 C</td><td>该点机床位置可以不变。</td><td>XYZ 不动不一定是故障。</td></tr></tbody></table><p class="small">“五轴联动”不要求每个时刻五轴速度都非零。非 RTCP 也能多轴同步加工：CAM/后置可以预先按指定机床几何计算轴目标，但这不等于控制器开启了实时刀尖补偿。</p></div>
|
||||
<div class="takeaway">每次解释一个动作，先说清哪些程序量保持不变、哪些程序量在改变。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">18 / 31</span></footer>
|
||||
</section><section class="slide " data-page="19">
|
||||
<div class="chapter">06 · 全过程的重要性</div><h1>终点都正确，不代表中间轨迹正确</h1>
|
||||
<div class="body"><div class="cols image-right"><div><p>同一个工件点绕 C 转动，理想半径为 100 mm。</p><p><b class="teal">RTCP：</b>刀尖跟随圆弧。<br><b class="red">不做 RTCP：</b>若只让 X/Y 线性插补到相同终点，刀尖可能走弦线。</p><table class="compact"><thead><tr><th>中间位置</th><th>X / Y</th></tr></thead><tbody><tr><td>圆弧，C=45°</td><td>70.711 / 70.711</td></tr><tr><td>弦线，50%进度</td><td>50.000 / 50.000</td></tr></tbody></table><p class="small">图示采用共同线性进度比较几何路径，不是断言所有控制器的加减速过程相同。</p></div><figure class=""><img src="assets/arc-chord.png" alt="中途差距 29.289 mm；起点和终点却完全相同。"><figcaption>中途差距 29.289 mm；起点和终点却完全相同。</figcaption></figure></div></div>
|
||||
<div class="takeaway">验收 RTCP 要看连续采样、刀尖相对轨迹和关节约束，不能只比首末坐标。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">19 / 31</span></footer>
|
||||
</section><section class="slide " data-page="20">
|
||||
<div class="chapter">07 · 模式切换</div><h1>M429 ↔ M428：坐标可以变，机床不能无故跳动</h1>
|
||||
<div class="body"><p class="intro">本项目 BC 示例：保持同一组物理关节，切换坐标解释。</p><table class=""><thead><tr><th>量</th><th>M429 / Identity</th><th>M428 / TCP</th></tr></thead><tbody><tr><td>物理关节 XYZ</td><td>(0.000, 0.000, 44.586)</td><td>(0.000, 0.000, 44.586)</td></tr><tr><td>物理关节 B / C</td><td>4.8675° / 179.88°</td><td>4.8675° / 179.88°</td></tr><tr><td>显示/解释的 XYZ</td><td>(0.000, 0.000, 44.586)</td><td>(-29.885, 27.975, 43.985)</td></tr><tr><td>三维刀尖</td><td>同一空间位置</td><td>同一空间位置</td></tr></tbody></table><div class="flow"><span>取当前关节 q</span><i>→</i><span>切换运动学</span><i>→</i><span>新模式正解 p</span><i>→</i><span>同步 TP / 解释器</span></div><p class="small">本例使用真实 BC 模型参数 P=(−18,14,12)、D=(22,0,−40) mm，刀长差0。切换之后再给运动指令，才产生运动。</p></div>
|
||||
<div class="takeaway">若切换时强行保持旧 XYZ 数字并重新逆解，就可能错误地改变物理关节。</div>
|
||||
<footer class="footer"><span class="source">[S2] 同步原则；本地 control.c::handle_kinematicsSwitch；WASM实算。</span><span class="page-number">20 / 31</span></footer>
|
||||
</section><section class="slide " data-page="21">
|
||||
<div class="chapter">07 · 控制器功能边界</div><h1>RTCP、旋转工作平面、刀补，不是同一个开关</h1>
|
||||
<div class="body"><table class=""><thead><tr><th>功能</th><th>主要解决的问题</th><th>不要误认为</th></tr></thead><tbody><tr><td>RTCP / TCP 运动学</td><td>姿态变化时，按机床结构实现目标刀尖相对轨迹。</td><td>所有控制器都会以完全相同方式解释XYZ。</td></tr><tr><td>工件坐标系 / 倾斜工作平面</td><td>选择编程参考原点或定义编程方向。</td><td>只旋转工作平面就自动具备完整五轴RTCP。</td></tr><tr><td>刀长补偿</td><td>把刀具参考点换算到实际受控刀尖。</td><td>更换刀具后只更新网格外观就够了。</td></tr><tr><td>机床标定</td><td>确定中心、偏置、轴向、正负号和长度。</td><td>只要支持RTCP，错误几何参数也会自动纠正。</td></tr></tbody></table><p class="small">不同控制器可能分别使用 TCP、TCPM、RTCP 等名称，并把倾斜平面/刀补组合进不同指令。本课明确讲本项目的 AC/BC 双转台语义，不推定所有品牌一致。</p></div>
|
||||
<div class="takeaway">换控制器时先核对“参考系、受控点、角度定义、指令组合”，不要只对照功能名称。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">21 / 31</span></footer>
|
||||
</section><section class="slide " data-page="22">
|
||||
<div class="chapter">08 · 程序对照</div><h1>同样写 C90，开关状态决定 XYZ 是否补偿</h1>
|
||||
<div class="body"><div class="cols"><div><h3>M429：直接映射</h3><pre>G21 G90 G94
|
||||
M429
|
||||
G1 X100 Y0 Z20 A0 C0 F300
|
||||
G1 C90 F60</pre><p>后一段只改变 C。<br>XYZ 关节保持 (100,0,20)，<br>工件标记点会离开刀尖。</p></div><div><h3>M428：RTCP</h3><pre>G21 G90 G94
|
||||
M428
|
||||
G1 X100 Y0 Z20 A0 C0 F300
|
||||
G1 C90 F60</pre><p>后一段保持编程 XYZ。<br>XYZ 关节变到 (0,100,20)，<br>刀尖仍对准同一个工件点。</p></div></div><p class="small">仅为零偏置/零刀长差 AC 教学片段，起始角度和当前模态需已知；BC 用 B0。现有下载模型参数非零，不能期待相同数字。M428/M429 为本项目重映射，不是通用标准M码；F值只作插补示意，实际需按机床的旋转/混合进给规则设定。</p></div>
|
||||
<div class="takeaway">程序字值相同，不代表开关前后表达的是同一个机械目标。</div>
|
||||
<footer class="footer"><span class="source">本项目 xyzac/xyzbc-trt.ini，428remap.ngc / 429remap.ngc。</span><span class="page-number">22 / 31</span></footer>
|
||||
</section><section class="slide " data-page="23">
|
||||
<div class="chapter">08 · 浏览器课堂实验</div><h1>用 AC/BC 桁架模型验证，而不是只看公式</h1>
|
||||
<div class="body"><ol class="steps"><li><b>加载：</b>打开“导入机床模型”，选 AC 或 BC 桁架示例；记录旋转中心与偏置。</li><li><b>准备：</b>确认空闲，开机并回零；选一个离 C 轴线有一定距离的刀尖位置。</li><li><b>Identity：</b>选择 M429，只 Jog A/B 或 C；观察 XYZ 关节是否保持。</li><li><b>切换：</b>停止后选择 M428；观察关节/刀尖不跳，XYZ 坐标可能变化。</li><li><b>TCP：</b>再次 Jog 旋转轴；观察 XYZ 关节按需补偿、刀尖相对工件点保持。</li><li><b>对照：</b>先停止，再切回 M429；重复方向相同的小幅 Jog，比较两种行为。</li></ol><p class="small">实验先用小幅角度并远离限位。记录的是“每次试验起点相对工件的同一点”；切换或重新定位后，不要把两个不同起点混作同一个目标。</p></div>
|
||||
<div class="takeaway">同时观察三项：程序XYZ、J0…J4、刀尖与工件的相对关系。</div>
|
||||
<footer class="footer"><span class="source">页面 http://127.0.0.1:5174/；浏览器仿真教学，不是机床现场操作规程。</span><span class="page-number">23 / 31</span></footer>
|
||||
</section><section class="slide " data-page="24">
|
||||
<div class="chapter">08 · 参数化实验</div><h1>改几何参数后，为什么仍应保留同一个模型？</h1>
|
||||
<div class="body"><div class="cols"><div><h3>正确的数据流</h3><div class="vertical-flow"><span>参数表：中心 / 偏置</span><b>↓</b><span>有效 URDF：节点零位关系</span><b>↓</b><span>INI → Worker → WASM</span><b>↓</b><span>关节 → 原导入模型</span></div></div><div><h3>课堂观察</h3><ul><li>同一 GLB 的网格、材质和文件身份保持。</li><li>新的轴心与偏置应进入运行结构和运动学。</li><li>相同程序点和角度，可能得到不同的 XYZ 关节值。</li><li>参数改变后需重新回零并重新解析程序。</li></ul><p class="small">源GLB不自动改写；可保存INI记录参数。改变轴心不等于自动重建支架、铸件等CAD外形，也不提供碰撞检测。</p></div></div></div>
|
||||
<div class="takeaway">模型保留和参数生效必须同时成立；只改外观或只改计算都会造成误导。</div>
|
||||
<footer class="footer"><span class="source">本项目 D11 / E09：AC、BC各18个姿态/刀长样本验证。</span><span class="page-number">24 / 31</span></footer>
|
||||
</section><section class="slide " data-page="25">
|
||||
<div class="chapter">09 · 约束与故障</div><h1>“工件点可达”不等于“每个关节都没到限位”</h1>
|
||||
<div class="body"><div class="cols"><div><h3>两层约束</h3><table class="compact"><thead><tr><th>约束</th><th>检查什么</th></tr></thead><tbody><tr><td>坐标限位</td><td>编程轴/坐标允许的范围</td></tr><tr><td>关节限位</td><td>实际执行机构的物理行程</td></tr><tr><td>动力学约束</td><td>速度、加速度等能力</td></tr></tbody></table><p>RTCP 旋转时，即使编程 XYZ 不变，补偿出来的 X/Y/Z 关节仍可能触及边界。</p></div><div><h3>本项目排障实例</h3><p>BC 配置允许较大的 B 坐标范围，但对应 JOINT_3 上限为 <b>50°</b>。</p><p>旧问题：越界 → 运动计算失败 → 事件时钟不同步 → Connection ERROR。</p><p>修复后：按关节约束停止，保留正确时钟，可松开并反向 Jog。</p></div></div><p class="small">本仿真对 RTCP 越界采用最后有效伺服样本停止，不等同于工业控制器的全路径限位预测与减速保护。范围和行为必须分别验证。</p></div>
|
||||
<div class="takeaway">正常限位阻止是一条运动诊断；序号缺口或连接错误是软件故障，不是RTCP原理。</div>
|
||||
<footer class="footer"><span class="source">本项目 R07 / E11；不据此宣称硬件安全或碰撞防护。</span><span class="page-number">25 / 31</span></footer>
|
||||
</section><section class="slide " data-page="26">
|
||||
<div class="chapter">09 · 常见误解</div><h1>六个问题，快速判断是否真正理解</h1>
|
||||
<div class="body"><table class="compact"><thead><tr><th>说法</th><th>准确解释</th></tr></thead><tbody><tr><td>“非RTCP时各轴互相没有影响。”</td><td>没有自动补偿；但工件转动当然会改变它与刀具的相对位置。</td></tr><tr><td>“RTCP把X/Y/Z导轨转了。”</td><td>导轨不转，是工件基方向改变，由固定导轨合成空间运动。</td></tr><tr><td>“RTCP时XYZ永远不变。”</td><td>只在保持同一编程点时程序XYZ不变；关节XYZ通常变化。</td></tr><tr><td>“只要开RTCP，刀尖在空间就不动。”</td><td>刀尖可在机床空间移动，以保持它相对工件的目标关系。</td></tr><tr><td>“C转了但XYZ没动，一定坏了。”</td><td>目标点恰在C轴线上时可能正确，应先检查几何。</td></tr><tr><td>“切换模式时XYZ数字跳，必须修好。”</td><td>要检查关节和物理刀尖是否跳；新参考系里的数值改变可能正确。</td></tr></tbody></table></div>
|
||||
<div class="takeaway">先说参考系，再说位置；先看结构，再说联动。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">26 / 31</span></footer>
|
||||
</section><section class="slide " data-page="27">
|
||||
<div class="chapter">10 · 课堂练习</div><h1>请先画箭头，再写结论</h1>
|
||||
<div class="body"><ol class="exercises"><li><b>点追踪：</b>零偏置，C=0°，工件点 p=(80,0,10)。只转 C 到90°，分别写出 Identity 和 RTCP 的 XYZ 关节目标。</li><li><b>方向合成：</b>C=30°且倾转角为0°，沿工件 +X 方向走20mm，机床 X/Y 各应增加多少？</li><li><b>模式切换：</b>M429切到M428时，XYZ显示值变化、J0…J4不变、刀尖不动，是否正常？为什么？</li><li><b>偏置识别：</b>BC模型 C 的局部 origin=(-0.022,0,0.040)m，倾转轴 origin=(0.004,0.014,-0.028)m。求本项目 P、D，单位mm。</li><li><b>结构判断：</b>C节点错误地挂在Z滑枕下。只Jog X时会发生什么？为什么不能靠RTCP开关解决？</li></ol></div>
|
||||
<div class="takeaway">建议分组讨论 8–10 分钟；答案在下一页。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">27 / 31</span></footer>
|
||||
</section><section class="slide " data-page="28">
|
||||
<div class="chapter">10 · 参考答案</div><h1>用“相对谁”检查每一步</h1>
|
||||
<div class="body"><ol class="answers"><li><b>Identity：</b>(80,0,10)；<b>RTCP：</b>(0,80,10)。前者刀尖留在机床原位置，后者继续对准同一工件点。</li><li><b>ΔX=20cos30°=17.321mm；ΔY=20sin30°=10.000mm。</b>方向向量长度仍为20mm，机床Z不变。</li><li><b>正常。</b>运动学切换重新解释当前物理状态。坐标可以变，关节和刀尖应保持。</li><li><b>P=T+U=(-18,14,12)mm；D=−U=(22,0,−40)mm。</b>先统一单位，再按父子关系相加，不能直接拿URDF的米当毫米。</li><li><b>C及工件会错误地随XYZ移动。</b>这是结构树错误，不是开关模式能修复的；需把A/B→C分支正确挂回底座。</li></ol></div>
|
||||
<div class="takeaway">检查顺序：轴数 → 层级 → 单位/正负号 → 几何参数 → 运动学 → 程序与状态。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">28 / 31</span></footer>
|
||||
</section><section class="slide " data-page="29">
|
||||
<div class="chapter">附录 A · 数学推导</div><h1>从一根 C 轴，推到两根旋转轴</h1>
|
||||
<div class="body"><div class="cols"><div><h3>绕 C 的平面变换</h3><pre class="math">x′ = x cos C − y sin C
|
||||
y′ = x sin C + y cos C
|
||||
z′ = z</pre><h3>AC：再绕 X 倾转 A</h3><pre class="math">q_x = x′
|
||||
q_y = y′ cos A − z′ sin A
|
||||
q_z = y′ sin A + z′ cos A</pre></div><div><h3>BC：再绕 Y 倾转 B</h3><pre class="math">q_x = x′ cos B + z′ sin B
|
||||
q_y = y′
|
||||
q_z = −x′ sin B + z′ cos B</pre><p>这里所有旋转中心、轴间偏置及刀长差为零，列向量采用右手正向变换。</p><p class="small">式中的 q 是关节目标；若导入的是其他结构、符号约定或参考点，必须重新建立变换链。</p></div></div></div>
|
||||
<div class="takeaway">先学会解释“这一步在谁的坐标系中发生”，再记忆公式。</div>
|
||||
<footer class="footer"><span class="source">与本地 trtfuncs.c 零偏置逆解一致；三角函数实际以弧度计算。</span><span class="page-number">29 / 31</span></footer>
|
||||
</section><section class="slide " data-page="30">
|
||||
<div class="chapter">附录 B · 本项目完整参数式</div><h1>加入旋转中心、偏置与 master-tool 刀长差</h1>
|
||||
<div class="body"><div class="equation">D<sub>L</sub> = D + L e<sub>z</sub></div><div class="equation">q<sub>XYZ</sub> = P + D<sub>L</sub> + R<sub>tilt</sub> [ R<sub>C</sub> (p − P) − D<sub>L</sub> ]</div><table class="compact"><thead><tr><th>符号</th><th>AC</th><th>BC</th></tr></thead><tbody><tr><td>R<sub>tilt</sub></td><td>R<sub>X</sub>(A)</td><td>R<sub>Y</sub>(B)</td></tr><tr><td>D</td><td>(0, D<sub>y</sub>, D<sub>z</sub>)</td><td>(D<sub>x</sub>, 0, D<sub>z</sub>)</td></tr><tr><td>旋转关节</td><td>q<sub>A</sub>=A，q<sub>C</sub>=C</td><td>q<sub>B</sub>=B，q<sub>C</sub>=C</td></tr></tbody></table><p class="small">P为原生rot-point；L为本项目/原生TRT的tool-offset标定量；e<sub>z</sub>=(0,0,1)。本式返回关节XYZ，不是未经处理的网格刀尖世界坐标。G54等解释器偏置在输入p形成前已按控制器规则处理。</p><p class="small">这一刀长表达是本项目约定，不能替代任意控制器的通用刀补说明。主课例子L=0；实际机床应以标定模型及其完整前后向验证为准。</p></div>
|
||||
<div class="takeaway">工程实现不在画面中“补一个偏移”；应让同一组结构数据贯穿解释器、运动学和模型。</div>
|
||||
<footer class="footer"><span class="source">原生源码：linuxcnc/src/emc/kinematics/trtfuncs.c，xyzac/xyzbcKinematicsInverse。</span><span class="page-number">30 / 31</span></footer>
|
||||
</section><section class="slide " data-page="31">
|
||||
<div class="chapter">附录 C · 教学安排与依据</div><h1>怎样讲、怎样验证、怎样继续学习</h1>
|
||||
<div class="body"><div class="cols references"><div><h3>建议授课节奏</h3><p>10分钟：结构、轴名与三种位置。<br>20分钟：C轴点跟踪、方向合成、AC/BC倾转。<br>15分钟：旋转中心、偏置、刀长与模式切换。<br>15分钟：浏览器实验与错误诊断。<br>10分钟：练习、答案和模型参数核对。</p><h3>本课验算</h3><p>12个姿态由真实WASM逆解计算，并通过正解回代；另核对C45°方向增量、BC切换示例及弧弦差。详见同目录 <code>numeric-evidence.json</code>。</p><p>图形为原创教学示意及本项目GLB截图，不用于制造尺寸标定。</p></div><div><h3>官方资料与本地实现</h3><p id="S1"><b>[S1]</b> <a href="https://linuxcnc.org/docs/html/motion/5-axis-kinematics.html">LinuxCNC · 5-Axis Kinematics</a><br>AC/BC结构、运动学及偏置。</p><p id="S2"><b>[S2]</b> <a href="https://linuxcnc.org/docs/html/motion/switchkins.html">LinuxCNC · Switchable Kinematics</a><br>模式切换、identityfirst、同步要求。</p><p id="S3"><b>[S3]</b> <a href="https://linuxcnc.org/docs/html/gcode/machining-center.html">LinuxCNC · CNC Machine Overview</a><br>轴名、坐标、受控点与协调运动。</p><p><b>本地：</b>trtfuncs.c；control.c；428remap.ngc / 429remap.ngc；docs/glb-machine/。M428=TCP、M429=Identity仅适用于本项目配置。</p><p class="small">资料核对日期：2026-09-18。不同版本/品牌的指令与坐标约定应另行核查。</p></div></div></div>
|
||||
<div class="takeaway">一句话记忆：程序描述相对工件的目标，运动学把目标换算成各关节应该怎样动。</div>
|
||||
<footer class="footer"><span class="source">五轴机床与 RTCP · 原创教学示意 · 以本课双转台结构为限</span><span class="page-number">31 / 31</span></footer>
|
||||
</section></body></html>
|
||||
481
docs/teaching/rtcp-five-axis/numeric-evidence.json
Normal file
481
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Normal file
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||||
157
docs/teaching/rtcp-five-axis/outline.json
Normal file
157
docs/teaching/rtcp-five-axis/outline.json
Normal file
@@ -0,0 +1,157 @@
|
||||
[
|
||||
{
|
||||
"page": 1,
|
||||
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|
||||
"title": "五轴机床与 RTCP"
|
||||
},
|
||||
{
|
||||
"page": 2,
|
||||
"chapter": "01 · 先统一理解",
|
||||
"title": "你的两点理解，怎样说得更准确？"
|
||||
},
|
||||
{
|
||||
"page": 3,
|
||||
"chapter": "01 · 结构与轴名",
|
||||
"title": "五轴 = 三个直线轴 + 两个旋转轴"
|
||||
},
|
||||
{
|
||||
"page": 4,
|
||||
"chapter": "01 · 机械拓扑",
|
||||
"title": "两条运动链，共用一个底座"
|
||||
},
|
||||
{
|
||||
"page": 5,
|
||||
"chapter": "01 · 真实模型",
|
||||
"title": "AC 与 BC：外层倾转轴不同"
|
||||
},
|
||||
{
|
||||
"page": 6,
|
||||
"chapter": "02 · 三种位置",
|
||||
"title": "不要把“程序点、关节位置、实际反馈”混为一谈"
|
||||
},
|
||||
{
|
||||
"page": 7,
|
||||
"chapter": "02 · G 代码含义",
|
||||
"title": "非 RTCP 时，G 代码也不总等于机械绝对位置"
|
||||
},
|
||||
{
|
||||
"page": 8,
|
||||
"chapter": "03 · 非 RTCP",
|
||||
"title": "只转 C，工件点会离开刀尖"
|
||||
},
|
||||
{
|
||||
"page": 9,
|
||||
"chapter": "03 · RTCP",
|
||||
"title": "同样只改变角度，刀尖跟住工件点"
|
||||
},
|
||||
{
|
||||
"page": 10,
|
||||
"chapter": "03 · 数值算例 1",
|
||||
"title": "C 转 90°：同一编程点，不同关节位置"
|
||||
},
|
||||
{
|
||||
"page": 11,
|
||||
"chapter": "04 · 坐标方向",
|
||||
"title": "C = 45° 时，“沿工件 X 走”意味着什么？"
|
||||
},
|
||||
{
|
||||
"page": 12,
|
||||
"chapter": "04 · 数值算例 2",
|
||||
"title": "BC 倾转后，沿工件 X 会同时改变机床 X、Y、Z"
|
||||
},
|
||||
{
|
||||
"page": 13,
|
||||
"chapter": "04 · AC 与 BC 对照",
|
||||
"title": "同样的 30° / 45°，不是同一个姿态"
|
||||
},
|
||||
{
|
||||
"page": 14,
|
||||
"chapter": "05 · 为什么还需要几何参数",
|
||||
"title": "同样转 90°，绕不同的中心会到不同的位置"
|
||||
},
|
||||
{
|
||||
"page": 15,
|
||||
"chapter": "05 · 轴间偏置与变换顺序",
|
||||
"title": "C 轴装在倾转轴上：父子关系不能交换"
|
||||
},
|
||||
{
|
||||
"page": 16,
|
||||
"chapter": "05 · 刀长与受控点",
|
||||
"title": "控制的是刀尖，不只是主轴箱"
|
||||
},
|
||||
{
|
||||
"page": 17,
|
||||
"chapter": "06 · 姿态的物理意义",
|
||||
"title": "双转台没有转动主轴，却改变了相对刀轴方向"
|
||||
},
|
||||
{
|
||||
"page": 18,
|
||||
"chapter": "06 · 三种常见联动情形",
|
||||
"title": "分清“保持点”“沿方向走”“同时改变位置和姿态”"
|
||||
},
|
||||
{
|
||||
"page": 19,
|
||||
"chapter": "06 · 全过程的重要性",
|
||||
"title": "终点都正确，不代表中间轨迹正确"
|
||||
},
|
||||
{
|
||||
"page": 20,
|
||||
"chapter": "07 · 模式切换",
|
||||
"title": "M429 ↔ M428：坐标可以变，机床不能无故跳动"
|
||||
},
|
||||
{
|
||||
"page": 21,
|
||||
"chapter": "07 · 控制器功能边界",
|
||||
"title": "RTCP、旋转工作平面、刀补，不是同一个开关"
|
||||
},
|
||||
{
|
||||
"page": 22,
|
||||
"chapter": "08 · 程序对照",
|
||||
"title": "同样写 C90，开关状态决定 XYZ 是否补偿"
|
||||
},
|
||||
{
|
||||
"page": 23,
|
||||
"chapter": "08 · 浏览器课堂实验",
|
||||
"title": "用 AC/BC 桁架模型验证，而不是只看公式"
|
||||
},
|
||||
{
|
||||
"page": 24,
|
||||
"chapter": "08 · 参数化实验",
|
||||
"title": "改几何参数后，为什么仍应保留同一个模型？"
|
||||
},
|
||||
{
|
||||
"page": 25,
|
||||
"chapter": "09 · 约束与故障",
|
||||
"title": "“工件点可达”不等于“每个关节都没到限位”"
|
||||
},
|
||||
{
|
||||
"page": 26,
|
||||
"chapter": "09 · 常见误解",
|
||||
"title": "六个问题，快速判断是否真正理解"
|
||||
},
|
||||
{
|
||||
"page": 27,
|
||||
"chapter": "10 · 课堂练习",
|
||||
"title": "请先画箭头，再写结论"
|
||||
},
|
||||
{
|
||||
"page": 28,
|
||||
"chapter": "10 · 参考答案",
|
||||
"title": "用“相对谁”检查每一步"
|
||||
},
|
||||
{
|
||||
"page": 29,
|
||||
"chapter": "附录 A · 数学推导",
|
||||
"title": "从一根 C 轴，推到两根旋转轴"
|
||||
},
|
||||
{
|
||||
"page": 30,
|
||||
"chapter": "附录 B · 本项目完整参数式",
|
||||
"title": "加入旋转中心、偏置与 master-tool 刀长差"
|
||||
},
|
||||
{
|
||||
"page": 31,
|
||||
"chapter": "附录 C · 教学安排与依据",
|
||||
"title": "怎样讲、怎样验证、怎样继续学习"
|
||||
}
|
||||
]
|
||||
268
docs/teaching/rtcp-five-axis/verification/acceptance.json
Normal file
268
docs/teaching/rtcp-five-axis/verification/acceptance.json
Normal file
@@ -0,0 +1,268 @@
|
||||
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|
||||
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|
||||
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|
||||
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|
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||||
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|
||||
}
|
||||
312
docs/teaching/rtcp-five-axis/verification/layout.json
Normal file
312
docs/teaching/rtcp-five-axis/verification/layout.json
Normal file
@@ -0,0 +1,312 @@
|
||||
{
|
||||
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|
||||
{
|
||||
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|
||||
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||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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||||
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||||
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|
||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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||||
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|
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|
||||
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|
||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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||||
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||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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"title": "C = 45° 时，“沿工件 X 走”意味着什么？",
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"title": "BC 倾转后，沿工件 X 会同时改变机床 X、Y、Z",
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{
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{
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"title": "分清“保持点”“沿方向走”“同时改变位置和姿态”",
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"page": 19,
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"title": "终点都正确，不代表中间轨迹正确",
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},
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{
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"page": 20,
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"title": "M429 ↔ M428：坐标可以变，机床不能无故跳动",
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"page": 21,
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"title": "RTCP、旋转工作平面、刀补，不是同一个开关",
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{
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"page": 22,
|
||||
"title": "同样写 C90，开关状态决定 XYZ 是否补偿",
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"clipped": [],
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"content_overflow": false,
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"title_right": 713.203125,
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{
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"page": 23,
|
||||
"title": "用 AC/BC 桁架模型验证，而不是只看公式",
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"clipped": [],
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"content_overflow": false,
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"title_right": 718.671875,
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"images": []
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},
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{
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"page": 24,
|
||||
"title": "改几何参数后，为什么仍应保留同一个模型？",
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||||
"clipped": [],
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"content_overflow": false,
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||||
"title_right": 774.015625,
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{
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"page": 25,
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"title": "“工件点可达”不等于“每个关节都没到限位”",
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"clipped": [],
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"content_overflow": false,
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"title_right": 810.015625,
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},
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{
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"page": 26,
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||||
"title": "六个问题，快速判断是否真正理解",
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||||
"clipped": [],
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"title_right": 594.015625,
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"images": []
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},
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{
|
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"page": 27,
|
||||
"title": "请先画箭头，再写结论",
|
||||
"clipped": [],
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"content_overflow": false,
|
||||
"title_right": 414.015625,
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"images": []
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},
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{
|
||||
"page": 28,
|
||||
"title": "用“相对谁”检查每一步",
|
||||
"clipped": [],
|
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"content_overflow": false,
|
||||
"title_right": 450.015625,
|
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"images": []
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},
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{
|
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"page": 29,
|
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"title": "从一根 C 轴，推到两根旋转轴",
|
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"clipped": [],
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|
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"title_right": 525.96875,
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{
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"page": 30,
|
||||
"title": "加入旋转中心、偏置与 master-tool 刀长差",
|
||||
"clipped": [],
|
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"content_overflow": false,
|
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"title_right": 744.5625,
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"images": []
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},
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{
|
||||
"page": 31,
|
||||
"title": "怎样讲、怎样验证、怎样继续学习",
|
||||
"clipped": [],
|
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"content_overflow": false,
|
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"title_right": 594.015625,
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"images": []
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Reference in New Issue
Block a user