Add AC/BC RTCP programs and 3D machine manager

docs/teaching/rtcp-beginners/README.md

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+# 五轴 RTCP 与工件坐标：初学者完整讲义
+
+[打开完整 PDF](五轴RTCP与工件坐标-初学者完整讲义.pdf) · [可编辑 HTML](handbook.html) · [逐页目录](outline.json)
+
+本版是面向初学者重新组织的 **72 页 A4 完整讲义**，不是只在原投影片后附几页补充。原 [31 页投影课件](../rtcp-five-axis/五轴机床与RTCP-教学课件.pdf) 保留为概要。本讲义适合独立阅读、打印及分 4–6 次授课。
+
+## 新增重点
+
+- 从原点、方向、单位、右手规则、点与增量讲起；区分物理机床参考 M、工件 W、关节 J、运动学输入 K 和刀具 T。
+- 工件原点如何选择、测量；为什么一个点不能确定方向；机械找正与初始坐标旋转分别解决什么。
+- 分开说明“固连零件的物理坐标架”“G54偏置表”“动态RTCP变换”；G54不是独立完成五轴跟随的开关。
+- 详细解释G54/G55、G10 L2/L20、G90/G91、G20/G21、省略轴与模态；说明G52/G92/G53、圆弧字、进给方式、刀补索引的边界。
+- 对同一份BC程序逐字、逐行计算工件XYZ、K输入XYZ、角度、实际关节位置，给出完整对照表和连续轨迹图。
+- 实验、排错、限位、术语、练习和答案；把数学推导放在附录，不要求初学者先会矩阵。
+
+## 章节与 PDF 页码
+
+| PDF 页码 | 内容 |
+| --- | --- |
+| 1–3 | 封面、阅读方法、可点击目录 |
+| 4–9 | 坐标基础、点与增量、五轴结构、关节与反馈 |
+| 10–14 | 各参考系、回零、工件坐标、随动原点、G54表与物理坐标架 |
+| 15–20 | 零位参考、原点选择与测量、方向确定、完整点变换 |
+| 21–26 | G54/G55、偏置、G10 L2/L20、G52/G92/G53 |
+| 27–33 | 非RTCP/RTCP、方向合成、AC/BC、结构参数与刀长 |
+| 34–43 | 地址字、模态、单位、G90/G91、G0/G1、圆弧、F及其他字的解析 |
+| 44–53 | 完整程序、N10–N110逐行实算、结果表与模式切换 |
+| 54–57 | 连续轨迹、姿态、模型显示与分层准备 |
+| 58–62 | 三个实验、排错、行程/动力学/碰撞边界 |
+| 63–67 | 常见问答、两组练习与答案 |
+| 68–72 | 术语、公式、软件实验范围、资料来源与复现 |
+
+正文编号01–69为“节号”，与PDF页码相差封面/导读/目录三页；内部引用按节号，目录按PDF页码。
+
+## 核心实算
+
+主例：XYZBC，零旋转中心/轴间偏置/刀长差，G54零位偏置 `(40,20,10)` mm，初始方向对齐。
+
+| 程序段 | 工件 XYZ | K 输入 XYZ | B/C | 关节 XYZ |
+| --- | --- | --- | --- | --- |
+| `N50 G1 X10 Y0 Z5 B0 C0 F600` | 10,0,5 | 50,20,15 | 0/0 | 50,20,15 |
+| `N60 C90` | 10,0,5 | 50,20,15 | 0/90 | -20,50,15 |
+| `N70 G91 X10` | 20,0,5 | 60,20,15 | 0/90 | -20,60,15 |
+| `N80 G90 X20 Y0 Z5 B30 C90 F300` | 20,0,5 | 60,20,15 | 30/90 | -9.821,60,22.990 |
+| `N90 X0 Y10` | 0,10,5 | 40,30,15 | 30/90 | -18.481,40,27.990 |
+
+这些数值来自 [实际 WASM 验证](gcode-evidence.json)，包括11个主程序段、11个额外单位/坐标设置段；N10–N90加M2通过真实Session/解释器/TP完整执行，记录53个轨迹样本，并核对最终关节。下载模型自带非零参数，不能不改条件就要求得到这张表的相同数值。
+
+## 验证与范围
+
+- [版面报告](verification/layout.json)：72页图文边界、图片加载、标题和正文检查。
+- [PDF核验](verification/acceptance.json)：页数、A4尺寸、逐页中文文本、内嵌字体、书签、文件与资产SHA256。
+- `verification/` 保留逐页截图及实际PDF的独立渲染总览。
+- 9张新增原创坐标示意图，复用此前11张原创原理图/模型图；不是许可不明的网络插画。
+- 依据LinuxCNC官方坐标/G代码/五轴/切换资料和当前仓库代码；最后一页有直接链接。
+- 当前WASM解释器属于功能切片。通用G52/G92、任意坐标方向变换、完整G43/H刀表、所有进给模式并未在本次全面验收；正文明确标出，不能把“解析接受”当作完整功能正确性。
+- 本讲义不修改应用功能，不宣称真实机床的探测/碰撞/硬件安全流程已被验证。
+
+## 重新生成
+
+```bash
+node scripts/generate_rtcp_beginner_data.mjs
+PYTHONPATH=/tmp/rtcp-course-deps python3 scripts/generate_rtcp_beginner_figures.py
+python3 scripts/generate_rtcp_beginner_html.py
+PYTHONPATH=/tmp/rtcp-course-deps python3 scripts/subset_rtcp_beginner_fonts.py
+PLAYWRIGHT_MODULE=/home/mes006/.npm/_npx/e41f203b7505f1fb/node_modules/playwright/index.mjs node scripts/render_rtcp_beginner_pdf.mjs
+PYTHONPATH=/tmp/rtcp-course-deps python3 scripts/verify_rtcp_beginner_pdf.py
+```
+
+生成工具依赖临时安装的Matplotlib/PyPDF/fontTools、Chrome、Playwright和Noto CJK字体；PDF成品不需要这些工具，可以离线阅读。HTML需与同目录assets一起保留。中文字体按本书实际字符制作子集，避免同形部首导致复制/搜索文字不同；字体许可证在assets/font-license.txt。

docs/teaching/rtcp-beginners/assets/font-license.txt

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+Format: https://www.debian.org/doc/packaging-manuals/copyright-format/1.0/
+Upstream-Name: noto-cjk
+Upstream-Contact: https://github.com/notofonts/noto-cjk/issues
+Source: https://github.com/notofonts/noto-cjk
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+
+Files: *
+Copyright: 2010-2012, Google Corporation
+License: SIL-1.1
+
+Files: debian/*
+Copyright: 2013, Vasudev Kamath <kamathvasudev@gmail.com>
+           2013-2015, Jonas Smedegaard <dr@jones.dk>
+           2015-2022, ChangZhuo Chen (陳昌倬) <czchen@debian.org>
+License: GPL-3+
+
+License: SIL-1.1
+ -----------------------------------------------------------
+ SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
+ -----------------------------------------------------------
+ .
+ PREAMBLE
+ .
+ The goals of the Open Font License (OFL) are to stimulate worldwide
+ development of collaborative font projects, to support the font
+ creation efforts of academic and linguistic communities, and to provide
+ a free and open framework in which fonts may be shared and improved in
+ partnership with others.
+ .
+ The OFL allows the licensed fonts to be used, studied, modified and
+ redistributed freely as long as they are not sold by themselves. The
+ fonts, including any derivative works, can be bundled, embedded,
+ redistributed and/or sold with any software provided that any reserved
+ names are not used by derivative works. The fonts and derivatives,
+ however, cannot be released under any other type of license. The
+ requirement for fonts to remain under this license does not apply to
+ any document created using the fonts or their derivatives.
+ .
+ DEFINITIONS
+ .
+ "Font Software" refers to the set of files released by the Copyright
+ Holder(s) under this license and clearly marked as such. This may
+ include source files, build scripts and documentation.
+ .
+ "Reserved Font Name" refers to any names specified as such after the
+ copyright statement(s).
+ .
+ "Original Version" refers to the collection of Font Software components
+ as distributed by the Copyright Holder(s).
+ .
+ "Modified Version" refers to any derivative made by adding to,
+ deleting, or substituting -- in part or in whole -- any of the
+ components of the Original Version, by changing formats or by porting
+ the Font Software to a new environment.
+ .
+ "Author" refers to any designer, engineer, programmer, technical writer
+ or other person who contributed to the Font Software.
+ .
+ PERMISSION & CONDITIONS
+ .
+ Permission is hereby granted, free of charge, to any person obtaining a
+ copy of the Font Software, to use, study, copy, merge, embed, modify,
+ redistribute, and sell modified and unmodified copies of the Font
+ Software, subject to the following conditions:
+ .
+ 1) Neither the Font Software nor any of its individual components, in
+ Original or Modified Versions, may be sold by itself.
+ .
+ 2) Original or Modified Versions of the Font Software may be bundled,
+ redistributed and/or sold with any software, provided that each copy
+ contains the above copyright notice and this license. These can be
+ included either as stand-alone text files, human-readable headers or
+ in the appropriate machine-readable metadata fields within text or
+ binary files as long as those fields can be easily viewed by the user.
+ .
+ 3) No Modified Version of the Font Software may use the Reserved Font
+ Name(s) unless explicit written permission is granted by the
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+ 4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
+ Software shall not be used to promote, endorse or advertise any
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+ Copyright Holder(s) and the Author(s) or with their explicit written
+ permission.
+ .
+ 5) The Font Software, modified or unmodified, in part or in whole, must
+ be distributed entirely under this license, and must not be distributed
+ under any other license. The requirement for fonts to remain under this
+ license does not apply to any document created using the Font Software.
+ .
+ TERMINATION
+ .
+ This license becomes null and void if any of the above conditions are
+ not met.
+ .
+ DISCLAIMER
+ .
+ THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
+ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
+ OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
+ COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
+ DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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+ OTHER DEALINGS IN THE FONT SOFTWARE.
+
+License: GPL-3+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+ .
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
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+ On Debian systems, the complete text of the GNU General
+ Public License version 3 can be found in "/usr/share/common-licenses/GPL-3".

docs/teaching/rtcp-beginners/examples/beginner-g54-rtcp.ngc

@@ -0,0 +1,12 @@
+; Teaching fixture only: XYZBC, P=D=tool-offset=0, known initial state.
+; Work origin (40,20,10) mm; this is not a production machining program.
+N10 G21 G90 G94 G17
+N20 G10 L2 P1 X40 Y20 Z10
+N30 G54
+N40 M428
+N50 G1 X10 Y0 Z5 B0 C0 F600
+N60 C90
+N70 G91 X10
+N80 G90 X20 Y0 Z5 B30 C90 F300
+N90 X0 Y10
+M2

docs/teaching/rtcp-beginners/outline.json

@@ -0,0 +1,362 @@
+[
+  {
+    "page": 1,
+    "chapter": "封面 · 完整讲义 / 2026.09",
+    "title": "五轴 RTCP 与工件坐标"
+  },
+  {
+    "page": 2,
+    "chapter": "导读",
+    "title": "怎样使用这份讲义"
+  },
+  {
+    "page": 3,
+    "chapter": "学习地图",
+    "title": "内容索引"
+  },
+  {
+    "page": 4,
+    "chapter": "第1章 · 坐标基础",
+    "title": "01　坐标是“按照约定量出来的位置”"
+  },
+  {
+    "page": 5,
+    "chapter": "第1章 · 坐标基础",
+    "title": "02　一套坐标系至少要规定什么？"
+  },
+  {
+    "page": 6,
+    "chapter": "第1章 · 坐标基础",
+    "title": "03　同一个点，可以有两套不同的坐标"
+  },
+  {
+    "page": 7,
+    "chapter": "第1章 · 坐标基础",
+    "title": "04　点坐标与移动增量不是一回事"
+  },
+  {
+    "page": 8,
+    "chapter": "第1章 · 机床结构",
+    "title": "05　五轴机床里，到底是哪五根轴？"
+  },
+  {
+    "page": 9,
+    "chapter": "第1章 · 机床结构",
+    "title": "06　关节位置，不等于工件坐标"
+  },
+  {
+    "page": 10,
+    "chapter": "第2章 · 参考系",
+    "title": "07　先认识 M、W、J，再引入 K 和 T"
+  },
+  {
+    "page": 11,
+    "chapter": "第2章 · 机床参考",
+    "title": "08　回零解决什么？工件对刀又解决什么？"
+  },
+  {
+    "page": 12,
+    "chapter": "第2章 · 工件参考",
+    "title": "09　工件坐标 W 代表什么？"
+  },
+  {
+    "page": 13,
+    "chapter": "第2章 · 工件随动",
+    "title": "10　工件转了，原点与方向一起转"
+  },
+  {
+    "page": 14,
+    "chapter": "第2章 · 最重要的区分",
+    "title": "11　“物理工件坐标架”和“G54表”不是同一对象"
+  },
+  {
+    "page": 15,
+    "chapter": "第3章 · 原点与方向的确定",
+    "title": "12　先约定机床零姿态，再谈工件装在哪里"
+  },
+  {
+    "page": 16,
+    "chapter": "第3章 · 原点选择",
+    "title": "13　工件原点放在哪里比较合适？"
+  },
+  {
+    "page": 17,
+    "chapter": "第3章 · 原点测量",
+    "title": "14　怎样把选好的原点告诉控制器？"
+  },
+  {
+    "page": 18,
+    "chapter": "第3章 · 方向测量",
+    "title": "15　一个原点不能确定三维方向"
+  },
+  {
+    "page": 19,
+    "chapter": "第3章 · 初始方向与动态方向",
+    "title": "16　装夹方向和转台姿态，要分开处理"
+  },
+  {
+    "page": 20,
+    "chapter": "第3章 · 原点和方向合起来",
+    "title": "17　一个点怎样从工件坐标换算到机床空间？"
+  },
+  {
+    "page": 21,
+    "chapter": "第4章 · G54与偏置",
+    "title": "18　G54究竟做了什么？"
+  },
+  {
+    "page": 22,
+    "chapter": "第4章 · 偏置的物理含义",
+    "title": "19　G54的40、20、10代表什么？"
+  },
+  {
+    "page": 23,
+    "chapter": "第4章 · 设置方法一",
+    "title": "20　G10 L2：把已知偏置写入坐标表"
+  },
+  {
+    "page": 24,
+    "chapter": "第4章 · 设置方法二",
+    "title": "21　G10 L20：让当前位置具有指定工件坐标"
+  },
+  {
+    "page": 25,
+    "chapter": "第4章 · 两个坐标系",
+    "title": "22　换G54/G55为什么可能只改数字、不动机床？"
+  },
+  {
+    "page": 26,
+    "chapter": "第4章 · 附加偏置与基础坐标",
+    "title": "23　G52、G92、G53：先学会不混用"
+  },
+  {
+    "page": 27,
+    "chapter": "第5章 · 非RTCP与RTCP",
+    "title": "24　非RTCP：“独立”的准确含义"
+  },
+  {
+    "page": 28,
+    "chapter": "第5章 · 非RTCP与RTCP",
+    "title": "25　RTCP控制的是相对目标关系"
+  },
+  {
+    "page": 29,
+    "chapter": "第5章 · RTCP工件原点",
+    "title": "26　用G54例子看“原点随动”"
+  },
+  {
+    "page": 30,
+    "chapter": "第5章 · RTCP方向",
+    "title": "27　沿工件X前进，哪些电机会动？"
+  },
+  {
+    "page": 31,
+    "chapter": "第5章 · 倾转与结构顺序",
+    "title": "28　加入B或A后，方向可以进入三个维度"
+  },
+  {
+    "page": 32,
+    "chapter": "第5章 · 三类偏置",
+    "title": "29　G54、旋转中心、轴间偏置各管什么？"
+  },
+  {
+    "page": 33,
+    "chapter": "第5章 · 刀具参考",
+    "title": "30　为什么必须知道刀尖究竟在哪里？"
+  },
+  {
+    "page": 34,
+    "chapter": "第6章 · 读懂G代码",
+    "title": "31　一行G代码由“地址字”组成"
+  },
+  {
+    "page": 35,
+    "chapter": "第6章 · 模态状态",
+    "title": "32　没有写出来的内容，可能沿用上一行"
+  },
+  {
+    "page": 36,
+    "chapter": "第6章 · 单位",
+    "title": "33　G20/G21改变长度单位，不把角度变成长度"
+  },
+  {
+    "page": 37,
+    "chapter": "第6章 · 绝对目标",
+    "title": "34　G90 X10：去当前编程系的X=10"
+  },
+  {
+    "page": 38,
+    "chapter": "第6章 · 相对增量",
+    "title": "35　G91 X10：在当前编程方向增加10"
+  },
+  {
+    "page": 39,
+    "chapter": "第6章 · 运动方式",
+    "title": "36　G0/G1分别如何产生运动？"
+  },
+  {
+    "page": 40,
+    "chapter": "第6章 · 圆弧地址",
+    "title": "37　G2/G3里的I、J、K不是三根新电机轴"
+  },
+  {
+    "page": 41,
+    "chapter": "第6章 · 进给",
+    "title": "38　F到底是速度、时间，还是每转进给？"
+  },
+  {
+    "page": 42,
+    "chapter": "第6章 · 其他常见字",
+    "title": "39　不是每个数字都代表位置"
+  },
+  {
+    "page": 43,
+    "chapter": "第6章 · 从文本到运动",
+    "title": "40　控制器不是从左到右逐个字移动"
+  },
+  {
+    "page": 44,
+    "chapter": "第7章 · 完整实算程序",
+    "title": "41　统一实验条件与完整程序"
+  },
+  {
+    "page": 45,
+    "chapter": "第7章 · 第一步",
+    "title": "42　N10–N30：设置模式与工件参考"
+  },
+  {
+    "page": 46,
+    "chapter": "第7章 · 第二步",
+    "title": "43　N40 M428：先切模式，不凭空移动"
+  },
+  {
+    "page": 47,
+    "chapter": "第7章 · 第三步",
+    "title": "44　N50：把第一个工件点送到刀尖"
+  },
+  {
+    "page": 48,
+    "chapter": "第7章 · 第四步",
+    "title": "45　N60 C90：XYZ字没出现，XYZ关节却动了"
+  },
+  {
+    "page": 49,
+    "chapter": "第7章 · 第五步",
+    "title": "46　N70 G91 X10：沿转后的工件方向走"
+  },
+  {
+    "page": 50,
+    "chapter": "第7章 · 第六步",
+    "title": "47　N80：工件点不变，B倾转带来X/Z补偿"
+  },
+  {
+    "page": 51,
+    "chapter": "第7章 · 第七步",
+    "title": "48　N90：省略的Z、B、C保持当前目标"
+  },
+  {
+    "page": 52,
+    "chapter": "第7章 · 全过程汇总",
+    "title": "49　把五组数字同时放在一张表里"
+  },
+  {
+    "page": 53,
+    "chapter": "第7章 · 再切回直接模式",
+    "title": "50　N100/N110：同一刀尖位置，坐标解释改变"
+  },
+  {
+    "page": 54,
+    "chapter": "第8章 · 中间轨迹",
+    "title": "51　RTCP要在运动过程中持续计算"
+  },
+  {
+    "page": 55,
+    "chapter": "第8章 · 姿态与刀轴",
+    "title": "52　RTCP不自动决定刀轴该朝哪里"
+  },
+  {
+    "page": 56,
+    "chapter": "第8章 · 三维显示",
+    "title": "53　预览画面中的三个对象要分开看"
+  },
+  {
+    "page": 57,
+    "chapter": "第8章 · 参数准备",
+    "title": "54　准备数据时，按三层顺序核对"
+  },
+  {
+    "page": 58,
+    "chapter": "第9章 · 课堂实验",
+    "title": "55　实验一：观察“转动后的坐标方向”"
+  },
+  {
+    "page": 59,
+    "chapter": "第9章 · 课堂实验",
+    "title": "56　实验二：G54与G90/G91的逐行记录"
+  },
+  {
+    "page": 60,
+    "chapter": "第9章 · 课堂实验",
+    "title": "57　实验三：原点移动，程序几何不改"
+  },
+  {
+    "page": 61,
+    "chapter": "第9章 · 排错",
+    "title": "58　位置不对时，从哪一层开始查？"
+  },
+  {
+    "page": 62,
+    "chapter": "第9章 · 限位与边界",
+    "title": "59　RTCP跟得上，还必须到得了"
+  },
+  {
+    "page": 63,
+    "chapter": "第10章 · 常见问答",
+    "title": "60　初学者最容易问错的八个问题"
+  },
+  {
+    "page": 64,
+    "chapter": "第10章 · 练习",
+    "title": "61　练习A：原点、模式和地址字"
+  },
+  {
+    "page": 65,
+    "chapter": "第10章 · 练习",
+    "title": "62　练习B：从工件点推到物理关节"
+  },
+  {
+    "page": 66,
+    "chapter": "第10章 · 参考答案",
+    "title": "63　练习A答案"
+  },
+  {
+    "page": 67,
+    "chapter": "第10章 · 参考答案",
+    "title": "64　练习B答案"
+  },
+  {
+    "page": 68,
+    "chapter": "附录A · 术语",
+    "title": "65　把常见名词翻译成容易理解的话"
+  },
+  {
+    "page": 69,
+    "chapter": "附录B · 可选数学",
+    "title": "66　用最少公式描述完整坐标链"
+  },
+  {
+    "page": 70,
+    "chapter": "附录B · 可选数学",
+    "title": "67　反过来：从当前物理位置求工件坐标"
+  },
+  {
+    "page": 71,
+    "chapter": "附录C · 软件实验范围",
+    "title": "68　这份讲义验证了什么，没有声称什么？"
+  },
+  {
+    "page": 72,
+    "chapter": "附录D · 来源与复现",
+    "title": "69　官方资料、验证数据与自学路径"
+  }
+]

docs/teaching/rtcp-beginners/verification/acceptance.json

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+      "title": "18　G54究竟做了什么？"
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+      "characters": 421,
+      "title": "19　G54的40、20、10代表什么？"
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+    },
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+      "title": "25　RTCP控制的是相对目标关系"
+    },
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+      "characters": 370,
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+      "characters": 415,
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+      "characters": 457,
+      "title": "29　G54、旋转中心、轴间偏置各管什么？"
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+      "page": 33,
+      "characters": 465,
+      "title": "30　为什么必须知道刀尖究竟在哪里？"
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+      "page": 34,
+      "characters": 521,
+      "title": "31　一行G代码由“地址字”组成"
+    },
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+      "page": 35,
+      "characters": 473,
+      "title": "32　没有写出来的内容，可能沿用上一行"
+    },
+    {
+      "page": 36,
+      "characters": 501,
+      "title": "33　G20/G21改变长度单位，不把角度变成长度"
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+      "characters": 485,
+      "title": "36　G0/G1分别如何产生运动？"
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+      "page": 40,
+      "characters": 466,
+      "title": "37　G2/G3里的I、J、K不是三根新电机轴"
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+      "characters": 528,
+      "title": "38　F到底是速度、时间，还是每转进给？"
+    },
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+      "page": 42,
+      "characters": 509,
+      "title": "39　不是每个数字都代表位置"
+    },
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+      "characters": 491,
+      "title": "40　控制器不是从左到右逐个字移动"
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+      "characters": 569,
+      "title": "41　统一实验条件与完整程序"
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+      "characters": 456,
+      "title": "42　N10–N30：设置模式与工件参考"
+    },
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+      "characters": 449,
+      "title": "43　N40 M428：先切模式，不凭空移动"
+    },
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+      "page": 47,
+      "characters": 450,
+      "title": "44　N50：把第一个工件点送到刀尖"
+    },
+    {
+      "page": 48,
+      "characters": 513,
+      "title": "45　N60 C90：XYZ字没出现，XYZ关节却动了"
+    },
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+      "characters": 498,
+      "title": "46　N70 G91 X10：沿转后的工件方向走"
+    },
+    {
+      "page": 50,
+      "characters": 507,
+      "title": "47　N80：工件点不变，B倾转带来X/Z补偿"
+    },
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+      "page": 51,
+      "characters": 477,
+      "title": "48　N90：省略的Z、B、C保持当前目标"
+    },
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+      "page": 52,
+      "characters": 737,
+      "title": "49　把五组数字同时放在一张表里"
+    },
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+      "characters": 511,
+      "title": "50　N100/N110：同一刀尖位置，坐标解释改变"
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+      "page": 54,
+      "characters": 336,
+      "title": "51　RTCP要在运动过程中持续计算"
+    },
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+      "page": 55,
+      "characters": 408,
+      "title": "52　RTCP不自动决定刀轴该朝哪里"
+    },
+    {
+      "page": 56,
+      "characters": 514,
+      "title": "53　预览画面中的三个对象要分开看"
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+      "characters": 497,
+      "title": "54　准备数据时，按三层顺序核对"
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+      "characters": 491,
+      "title": "56　实验二：G54与G90/G91的逐行记录"
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+      "title": "57　实验三：原点移动，程序几何不改"
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+    {
+      "page": 61,
+      "characters": 497,
+      "title": "58　位置不对时，从哪一层开始查？"
+    },
+    {
+      "page": 62,
+      "characters": 473,
+      "title": "59　RTCP跟得上，还必须到得了"
+    },
+    {
+      "page": 63,
+      "characters": 434,
+      "title": "60　初学者最容易问错的八个问题"
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+      "title": "61　练习A：原点、模式和地址字"
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+      "title": "63　练习A答案"
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+      "characters": 419,
+      "title": "64　练习B答案"
+    },
+    {
+      "page": 68,
+      "characters": 472,
+      "title": "65　把常见名词翻译成容易理解的话"
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+    {
+      "page": 69,
+      "characters": 477,
+      "title": "66　用最少公式描述完整坐标链"
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+      "characters": 500,
+      "title": "67　反过来：从当前物理位置求工件坐标"
+    },
+    {
+      "page": 71,
+      "characters": 525,
+      "title": "68　这份讲义验证了什么，没有声称什么？"
+    },
+    {
+      "page": 72,
+      "characters": 731,
+      "title": "69　官方资料、验证数据与自学路径"
+    }
+  ],
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+}

docs/teaching/rtcp-beginners/verification/layout.json

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