70 lines
5.5 KiB
XML
70 lines
5.5 KiB
XML
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<defs>
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<text x="490" y="34" text-anchor="middle" font-size="21" font-weight="bold" fill="#16324f">正运动学：枢轴变换与链式累积</text>
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<!-- 左：单关节枢轴 -->
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<text x="230" y="66" text-anchor="middle" font-size="14.5" font-weight="bold" fill="#1f4f8f">单关节：绕“不在原点的轴”旋转</text>
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<circle cx="230" cy="160" r="7" fill="#7c5cd6"/>
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<text x="296" y="148" font-size="12.5" fill="#3d5164">枢轴点 P + 轴方向 d</text>
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<text x="296" y="166" font-size="12.5" fill="#3d5164">θ=0 位形（虚线）→ θ 位形（蓝）</text>
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<text x="296" y="184" font-size="12.5" fill="#3d5164">关节角 θi = 绕轴 d 的有符号转角</text>
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<text x="80" y="344" font-size="13" fill="#16324f" font-family="Consolas,monospace">A(θ) = T(P) · R(d,θ) · T(−P)</text>
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<text x="80" y="368" font-size="13" fill="#16324f" font-family="Consolas,monospace">x' = R·(x − P) + P</text>
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<text x="80" y="396" font-size="12" fill="#5c7185">先平移枢轴点到原点 → 绕轴转 θ → 平移回去。关节表只存</text>
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<text x="80" y="412" font-size="12" fill="#5c7185">P（rear）与 d（单位轴向量），六个关节共 12 个常量。</text>
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<!-- 右：链 -->
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<text x="735" y="66" text-anchor="middle" font-size="14.5" font-weight="bold" fill="#1f4f8f">六链累积：World = A₁·A₂·A₃·A₄·A₅·A₆·TCP</text>
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<text x="536" y="157" fill="#153a6e">A1</text>
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<rect x="578" y="130" width="52" height="44" rx="6" fill="#dbe9fb" stroke="#3572c9" stroke-width="1.5"/>
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<text x="604" y="157" fill="#153a6e">A2</text>
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<rect x="646" y="130" width="52" height="44" rx="6" fill="#dbe9fb" stroke="#3572c9" stroke-width="1.5"/>
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<text x="672" y="157" fill="#153a6e">A3</text>
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<rect x="714" y="130" width="52" height="44" rx="6" fill="#dbe9fb" stroke="#3572c9" stroke-width="1.5"/>
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<text x="740" y="157" fill="#153a6e">A4</text>
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<text x="808" y="157" fill="#153a6e">A5</text>
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<rect x="850" y="130" width="52" height="44" rx="6" fill="#dbe9fb" stroke="#3572c9" stroke-width="1.5"/>
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<text x="876" y="157" fill="#153a6e">A6</text>
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</g>
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<g font-size="11" fill="#5c7185" text-anchor="middle">
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<text x="536" y="190">θ1</text><text x="604" y="190">θ2</text><text x="672" y="190">θ3</text>
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<text x="740" y="190">θ4</text><text x="808" y="190">θ5</text><text x="876" y="190">θ6</text>
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</g>
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<g stroke="#5a7d9a" stroke-width="1.5">
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<line x1="562" y1="152" x2="576" y2="152"/>
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<line x1="630" y1="152" x2="644" y2="152"/>
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<line x1="698" y1="152" x2="712" y2="152"/>
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<line x1="766" y1="152" x2="780" y2="152"/>
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<line x1="834" y1="152" x2="848" y2="152"/>
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</g>
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<text x="462" y="157" text-anchor="end" font-size="13" font-weight="bold" fill="#16324f">World</text>
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<text x="960" y="157" text-anchor="end" font-size="13" font-weight="bold" fill="#b06a10">TCP</text>
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<text x="735" y="216" text-anchor="middle" font-size="12" fill="#5c7185">每级只读父级位姿与自己 —— 与 three.js 场景图 6 级嵌套 pivot 逐位一致</text>
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<rect x="510" y="240" width="420" height="192" rx="8" fill="#f4f6f8" stroke="#9db0c0" stroke-width="1.2"/>
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<text x="530" y="266" font-size="13" font-weight="bold" fill="#16324f">两套实现，互为对账：</text>
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<text x="530" y="290" font-size="12.5" fill="#3d5164">· fkChain()：严格 4×4 同质矩阵链 —— 对照基准，慢而直白</text>
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<text x="530" y="312" font-size="12.5" fill="#3d5164">· fk()：按结构常量展开三角函数的闭式快路径 —— 求解器</text>
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<text x="530" y="332" font-size="12.5" fill="#3d5164"> 热路径专用，每姿态仅 ~20 次乘加</text>
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<text x="530" y="360" font-size="12.5" fill="#3d5164">· 自检：5000 个随机位形，两实现的 TCP 差 ≤ 5.7e-13 mm</text>
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<text x="530" y="384" font-size="12.5" fill="#3d5164">· 工具长度 tool 沿 J6 轴外伸：TCP_z 随 tool 平移（ax=J6 轴）</text>
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<text x="530" y="406" font-size="11.5" fill="#8a9aa8">指纹校验：预置自检值绑定（限位表+常量+源码）的 FNV-1a 指纹，</text>
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<text x="530" y="422" font-size="11.5" fill="#8a9aa8">模型或求解器一变即提示重算。</text>
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