57 lines
4.6 KiB
XML
57 lines
4.6 KiB
XML
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<defs>
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<marker id="zb" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="6.5" markerHeight="6.5" orient="auto-start-reverse">
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<path d="M0,0 L10,5 L0,10 z" fill="#3572c9"/>
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</marker>
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<marker id="zo" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="6.5" markerHeight="6.5" orient="auto-start-reverse">
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<path d="M0,0 L10,5 L0,10 z" fill="#e08a1e"/>
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</marker>
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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">工具姿态参数化：方位角 az · 仰角 el · 滚转 roll</text>
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<!-- 左：球面示意 -->
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<circle cx="240" cy="220" r="130" fill="#f4f8fb" stroke="#b9c8d6" stroke-width="1.4"/>
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<ellipse cx="240" cy="220" rx="130" ry="40" fill="none" stroke="#b9c8d6" stroke-width="1" stroke-dasharray="4 3"/>
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<line x1="240" y1="220" x2="240" y2="70" stroke="#3572c9" stroke-width="2" marker-end="url(#zb)"/>
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<text x="252" y="80" font-size="12.5" fill="#2a4a6e">CAD +Z</text>
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<line x1="240" y1="220" x2="400" y2="220" stroke="#8a9aa8" stroke-width="1.4"/>
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<text x="406" y="224" font-size="12" fill="#5c7185">方位基线</text>
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<!-- 工具轴 -->
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<line x1="240" y1="220" x2="296" y2="96" stroke="#e08a1e" stroke-width="2.6" marker-end="url(#zo)"/>
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<text x="306" y="94" font-size="12.5" font-weight="bold" fill="#b06a10">工具轴</text>
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<text x="306" y="112" font-size="11.5" fill="#b06a10">（法兰 +Z 外伸）</text>
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<!-- el 弧 -->
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<path d="M 240 128 A 92 92 0 0 1 277 136" fill="none" stroke="#7c5cd6" stroke-width="1.7"/>
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<text x="92" y="140" font-size="12.5" fill="#7c5cd6">el（仰角，自 +Z 抬起）</text>
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<text x="92" y="158" font-size="12.5" fill="#7c5cd6">0…180°</text>
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<line x1="216" y1="136" x2="258" y2="131" stroke="#7c5cd6" stroke-width="1" stroke-dasharray="3 3"/>
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<!-- roll 环绕工具轴 -->
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<ellipse cx="270" cy="153" rx="20" ry="9" fill="none" stroke="#d64545" stroke-width="1.7" transform="rotate(-24 270 153)"/>
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<text x="92" y="196" font-size="12.5" fill="#b03030">roll（绕轴滚转）</text>
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<text x="92" y="214" font-size="12.5" fill="#b03030">= θ6，绕工具轴</text>
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<line x1="212" y1="198" x2="256" y2="160" stroke="#d64545" stroke-width="1" stroke-dasharray="3 3"/>
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<!-- az 弧（水平面内） -->
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<path d="M 362 220 A 122 38 0 0 0 330 182" fill="none" stroke="#1f9d63" stroke-width="1.7"/>
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<text x="320" y="262" font-size="12.5" fill="#1f7a4d">az（绕 Z 方位角，−180…180°）</text>
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<circle cx="240" cy="220" r="4" fill="#16324f"/>
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<text x="160" y="248" font-size="12" fill="#5c7185">法兰中心</text>
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<!-- 右：公式 -->
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<rect x="470" y="70" width="470" height="180" rx="8" fill="#f4f6f8" stroke="#9db0c0" stroke-width="1.2"/>
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<text x="488" y="96" font-size="13" font-weight="bold" fill="#16324f">poseMat(az, el, roll) → 工具系旋转矩阵（列 = x/y/z）</text>
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<text x="488" y="122" font-size="12.5" fill="#16324f" font-family="Consolas,monospace">z = (sin el·cos az, sin el·sin az, cos el)</text>
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<text x="488" y="146" font-size="12.5" fill="#16324f" font-family="Consolas,monospace">x0 = (−sin az, cos az, 0) （子午面基，恒⊥z）</text>
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<text x="488" y="170" font-size="12.5" fill="#16324f" font-family="Consolas,monospace">x = R(z, roll)·x0 y = z × x</text>
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<text x="488" y="200" font-size="11.5" fill="#5c7185">poseAng() 为其逆分解；el ∈ [0,180]，az/roll ∈ (−180,180]。</text>
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<text x="488" y="220" font-size="11.5" fill="#5c7185">界面以「工具朝外」描述；求解器内部法兰法向朝臂内，</text>
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<text x="488" y="236" font-size="11.5" fill="#5c7185">两者相差绕工具 x 轴 180°（RX180），入栈/出栈各翻一次。</text>
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<rect x="470" y="266" width="470" height="140" rx="8" fill="#fdf6ec" stroke="#c99418" stroke-width="1.3"/>
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<text x="488" y="292" font-size="13" font-weight="bold" fill="#7a5a08">为什么姿态任务只剩 2 个未知数</text>
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<text x="488" y="316" font-size="12" fill="#6b5312">· θ6 只提供绕工具轴的滚转，不改变工具轴 ⇒ 工具轴 = (R1…R5)·ẑ</text>
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<text x="488" y="338" font-size="12" fill="#6b5312">· 滚转由 rollClose 闭式补出：θ6 = −atan2(N[1,0], N[0,0])，N = R5ᵀ·Rtar</text>
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<text x="488" y="360" font-size="12" fill="#6b5312">· 推论：全姿态偏差 oerr ≥ 工具轴夹角（20 万随机样本验证零违反）——</text>
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<text x="488" y="380" font-size="12" fill="#6b5312"> 粗扫用一次点积预筛（1−cos2°）挡掉必被拒的候选，省掉矩阵链+acos</text>
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</svg>
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