Loading... ### D-H Table For Kuka Med R820 | $i$ | $a_i$ | $\alpha _{i}$ | $d_{i}$ | $\theta _{i}$ | | --- | ----- | ----------------- | ------- | ------------- | | 1 | 0 | $- \frac{\pi}{2}$ | 360 | $\theta _{1}$ | | 2 | 0 | $\frac{\pi}{2}$ | 0 | $\theta _{2}$ | | 3 | 0 | $\frac{\pi}{2}$ | 420 | $\theta _{3}$ | | 4 | 0 | $- \frac{\pi}{2}$ | 0 | $\theta _{4}$ | | 5 | 0 | $- \frac{\pi}{2}$ | 400 | $\theta _{5}$ | | 6 | 0 | $\frac{\pi}{2}$ | 0 | $\theta _{6}$ | | 7 | 0 | 0 | 126 | $\theta _{7}$ | ### 正运动学求解（SDH） $$ ^{i-1}_{\ \ \ \ \ i}T = \begin{bmatrix} \cos{\theta_{i}} & -\sin{\theta_{i}}\cos{\alpha_{i}} & \sin{\theta_{i}}\sin{\alpha_{i}} & a_{i}\cos{\theta_{i}} \\ \sin{\theta_{i}} & \cos{\theta_{i}}\cos{\alpha_{i}} & -\cos{\theta_{i}}\sin{\alpha_{i}} & a_{i}\sin{\theta_{i}} \\ 0 & \sin{\alpha_{i}} & \cos{\alpha_{i}} & d_{i} \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{0}_{1}T = \begin{bmatrix} \cos{\theta_{1}} & 0 & -\sin{\theta_{1}} & 0 \\ \sin{\theta_{1}} & 0 & \cos{\theta_{1}} & 0 \\ 0 & -1 & 0 & 360 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{1}_{2}T = \begin{bmatrix} \cos{\theta_{2}} & 0 & \sin{\theta_{2}} & 0 \\ \sin{\theta_{2}} & 0 & -\cos{\theta_{2}} & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{2}_{3}T = \begin{bmatrix} \cos{\theta_{3}} & 0 & \sin{\theta_{3}} & 0 \\ \sin{\theta_{3}} & 0 & -\cos{\theta_{3}} & 0 \\ 0 & 1 & 0 & 420 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{3}_{4}T = \begin{bmatrix} \cos{\theta_{4}} & 0 & -\sin{\theta_{4}} & 0 \\ \sin{\theta_{4}} & 0 & \cos{\theta_{4}} & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{4}_{5}T = \begin{bmatrix} \cos{\theta_{5}} & 0 & -\sin{\theta_{5}} & 0 \\ \sin{\theta_{5}} & 0 & \cos{\theta_{5}} & 0 \\ 0 & -1 & 0 & 400 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{5}_{6}T = \begin{bmatrix} \cos{\theta_{6}} & 0 & \sin{\theta_{6}} & 0 \\ \sin{\theta_{6}} & 0 & -\cos{\theta_{6}} & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ ^{6}_{7}T = \begin{bmatrix} \cos{\theta_{7}} & -\sin{\theta_{7}} & 0 & 0 \\ \sin{\theta_{7}} & \cos{\theta_{7}} & 0 & 0 \\ 0 & 0 & 1 & 126 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} $$ $$ \begin{align} \label{eq} ^{0}_{7}T &=^{0}_{1}T\cdot ^{1}_{2}T\cdot ^{2}_{3}T\cdot ^{3}_{4}T\cdot ^{4}_{5}T\cdot ^{5}_{6}T\cdot ^{6}_{7}T \\ &= \begin{bmatrix} r_{11} & r_{12} & r_{13} & p_{x} \\ r_{21} & r_{22} & r_{23} & p_{y} \\ r_{31} & r_{32} & r_{33} & p_{z} \\ 0 & 0 & 0 & 1 \\ \end{bmatrix} \end{align} $$ $$ \begin{align} r_{11} &= \text{c}_{4}\text{s}_{1}\text{s}_{3}\text{s}_{5}\text{s}_{7}-\text{c}_{1}\text{c}_{2}\text{c}_{5}\text{s}_{3}\text{s}_{7}-\text{c}_{1}\text{c}_{4}\text{c}_{7}\text{s}_{2}\text{s}_{6}-\text{c}_{3}\text{c}_{6}\text{c}_{7}\text{s}_{1}\text{s}_{5}-\text{c}_{1}\text{s}_{2}\text{s}_{4}\text{s}_{5}\text{s}_{7}-\text{c}_{3}\text{c}_{5}\text{s}_{1}\text{s}_{7} \\ &- \text{c}_{7}\text{s}_{1}\text{s}_{3}\text{s}_{4}\text{s}_{6} - \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{s}_{5}\text{s}_{7} + \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{7}\text{s}_{4}\text{s}_{6} - \text{c}_{1}\text{c}_{2}\text{c}_{6}\text{c}_{7}\text{s}_{3}\text{s}_{5} + \text{c}_{1}\text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{2}\text{s}_{4} \\ &- \text{c}_{4}\text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{1}\text{s}_{3} + \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{c}_{7} \end{align} $$ $$ \begin{align} r_{12} &= \text{c}_{1}\text{c}_{4}\text{s}_{2}\text{s}_{6}\text{s}_{7} - \text{c}_{1}\text{c}_{2}\text{c}_{5}\text{c}_{7}\text{s}_{3} - \text{c}_{1}\text{c}_{7}\text{s}_{2}\text{s}_{4}\text{s}_{5} - \text{c}_{3}\text{c}_{5}\text{c}_{7}\text{s}_{1} + \text{c}_{4}\text{c}_{7}\text{s}_{1}\text{s}_{3}\text{s}_{5} + \text{c}_{3}\text{c}_{6}\text{s}_{1}\text{s}_{5}\text{s}_{7} \\ &+ \text{s}_{1}\text{s}_{3}\text{s}_{4}\text{s}_{6}\text{s}_{7} - \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{7}\text{s}_{5} - \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{s}_{4}\text{s}_{6}\text{s}_{7} + \text{c}_{1}\text{c}_{2}\text{c}_{6}\text{s}_{3}\text{s}_{5}\text{s}_{7} - \text{c}_{1}\text{c}_{5}\text{c}_{6}\text{s}_{2}\text{s}_{4}\text{s}_{7} \\ &+ \text{c}_{4}\text{c}_{5}\text{c}_{6}\text{s}_{1}\text{s}_{3}\text{s}_{7} - \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{s}_{7} \end{align} $$ $$ \begin{align} r_{13} &= \text{c}_{6}\text{s}_{1}\text{s}_{3}\text{s}_{4} - \text{c}_{3}\text{s}_{1}\text{s}_{5}\text{s}_{6} + \text{c}_{1}\text{c}_{4}\text{c}_{6}\text{s}_{2} - \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{6}\text{s}_{4} - \text{c}_{1}\text{c}_{2}\text{s}_{3}\text{s}_{5}\text{s}_{6} + \text{c}_{1}\text{c}_{5}\text{s}_{2}\text{s}_{4}\text{s}_{6} \\ &- \text{c}_{4}\text{c}_{5}\text{s}_{1}\text{s}_{3}\text{s}_{6} + \text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{s}_{6} \end{align} $$ $$ \begin{align} r_{21} &= \text{c}_{1}\text{c}_{3}\text{c}_{5}\text{s}_{7} + \text{c}_{1}\text{c}_{3}\text{c}_{6}\text{c}_{7}\text{s}_{5} - \text{c}_{2}\text{c}_{5}\text{s}_{1}\text{s}_{3}\text{s}_{7} - \text{c}_{1}\text{c}_{4}\text{s}_{3}\text{s}_{5}\text{s}_{7} - \text{c}_{4}\text{c}_{7}\text{s}_{1}\text{s}_{2}\text{s}_{6} + \text{c}_{1}\text{c}_{7}\text{c}_{3}\text{c}_{4}\text{c}_{6} \\ &- \text{s}_{1}\text{s}_{2}\text{s}_{4}\text{s}_{5}\text{s}_{7} + \text{c}_{1}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{3} - \text{c}_{2}\text{c}_{3}\text{c}_{4}\text{s}_{1}\text{s}_{5}\text{s}_{7} + \text{c}_{2}\text{c}_{3}\text{c}_{7}\text{s}_{1}\text{s}_{4}\text{s}_{6} - \text{c}_{2}\text{c}_{6}\text{c}_{7}\text{s}_{1}\text{s}_{3}\text{s}_{5} \\ &+ \text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{1}\text{s}_{2}\text{s}_{4} + \text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{1} \end{align} $$ $$ \begin{align} r_{22} & = \text{c}_{1}\text{c}_{3}\text{c}_{5}\text{c}_{7} - \text{c}_{2}\text{c}_{5}\text{c}_{7}\text{s}_{1}\text{s}_{3} - \text{c}_{1}\text{c}_{4}\text{c}_{7}\text{s}_{3}\text{s}_{5} - \text{c}_{1}\text{c}_{3}\text{c}_{6}\text{s}_{5}\text{s}_{7} - \text{c}_{7}\text{s}_{1}\text{s}_{2}\text{s}_{4}\text{s}_{5} + \text{c}_{4}\text{s}_{1}\text{s}_{2}\text{s}_{6}\text{s}_{7} \\ &- \text{c}_{1}\text{s}_{3}\text{s}_{4}\text{s}_{6}\text{s}_{7} - \text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{7}\text{s}_{1}\text{s}_{5} - \text{c}_{1}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{s}_{3}\text{s}_{7} - \text{c}_{2}\text{c}_{3}\text{s}_{1}\text{s}_{4}\text{s}_{6}\text{s}_{7} + \text{c}_{2}\text{c}_{6}\text{s}_{1}\text{s}_{3}\text{s}_{5}\text{s}_{7} \\ &- \text{c}_{5}\text{c}_{6}\text{s}_{1}\text{s}_{2}\text{s}_{4}\text{s}_{7} - \text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{s}_{1}\text{s}_{7} \end{align} $$ $$ \begin{align} r_{23} &= \text{c}_{4}\text{c}_{6}\text{s}_{1}\text{s}_{2} - \text{c}_{1}\text{c}_{6}\text{s}_{3}\text{s}_{4} + \text{c}_{1}\text{c}_{3}\text{s}_{5}\text{s}_{6} - \text{c}_{2}\text{c}_{3}\text{c}_{6}\text{s}_{1}\text{s}_{4} + \text{c}_{1}\text{c}_{4}\text{c}_{5}\text{s}_{3}\text{s}_{6} - \text{c}_{2}\text{s}_{1}\text{s}_{3}\text{s}_{5}\text{s}_{6} \\ &+ \text{c}_{5}\text{s}_{1}\text{s}_{2}\text{s}_{4}\text{s}_{6} + \text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{s}_{1}\text{s}_{6} \end{align} $$ $$ \begin{align} r_{31} &= \text{c}_{5}\text{s}_{2}\text{s}_{3}\text{s}_{7} - \text{c}_{2}\text{s}_{4}\text{s}_{5}\text{s}_{7} + \text{c}_{2}\text{c}_{4}\text{c}_{7}\text{s}_{6} + \text{c}_{2}\text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{4} + \text{c}_{3}\text{c}_{4}\text{s}_{2}\text{s}_{5}\text{s}_{7} - \text{c}_{3}\text{c}_{7}\text{s}_{2}\text{s}_{4}\text{s}_{6} \\ &+ \text{c}_{6}\text{c}_{7}\text{s}_{2}\text{s}_{3}\text{s}_{5} - \text{c}_{3}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{c}_{7}\text{s}_{2} \end{align} $$ $$ \begin{align} r_{32} &= \text{c}_{5}\text{c}_{7}\text{s}_{2}\text{s}_{3} - \text{c}_{2}\text{c}_{7}\text{s}_{4}\text{s}_{5} + \text{c}_{2}\text{c}_{4}\text{s}_{6}\text{s}_{7} + \text{c}_{3}\text{c}_{4}\text{c}_{7}\text{s}_{2}\text{s}_{5} - \text{c}_{2}\text{c}_{5}\text{c}_{6}\text{s}_{4}\text{s}_{7} + \text{c}_{3}\text{s}_{2}\text{s}_{4}\text{s}_{6}\text{s}_{7} \\ &- \text{c}_{6}\text{s}_{2}\text{s}_{3}\text{s}_{5}\text{s}_{7} + \text{c}_{3}\text{c}_{4}\text{c}_{5}\text{c}_{6}\text{s}_{2}\text{s}_{7} \end{align} $$ $$ \begin{align} r_{33} &= \text{c}_{2}\text{c}_{4}\text{c}_{6} + \text{c}_{3}\text{c}_{6}\text{s}_{2}\text{s}_{4} + \text{c}_{2}\text{c}_{5}\text{c}_{4}\text{c}_{6} + \text{s}_{2}\text{s}_{3}\text{s}_{5}\text{s}_{6} - \text{c}_{3}\text{c}_{4}\text{c}_{5}\text{s}_{2}\text{s}_{6} \end{align} $$ $$ \begin{align} p_{x} &= 420\text{c}_{1}\text{s}_{2} + 400\text{c}_{1}\text{c}_{4}\text{s}_{2} + 400\text{s}_{1}\text{s}_{3}\text{s}_{4} + 126\text{c}_{6}\text{s}_{1}\text{s}_{3}\text{s}_{4} - 126\text{c}_{3}\text{s}_{1}\text{s}_{5}\text{s}_{6} - 400\text{c}_{1}\text{c}_{2}\text{c}_{3}\text{s}_{4} \\ &+ 126\text{c}_{1}\text{c}_{4}\text{c}_{6}\text{s}_{2} - 126\text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{6}\text{s}_{4} - 126\text{c}_{1}\text{c}_{2}\text{s}_{3}\text{s}_{5}\text{s}_{6} + 126\text{c}_{1}\text{c}_{5}\text{s}_{2}\text{s}_{4}\text{s}_{6} - 126\text{c}_{4}\text{c}_{5}\text{s}_{1}\text{s}_{3}\text{s}_{6} \\ &+ 126\text{c}_{1}\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{s}_{6} \end{align} $$ $$ \begin{align} p_{y} &= 420\text{s}_{1}\text{s}_{2} + 400\text{c}_{4}\text{s}_{1}\text{s}_{2} - 400\text{c}_{1}\text{s}_{3}\text{s}_{4} - 400\text{c}_{2}\text{c}_{3}\text{s}_{1}\text{s}_{4} + 126\text{c}_{4}\text{c}_{6}\text{s}_{1}\text{s}_{2} - 126\text{c}_{1}\text{c}_{6}\text{s}_{3}\text{s}_{4} \\ &+ 126\text{c}_{1}\text{c}_{3}\text{s}_{5}\text{s}_{6} - 126\text{c}_{2}\text{c}_{3}\text{c}_{6}\text{s}_{1}\text{s}_{4} + 126\text{c}_{1}\text{c}_{4}\text{c}_{5}\text{s}_{3}\text{s}_{6} - 126\text{c}_{2}\text{c}_{1}\text{c}_{3}\text{c}_{5}\text{c}_{6} + 126\text{c}_{5}\text{s}_{1}\text{s}_{2}\text{s}_{4}\text{s}_{6} \\ &+ 126\text{c}_{2}\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{s}_{1}\text{s}_{6} \end{align} $$ $$ \begin{align} p_{z} &= 420\text{c}_{2} + 400\text{c}_{2}\text{c}_{4} + 126\text{c}_{2}\text{c}_{4}\text{c}_{6} + 400\text{c}_{3}\text{s}_{2}\text{s}_{4} + 126\text{c}_{3}\text{c}_{6}\text{s}_{2}\text{s}_{4} + 126\text{c}_{2}\text{c}_{5}\text{s}_{4}\text{s}_{6} \\ &+ 126\text{s}_{2}\text{s}_{3}\text{s}_{5}\text{s}_{6} - 126\text{c}_{3}\text{c}_{4}\text{c}_{5}\text{s}_{2}\text{s}_{6} + 360 \end{align} $$ 以上是Med R820运动学正解结果，已通过MATLAB实验验证结果的正确性 最后修改：2024 年 06 月 03 日 © 允许规范转载 赞 0 如果觉得我的文章对你有用，请随意赞赏
