mirror of
https://github.com/janishutz/eth-summaries.git
synced 2026-09-10 19:15:25 +02:00
16 lines
673 B
TeX
16 lines
673 B
TeX
\subsection{Inverse Kinematics (IK)}
|
|
\begin{wrapfigure}[10]{r}{0.35\columnwidth}
|
|
\includegraphics[width=0.35\columnwidth]{assets/inverse-kinematics.png}
|
|
\end{wrapfigure}
|
|
\bi{Option}: Solve FK for angles.\\
|
|
\bi{Better}: Law of cosine with polar coordinates. Compute angle using cosine rule,
|
|
$\theta_1 = \varphi \pm \alpha$, $\theta_2 = \pm(\pi - \beta)$
|
|
(Positive for {\color{ForestGreen} Elbow Down}, Neg. for {\color{red} Elbow Up})
|
|
|
|
\bi{Extension to 6R}:
|
|
1. Waist: spherical coords (2 sol.)\\
|
|
2. 2 sols from 2R for shoulder + elbow\\
|
|
3. Solve for wrist joints (no infl. on pos)
|
|
|
|
\bi{For Inv. velocity}: $\vec{\dot{\theta}} = J_S^{-1}(\vec{\theta}) {_W} \vec{t}_{WE}$
|