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26 lines
1015 B
TeX
26 lines
1015 B
TeX
\subsection{Inverse Kinematics (IK)}
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\begin{wrapfigure}[10]{r}{0.35\columnwidth}
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\includegraphics[width=0.35\columnwidth]{assets/inverse-kinematics.png}
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\end{wrapfigure}
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\bi{Option}: Solve FK for angles.\\
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\bi{Better}: Law of cosine with polar coordinates. Compute angle using cosine rule,
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$\theta_1 = \varphi \pm \alpha$, $\theta_2 = \pm(\pi - \beta)$
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(Positive for {\color{ForestGreen} Elbow Down}, Neg. for {\color{red} Elbow Up})
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\bi{Extension to 6R}:
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1. Waist: spherical coords (2 sol.)\\
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2. 2 sols from 2R for shoulder + elbow\\
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3. Solve for wrist joints (no infl. on pos)
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\bi{For Inv. velocity}: $\vec{\dot{\theta}} = J_S^{-1}(\vec{\theta}) {_W} \dot{\vec{t}}_{WE}$
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% \shortdefinition[Denavit-Hartengerb (DH)] Serial chains
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% \[
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% \mat{T}_{L_j L_{j + 1}} = \mat{T}^{R_z}(\theta_j) \mat{T}^{t_z}(d_j) \mat{T}^{t_x}(a_j) \mat{T}^{R_x}(\alpha_j)
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% \]
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% with $
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\shortdefinition[Underactuated] workspace $<6$D; IK solvable
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\shortdefinition[Overactuated] $\8$ IK sol; Reduced singularities; Num. sol.
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