\subsection{Forward Kinematics (FK)}
$\mat{T}_{WB_n}(\vec{\theta}) = \mat{T}_{WB_0} \mat{T}_{B_0B_1}(\theta_1) \cdots \mat{T}_{B_{n - 1}B_n}(\theta_n)$.

For 2R system: ${_W}\vec{t}_{WE} =$
{\scriptsize
$ \begin{bmatrix}
        L_1 \cos(\theta_1) + L_2 \cos(\theta_1 + \theta_2) \\
        L_1 \sin(\theta_1) + L_2 \sin(\theta_1 + \theta_2)
    \end{bmatrix}$\\
}
Workspace $W$: $\theta_1, \theta_2 \in [-\pi, \pi]$.
\bi{Computation} Similar for $n$R sys (more angles, more lengths).
Last dim is typically sum of angles (or equiv).
\bi{For velocity kinematics}: Comp. Jacobian of this $nD$ position ($nD$ pos is vec). ${_W}\vec{t}_{WE} \mat{J}(\vec{\theta}) \cdot \vec{\dot{\theta}}$
\bi{Jacobian}: see \ref{sec:ms-lin}.

\shortdefinition[Singularity] Loss of deg of Freedom $\det(\mat{J}(\vec{\theta})) = 0$