I am struggling to understand the results of a partial derivative of a vector function with respect to a vector.
A plane has equation $\begin{bmatrix} a&b&c&d\end{bmatrix}\begin{bmatrix}x\\ y\\ z \\ 1 \end{bmatrix} =0$ which can be written in terms of $\textbf{p}$, the position vector of the points on the plane $\begin{bmatrix} a&b&c&d\end{bmatrix}\begin{bmatrix} \textbf{p} \\ 1 \end{bmatrix} =0$.
The end effector of a manipulator has position vector $ \textbf{q} = \begin{bmatrix} x_q \\y_q \\ z_q \end{bmatrix} $. So if the end effector is to be in contact with the plane then the constraint equation is $ \Phi(\textbf{q}) = \begin{bmatrix} a&b&c&d\end{bmatrix}\begin{bmatrix} \textbf{q} \\ 1 \end{bmatrix} =0$
My notes then say the corresponding velocity constraint for the end effector of the manipulator is $ \frac{\partial\Phi(\textbf{q})}{\partial\textbf{q}} = \begin{bmatrix} a&b&c\end{bmatrix} \dot{\textbf{q}}=0$. Can anyone explain where this result comes from? I cannot understand why the $\dot{\textbf{q}}$ is there.
Many thanks!