I am working on a flexible robotic arm. At a point (c) on its surface a wrench is exerted, causing the deformation of the arm. For rigid bodies it is possible to transform a wrench from one coordinate frame (c) to another (b) (e.g. see "A mathematical introduction to robotic manipulation") using

$\begin{bmatrix} F_b \newline \tau_b \end{bmatrix} = \begin{bmatrix} {R^b_c}^\top & 0 \newline - {R^b_c}^\top \hat{p}^b_c & {R^b_c}^\top\end{bmatrix} \begin{bmatrix} F_c \newline \tau_c \end{bmatrix}$

where $R$ is the rotation matrix and

$\hat{p}^b_c = \begin{bmatrix} 0 & −{p}^b_c(z) & {p}^b_c(y) \newline {p}^b_c(z) & 0 & -{p}^b_c(x) \newline -{p}^b_c(y) & {p}^b_c(x) & 0 \end{bmatrix}$.

My question is the following. Can I use the same transformation when the body under consideration is flexible? Or is it the case that, by doing so, the resulting deformation will be different than the one resulting from the wrench applied on point c? Any source on this matter would be highly appreciated, too.


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