The Rod component models a massless flexible rod. Rod can be seen as a spring/damper connection between two end frames with a given unstretched length and spring/damping constants.

Assuming that the translation vector, $\mathbf{r}$, is directed from frame_a, $\left[\mathrm{X1}\,\mathrm{Y1}\,\mathrm{Z1}\right]\,$to frame_b, $\left[\mathrm{X2}\,\mathrm{Y2}\,\mathrm{Z2}\right]$, the resultant forces of the rod are

${\mathbf{f}}_1\=\frac{f}{‖\mathbf{r}‖}\mathbf{\cdot }\left(\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X1}}\+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y1}}\+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z1}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z1}}\right)$

${\mathbf{f}}_2\=-\frac{f}{‖\mathbf{r}‖}\mathbf{\cdot }\left(\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{X2}}\+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Y2}}\+\left(\mathbf{r}\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z2}}\right)\mathbf{\cdot }{\mathbf{e}}_{\mathrm{Z2}}\right)$

where $\mathbf{e}\mathbf{ }$denotes unit vectors and $\mathrm{f\_\_1}$and $\mathrm{f\_\_2}$are the reaction forces applied to frame_a and frame_b, respectively, and

$f\=\{\begin{array}{cc}\mathrm{K\_\_d} \left(\frac{\ⅆ}{\ⅆt}L\right) \+\mathrm{K\_\_s}\left(L-\mathrm{L0}\right) & L\ne 0\\ 0& L\=0\end{array}$

where $L\=‖\mathbf{r}‖$is the instantaneous rod length. Note that in these equations, bold non-italic symbols denote vectors. Figure 1 shows the rod and the end frames.

Figure 1: Rod and end frames