The initial length of rod $$\begin{gathered} \left(2\right){ \\ }_{ \\ } \end{gathered}$$ is:

$$\begin{gathered} {\mathrm{L}}_{\mathrm{init}}={\mathrm{L}}_2{ \\ }_{ \\ } \end{gathered}$$

Based on the sketch of the rotated rigid bar, the final length of rod $$\begin{gathered} \left(2\right){ \\ }_{ \\ } \end{gathered}$$ is:

$$\begin{gathered} {\mathrm{L}}_{\mathrm{final}}={\mathrm{L}}_2-{\mathrm{v}}_{\mathrm{D}}{ \\ }_{ \\ } \end{gathered}$$

The elongation of bar $$\begin{gathered} \left(2\right){ \\ }_{ \\ } \end{gathered}$$ is thus:

$$\begin{gathered} {\mathrm{\delta }}_2={\mathrm{L}}_{\mathrm{final}}-{\mathrm{L}}_{\mathrm{init}} \\ =({\mathrm{L}}_2-{\mathrm{v}}_{\mathrm{D}})-{\mathrm{L}}_2 \\ =-{{\mathrm{v}}_{\mathrm{D}}}_{ \\ } \end{gathered}$$