Example 3. For a cylinder with a base radius of $\mathrm{R}$, the radii of the two bases $\mathrm{OM}$ and $\mathrm{O}_{1} \mathrm{~N}_{1}$ form a $60^{\circ}$ angle. Find the distance between the skew lines $\mathrm{MN}_{1}$ and the cylinder axis $\mathrm{OO}_{1}$.
From Fig. 4, it is easy to know that the dihedral angle $\mathrm{M}-\mathrm{OO}_{1}-\mathrm{N}_{1}$ is $60^{\circ}, \mathrm{M}$ and $\mathrm{~N}_{1}$ are both at a distance of $R$ from $\mathrm{OO}_{1}$. Using formula (3), the distance $\mathrm{h}$ between the skew lines $\mathrm{MN}_{1}$ and $\mathrm{OO}_{1}$ is $\mathrm{h}:=\frac{\sqrt{3}}{2} \mathrm{R}$.