Hi!
Think of your logs as of 3D-lines with some radii. When the distance between these logs is equal or less than the sum of their radii, then their collided.
Three.js has Line3 class, but AFAIK, there is no methods for finding the distance between lines.
You can start from here: geometry - Find shortest distance between lines in 3D - Mathematics Stack Exchange
@Immugio Can the set of utilities for lines help in this case? 