NEW info considering to your images...
** Your type of closet rod **
Your bar is horizontally held in place by a set screw which is located on the underside of the holder.
If the bar cannot reach two holders or walls to hold each end, then the rod cannot be held into position.
** A different type of closet rod **
Yes, there is a threaded insert. The insert of lobed.
- Insert the smaller rod (with the insert) into the bigger rod.
- Turn the small rod clockwise to tighten so that the small rod will not longer side in or out of the bigger rod.
- Turn the small rod counter-clockwise to loosen.
- After you understand, insert the rod into the closet, expand to desired length, and tighten.
Note: Do not over tighten or it will be very difficult to loosen and/or you may break/reshape the insert or the larger pipe. This is not a connection which slowly tightens. You will discover that the tight/loose difference is only about 1/4 turn.