I am trying to put together a TV Stand with 3 legs- 2 of which are supported via 18 inch metal rods within plastic tubes, screwed into the base. The depth of the hole in one of these is too shallow so the rod is easily loosened- rendering it useless. How can I increase the depth of the threads in this (aluminium) hole; or increase the rigidity of the rod?
If the hole is there but not threaded you can cut the thread deeper with a tap. You need to be sure of the size, which is easier to measure on the external thread of the mating part. Often the hole is also too loose though.
If the hole is not deep enough it will need to be drilled deeper, first the correct tap size would be needed once the correct size/ pitch of the tap is identified then the correct drill size can be found online. Don't use a clearance drill size or you will wipe out the threads use the tap drill size to make the hole deeper, once the hole is deep enough a "bottoming" tap can be used or a standard tap (a bottoming tap has a shorter tip so the hole dosent need to be as deep if there is not enough material to drill into.
Sounds like the hole is badly threaded. You have several options:
There are thread repair kits like the Helicoil in which you install a wire effectively creating new threads.
There are repair kits in which you drill out the hold and tap into it a plug which bites into the sides of the hole and has a threaded center.
You could drill out the hole, thread it for the larger size and get a new rod threaded for that.
You could epoxy the original rod into the existing hole. Clean both sides first. (Kind of permanent).
You could try and fill the hole in with something like JB Weld and redrill and retap (possibly weak).