I recently tried to find a way to do this. I'm not the only one looking so hopefully this helps someone else. My tree happens to be wide enough that not a lot of extra thought had to go into it. I also wanted to avoid digging holes and using concrete. Items needed are 2 x 4, 2 x 6, drill, screws, bar for pull-ups (desired diameter, mine is 1.75" because that's what was in the yard from an old chain link fence.), and a drill bit matching the diameter of the bar. The TRX type straps are of course optional but are simply ratchet straps, pvc pipe, rope, and a carabiner.
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Step 1: Cut Wood
Cut a 2 x 6 into 2 boards of desired length. Mine are 5'. Also a 2 x 4 to desired length for support. Mine are 4' with 45 degree angles against the main posts. Go ahead and drill the holes your bar will be going through.
Step 2: Step 2
This is much easier with 2 people but possible with one. Ratchet straps help. Screw the first 2 x 6 to one side of the tree to your desired height. Put the bar through the hole. This is where 2 people comes in handy. Put the other end of the bar through the 2nd 2 x 6 and screw it to the other side.
Step 3: Step 3- Attaching the Support
Take the 2 x 4's one at a time and attach them to the 2 x 6's and the sides of the tree. It might be important to note that it's not important for the wood to be level so much as the bar itself is level. Make sure to use enough screws to ensure the whole thing is secure. 4-5 each time in the tree should do.