Toss a length of steel chain over an exposed beam in your basement or attic. Use a steel chain coupling link to close the two ends of the chain into a loop. The chain loop should hang down far enough so that you can reach it when you extend your arms upward as high as you can.
Install a second length of chain about 3 feet to one side of the first in the same manner. Test the chains by hanging on each one to ensure strength.
Install steel mounting plates with 1 1/2-inch female threads to each end of a 4-foot length of steel pipe with male threads at each end as a safety measure. Tighten the plates into the ends of the pipe by hand and use a wrench to finish the job. Slide the pipe through the two chain loops so it is centered evenly. Test the pull-up bar.