Thank you, Skip.
I assumed that screw was just holding the handle and peg together! I tightened that screw and there is plenty of friction now.
Thanks!!

Try tightening the screw on the end of the peg. If that doesn't work, disassemble the tuning machine by remove the screw and carefully removing the handle ant the washers. The plastic disk can then be roughed up with a piece of sand paper to increase friction. Reassemble and adjust.

I am having a problem with my Lynn McSpadden mountain dulcimer model M-12S. One of the high unison string pegs will not hold the pitch. I tune it up, the peg turns and lowers pitch immediately. Is there a way to tighten these pegs? I have attached picture of peg box. Thanks!