Welcome to the forum, Jim.
The solution will depend on the OEM of the router. Over the years they have been supplied by several different manufacturers under the Craftsman name to Sears. However, first thoughts are right there with Stick and Andy. Sounds like a tightness problem. I had one that had a hairline crack in the "friction band", for lack of a better descriptor. It wasn't visible until it was under tension and of course the motor walked in the base.
Hi, sorry I missed you. I have gone to find myself, but if I return before I get back, please ask me to wait.
Nothing ever gets built on schedule or within budget.
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