This article is from the Chrysler-Plymouth-Dodge FAQ, by Dr. David Zatz with numerous contributions by others.
(e-mail address removed).net responds to a complaint of shimmy in a 96,000
mile 1986 Dodge Aries from 35-45 mph under accleration. He said that the
inner CV joint housing on the passenger side axle is worn. Probably easiest
repair is to replace passenger side axle with rebuilt unit. There is a
possiblity of it being in the drivers axle. But it is more common in the
passenger axle based on your complaint.