Greetings Digesters, I thought I'd comment on this subject in general,
though I am not familiar with any specific motors you use.
Induction motors have to be given a direction if only during the
starting process. 3-phase motors automatically get this according to
the rotation of the phases, so to reverse the direction of a 3-phase
motor you just swap any two phases over.
With single-phase motors an artificially created second phase, either
lagging or leading the first phase, must be introduced. One way to do
this is to have a second field winding placed 90 degrees from the first
winding and introducing a phase shift in the current by means of a
capacitor in series with it. Sometimes these windings are switched off
by means of a centrifugal switch once the motor has accelerated up to
speed, but sometimes they remain on continuously. As Don says,
reversing one of these pairs of connections will reverse the motor.
Another type of induction motor generally used in small motors
(e.g., record players, electric fans, etc.) uses the shaded pole motor.
Often they cannot be reversed, but they can if they are manufactured
symmetrically. A shaded pole motor only has a single phase winding, but
to one side of the main poles are another small pair of poles which
have thick copper shorted turns on them. These are the "shaded poles".
As the main poles magnetic flux rises, the flux in the shaded poles
follow, but lagged due to the shorted turn inductor.
Sometimes these motors can be reversed simply by putting the "middle
block of the sandwich", which is the field assembly, in back-to-front
within the bearing housings. It's like reassembling the motor with the
rotor shaft poking out the other end of the motor.