Looks like universal motors are built just like a DC motor. Two series wound coils connected to the commutators so that no matter the polarity of the current, the torque is still unidirectional.
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I pulled this image from this article that gives a pretty concise description of Universal Motors:
http://www.electricaleasy.com/2014/02/universal-motor-construction-working.html
I added some polarity markings so you can see that when the polarity shifts, the armature will still be pushed in a clockwise direction.
In this diagram, the top part where the commutator connects is always repelled by the like charged N pole and the attracted to the S pole, just like a DC motor. This article does point out that when it operates on AC, there is a performance loss due to reactance, which doesn't come into play when a DC current is applied