A common easily reversed type of single phase motor has two identical windings, mechanically displaced.
The windings are wire in a wye arrangement, connected together at one end and with a starting capacitor across the free ends of the windings.
One wire goes to the common point and one wire goes to each end of the capacitor.
When either winding is energized directly the other winding is in series with the capacitor and becomes the starting winding.
While this motor could be controlled by a pair of solid state relays, using a pair of interlocked, single pole contactors or switches allows a safety interlock.
While many dual voltage conventional single phase motors may be reversed with only three wires, this is only possible on the higher voltage setting.
Reversing when the lower voltage is used requires four wires.
Bill
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Jimmy Carter