When you use a wye - delta motor starter it starts on wye and runs on delta. at what point does it switch is it based on RPM or time or current and how does the wye use less current to start the motor are the motors wound for wye or delta or both ?
The transition is based on time, I have NEVER seen it done with anything else. There are special little timers, called "Star-Delta Timers" that are frequently used for this, because there must be an "open" transition delay, where the motor circuit is open, no power, to prevent the connections from creating a short circuit. But it can also be done with off-the-shelf timers, it just usually takes two of them, or a timer and a relay with special contacts that are "early-make / late-break". This starter is usually ONLY used by OEMs who want the cheapest thing they can use and call it "reduced voltage", but the entire complicated process can cause SERIOUS issues and is the reason why I NEVER use Wye-Delta, but that's just a personal preference based on some very expensive lessons learned. YMMV.
The reason for the lower current is that when started, the motor windings are connected in a Wye (star) pattern referenced to each other, so the effective voltage across the windings is reduced by the sq. rt. of 3, 1.732, so 1/1.732 = .577, hence why we say the voltage is reduced to 58%. When you reduce voltage on an accelerating motor, the torque is reduced by the SQUARE of the voltage reduction, and current follows torque. So your torque and current are reduced to .58 squared = .3333, or 33% of what it normally would be. The transition from Wye to full Delta / Run must take place AFTER the motor gets to at last 80% speed, otherwise the entire exercise was pointless. So in most cases with an OEM, the designer knows the acceleration time and torque curves so they can properly set that timer. Otherwise it is a total crap shoot, hence most people do not retrofit Wye-Delta starters to existing machines. That's why very few electricians have ever worked on one (another reason why I never use them).
And finally, yes, the motor must be wound and terminals brought out in such a way as to allow this to be done.