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A three phase machine, instead of having six terminals, two for each slip ring, has only four terminals. Because the starting point of all the three coils have a common junction which is usually earthed and the other three coils are connected to three separate terminals on the machine.
What does the starting point mean here? And how do we have 4 terminals when we are having six slip rings. Terminal from each slip ring would make it 6 terminals.
The machine is wired to have 3 winding at \$ 120^o \$ spacings, physically. If they are all driven by the right phase with the current flowing in the consistent pattern then the machine will operate correctly. This access to both sides of the windings allow you to wire up the machine to be Delta, Wye, reverse direction Delta, reverse direction Wye.
If you take all the same polarity winding pairs and join them together you will wire the winding as a Wye configuration which has 4 terminals with a common neutral. Your choice of which slip rings are wired together and which phases go to which matched windings will determine the which way the motor rotates. If you reverse one of the windings instead of having 0, 120, 240, you may end up with 120,180,240 degrees which will not run, and might burn.
You don't say if you have the winding diagram or if there is any numbering on a name plate. You can find related start and end of windings with a continuity tester and you can determine relationships between phases with a "flick test".
Even if you start with knowing which winding pairs belong together there are 8 combinations of phase wirings to get a Wye configuration and only 2 will work (but in opposite rotation). for each of these there are 4 wirings of the power to the phases to bring to a total of 32 different combinations of which only 4 will work. And if you wire it wrong this could be dangerous given the power levels of some of these motors. If you don't understand which of the pairs of slip rings belong together the problem gets even deeper.
