Charging issue 68 barracuda

I'll add some pictures since its hard to photograph the back of an alternator on the engine.

In no particular order:
Voltage Regulator's fusible links shown here.
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from 1968 Dodge Service Manual

Those links melt if the rotor draws too much current, or what probably happened, there is a short to ground.
If the green wire touches a ground while the key is in Run position, one or both of those links will melt.
More about that here: Blowing voltage regulators

Alternators with two field terminals like this 'square back'
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..need one of them grounded to work in a pre-70 system, as shown with this 'round back'.
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A pre-1970 'round back' will have one of the brushes grounded to the housing, and so only have one field terminal.
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In a '68 the regulator controls the current feeding the rotor (aka field).
Field is short for Electro-magnetic field. Electrical current through rotor's windings makes a magnetic field.
Alternators create electric power by spinning that magnetic field and inducing current in fixed set of wire windings. The regulator controls how strong the magnetic field becomes by quickly restricting and letting current through as needed.

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edit: An alternator should turn easily when there's no field. So spinning freely is not a problem.