If you are uncertain as to which brand and model spindle you have, compare your spindle to these pictures, listed in order of probability:

HSD Fixed collet spindle

HSD Toolchanging Spindle

Columbo Toolchanging Spindle

Kress Spindle (common on smaller machines, Patriots, 3024s, etc.)

Once you have found your spindle, examine the spindle nameplate for more information which may become necessary.