How do you know a motor is ok or not? How do you have a preliminary idea about a non-functioning/ malfunctioning motor? Especially, if you don't want to remove the motor from its mounting?
There are a couple of preliminary tests you could do.
First, try finding the ground resistence of the motor. Put the multi-meter in kilo-ohms and check the resistence between the motor body(or your metallic connector box) and the terminals of the motor. It should show a fairly high value- could be 100 K-ohms or above. Else, there is a ground leakage- this is probably the reason why you get shock (if you're getting!).
Next, you could find the resistance of the winding. Connect between the terminals. (I don't know the type of motor used). Across the motor windings you should get a low finite value- could be a couple of hundred ohms- or less.
Both the ohm values depend on the rating and type of the motor. What I've specified are indicative only. For example, for a large motor, the winding resistance could be tens ohms or less. For smaller motors, it could be a hundred ohms or so.
Now, you have to go to the motor!
I feel it is always better to check the motor at the winding terminals rather than the cable end. Ideally, this should not matter- but take into consideration the working environment - if it's moist and salty, I guess there is a probability that the insulation can become bad, and over many feet of cable length, there could be so much leakage if the cabling is old.
I've come across many instances where there is a cable fault. So, if there is a bad cable, we may be suspecting that the poor motor is guilty if we don't check the motor at the winding terminals.
Hence what we usually do is:
1. Disconnect the conductors from the drive control end, and megger between cables and each cable to ground. Between cables, it should give almost equal value, in the range of 1-3 ohms for medium rating motors and higher for smaller motors. Between each conductor and ground, megger value should be relatively high, above 100 Kohms or above. (More exact values will be specified by the manufacturer; it will also depend on the working environment and type of motor enclosure)
2. If there is any problem, go to the motor, disconnect the cable - thus isolate the motor- and check the motor terminals again. Now, we can identify the problem to either the cable or the motor.