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Question:

can an electric motor lock its position?

and act as a brake or actuator? I realize an electric motor can act as a brake but can its position be locked solid?

Answer:

Yes. An AC induction motor can be locked by introducing a sufficient dc current of proper polarity across two phases . This is a common way of preventing e.g.fan motors from windmilling backwards during idle periods on ,say. cooling towers. This application of DC current is also used as a braking technique for induction motors.
not an ordinary one. A stepper motor can. Blocking movement with an ordinary motor, normally possible only if gearing is involved and a delicate adjustment of forces/current is done requires a fairly high current flow and can burn out the stalled motor.
Stepping motors have a holding torque. Otherwise you are hoping for the gears (think worm gear) to do it. There are motors with a brake operated by a solenoid. Take note of some electric wheel chairs, but also gear drives with solenoid brake are in the industrial market. Some speed controllers have an output to operate this brake.
In some inverter controlled cases, the VFD controller can hold 0 speed using various methods such as a DC hold, or plain speed control. Locked solid is relative to the the slow speed characteristics of the motor.

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