need a help plz

[XL-power]

I have a mechanism for my robot,

The mechanism is to move a shaft of the (x-12) motor inside a shaft of the pulley by a solenoid,
And the motor will rotate a pulley for a certain time then the motor will move back to its first position, at this time the pulley will keep moving, then the motor will repeat its movement and again rotate the pulley, I do this in order to keep the pulley to move all the time,
My problem is that how I attached the shaft of the motor to the shaft of the pulley for a certain time,
And then release it, (of course the motor will repeat this motion so I don’t need to loss the connection place between both shafts), and if the is any other suggestion to do my mechanism
My mechanism is in the attachment

 

[KMoffett]

The logical mechanism would be an electro-mechanical "clutch". But, why not leave the motor attached to the pulley and just connect and disconnect power to the motor. Most motors will "freewheel" with no power applied. It might help if you explained the purpose of this system.

Ken