What you are describing, is what's known as a servo-motor. A servo-motor uses feedback, usually from a pulse generator, to let the control circuitry "know" the exact position and speed of the motor. Of course this usually requires an IC based designed circuit to perform this.

Depending on what you are driving with the motor, you may be able to create a micro-switch based logic circuit to stop at the same point each time, similar to something like old-style ignition points. Something like a notch that the micro-switch could drop into and stop the motor. The next "on" signal would then restart the process.

yosemitebill:
thank you for your reply:
I have come across another site where I have gotten an answer.
I know about servos etc but didn't want anything that sophicated mainly becasue of the controler requirements and the cost. The solution I now have uses a flipflop and other electronic components which will be easy for me to build. Thanks again for your input.

Regards,
Richard