How can I move a part along a CylindricalConstraint by draging your cursor?

I am trying to make a part with a ClickDetector move along a CylindricalConstraint when a player holds down there mouse on the part and moves it. I want to know what I would need to script and how to implement it.

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You probably want a PrismaticConstraint, with the ActuatorType set to Servo.
Iā€™m not sure how to read the Mouse position from the screen location to change the PrismaticConstraint.TargetPosition, but you may be able to put a clickdetector in a transparent parts on either side of the moving part and get the movement input direction from those.