I want to make a device that I can place on a capacitive touch screen and it will start tapping the screen repeatedly. Is there any way to do this with the Arduino?
This can be done if you get an Arduino plus a servo controller that has a rig that controls a stylus. The stylus must be able to work with capacitive touch screen (not all do).
Look for Arduino Servo Controller shield
Yes, this is quite possible to do. Simply place a small piece of copper foil on the screen. Connecting the foil to ground will simulate a finger press. You can use an N-channel FET to switch the foil between connected and not connected. The gate of the FET goes to your microcontroller.
Copper foil method mentioned above the best way ... Or you can use small sized copper coins alternatively to the foils ... Connect it to the grnd pin of Arduino And regulate the connection with an npn transistor Whenever you give 5v to the base of NpN the ground is established in the coin and touch is simulated