How can I make a player controlled sprite move on a fixed path?

I have a pre-defined non-linear path. I want the player to be able to slide the circle using his thumb to move it along the path. So when the circle is on a horizontal part of the path the player can only slide left and right and when the circle is on the vertical part of the path the player can only slide it up and down. At the corners players can drag in 2 axis. Please help!!! I am trying to understand what approach to take. Should I use Itween or something else? ![alt text][1] Hope this is clear [1]: /storage/temp/46787-reference.png