Delivering RPM from a fixed wheel to a moving wheel

I have spent the past few days thinking about a good way to get power/RPM from a fixed wheel delivered to a wheel that is able to move in a 2D plane relative to the fixed wheel. I am not too good at CAD, but I tried to make a schematic to make it easier to understand:

The orange "wheel" is fixed and is driven by a shaft. I want to get that RPM to the purple wheel in the middle. The purple wheel will be moved within the red frame (but not up/down). Some other constraint or actually simplification: I dont care if the RPM fluctuates during movement, so it can get lower/higher if the purple wheel is moving. Also the position of the orange wheel can be changed as needed, but once it is attached, it can no longer move. The orange wheel can be outside of the red frame too. The purple wheel drives a tool that needs to work against some resistance (say drilling through wood).

I was thinking about using a belt or a chain with a tensioner. My idea was to install another wheel either diagonally opposite of the orange wheel or at the bottom of the frame that is attached to spring loaded tensioner, but I failed to figure out how long my belt would have to be and how to make sure there is always enough tension to make sure the purple wheel gets enough torque to be able to deliver enough force to the tool it drives.

Are there some well known patterns for my problem? Or what would be a good way to tackle that problem?