How can I use Scala's cake pattern to implement robot legs?

My development makes extensive use of the robot legs binding problem. I know how to solve it with PrivateModule in Guice, but it isn't clear how this would be done with Scala's cake pattern.

Could someone explain how this would be done, ideally with a concrete example based off of Jonas Boner's coffee example at the end of his blog post? Maybe with a warmer that could be configured for left and right sides, injected with an orientation and a def isRightSide?