Trochoidal Tool Path

Hi all I am trying to model elliptical vibration cutting in Abaqus and need to define boundary conditions such that the tool can follow a trochoidal path across the workpiece. I tried to define a displacement BC for the y motion and another for the z motion, but it seems they contradict each other, resulting in no motion. 

I have attached an image showing the tool-path I want to achieve (side view).

Does anyone know how to apply more than one displacement BC to a single part, such that the tool can displace in the y direction AND the z direction simultaneously?


Cheers!