I'm trying to model the planar dynamics of a mass travelling about an epitrochoidal path due to being rigidly attached to a planet gear that rotates about a sun gear. Assume the gears to be circles that rotate about each other with no slip for reasons of simplicity.
Both the sun and the planet can rotate. The input to the system is a torque on the planet carrier, pushing the planet parallel to its path about the sun. The output is the torque of the sun.
As i have very little experience with modelling dynamics, i don't know where to start. I was thinking that separating the problem into a fixed and inertial frame may be best, but i'm not sure.
How should i go about showing the output torque as a function of the input torque and the system constants (e.g. planet mass, sun diametre, etc.)?
I drew a quick diagram of the system as a simple model with circles for reference.
EDIT: To clarify, i've already solved the kinematics of the problem and have equations governing position, velocity, and acceleration for the mass according to the rotation, rotational velocity, and rotational velocity acceleration of the planet and Sun. What I want to find out is the dynamics. Specifically how torque on the planet carrier will affect torque on the sun.