I tried posting this on a similar post but didn't get a response:

I'm trying a similar thing but the intermediate voltages (in my case Va, and Vb) are not being removed.  Here are my equations:

The attached file is an example of a set of equations that define a gearbox composed of 4 planetary gearsets. The first 4 equations are the kinematic constraints. Where "r" indicates the size the sun or ring gear and "w" is the speed of the sun, ring, or carrier. The next 4 equations simply define new parameters (R_n) for the ratio between the size of the ring and sun gears. The last 5 equations define how these gears are connected. My question is how can I (or is it possible) to complete this worksheet in a generic way to solve for the speeds of any of the nodes in terms of some defined list of nodes and the parameterized gearbox sizes? In this example, there are 3 degrees of freedom so I might wish to solve for w[R3] (a dependent variable) in terms of w[R1], w[S2], w[S4] (independent variables), and all the parameters. The generic part comes from needing to be able to change the last 5 equations (including adding or subtracting equations) and perhaps the list of dependent and independent variables.