Cycloidal mechanisms

I've done work in the past with cycloidal drive systems both in industry and at home (hobby 3D printing and FIRST Robotics) and I understand how they operate in a single stage and double stage format including which frame of reference you 'fix' relative to the others.

Yesterday I came across this (YouTube link below) and can't quite seem to wrap my head around the motion and the gear ratios produced.

I get the example they used of stacked 13:1 stages creating a 169:1 and even recreated it at home in SolidWorks with stacked 10:1s for a 100:1 stage. What I don't get is the math that determines the output when you get away from the 'perfect squares', for example I made a model with a 10:1 input with a 5 lobe (6 pins) output bonded to it. This configuration gave me the expected 10:1 rotation of the disc body I am used to with a single stage but the output disc put in an additional 1.2:1 for a total of 12:1 from input to out.

Does anyone have any documentation or examples for the math that defined this output stage being bonded to the input side disc? All of the two stage material I've found is done by feeding the already concentric output of one stage into the next.

Again see below for the example I am trying to work with.

Thanks!

https://youtu.be/Eds48L4cJjM

submitted by /u/Zeplus_88
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