I am trying to get a left trochoid (R=1, d=2) of a left trochoid of a left trochoid. To do so, I try to establish a Frenet system and get a curve derived from the first one, that makes two turn when the first make one and then by the same way, i try to get a second curve that makes four turns when the second makes two and the first makes one.

But I can't get Mathematica do it. I must make a lot of mistakes, as I am not so familiar with Frenet and Mathematica.

I need to obtain equations for C1, C2 and C3 (see graphic attached). I think C1 is a left trochoïd, where R=1 and d=2 for example (elongated trochoÏd), C2 and C3 are the same, only perioding faster , C2 along C1, and C3 along C2 along C1.

Here is the code I made so far (see notebook)