It is worth running a search through PPRuNe on Vmcg and Vmc/Vmca as the subject has been canvassed numerous times.
At the end of the day, there is no necessary connection between the two figures for a given aircraft and the "arm to the rudder" argument is far too simplistic to be of any real value.
It is important to keep in mind that both values, as quoted in the AFM, are certification figures designed to put a line in the sand for handling qualities and to give the pilot some protection for most, if not all, likely real world cases.
The actual figures on the day (if one were to run the tests for the specific conditions) generally will be lower than the published figures.
Real world Vmcg, in particular, is very sensitive to crosswind, which is not addressed in most certification cases.
Real world Vmca is very sensitive to bank angle, where the certification figure normally is determined for the usual 5 degrees into the live side.
Both are very sensitive to actual cg and thrust output.