If I understand correctly the key was to use the neutral Diff instead of diff in the definition of kin?
So I generalized what you said to a more complex problem which consists in buiding a single dof (degree of freedom) system equivalent, in a given sense, to a 2 dof system.
There still remain a little problem for more complex expressions of phi. as illustrated below
value(eval((Diff(Phi, t, t), Phi=psi))
/ d / d \\
k |--- |--- X||
\ dt \ dt //
value(eval(Diff(Phi, t, t), Phi=psi))
/ 2 \
|/ d / d \\ / d \ |
||--- |--- X|| cos(X) - |--- X| psi|
\\ dt \ dt // \ dt / /
How can I get rid of psi and have sin(X) instead?