We can use the Recursive Newton-Euler Algorithm to solve the dynamic problems of open chains manipulator, but how about the Cardan-joint manipulator?
In order to solve the inverse dynamics of this model, my idea is to set the virtual link between $\theta_1$(assume rotation axis is z-axis) and $\theta_2$(rotation around y-axis), and then the problems become open chains, so in forwarding iterations of Newton-Euler Algorithm, the velocity of $\theta_1$ can transfer to the velocity of $\theta_2$ by virtual link, and finally, the wrench of end-effector can be transfer by backward iterations. But the inertia matrix of virtual link is
diag([0,0,0,0,0,0]), is my idea correct?
I didn't know how to transfer the velocity and wrench between $\theta_1$ and $\theta_2$ in the Recursive Newton-Euler Algorithm Framework, Or maybe I should use another method to build the dynamics of this model.