# Formulas for calculating the passive joints angular velocities

We have the following parallel robot architecture:

Positions of the vectors $$u_i, v_i, w_i$$, the angles $$\theta_i$$, angular velocity $$\dot{\theta_i}$$ and the Jacobian $$J$$, that mapping vector of angular velocities $$[\dot{\theta_1},\dot{\theta_2},\dot{\theta_3}]$$ into the angular velocity $$[\omega_x,\omega_y,\omega_z]$$ of the platform are known. Is it possible, using these parameters, to calculate the angular velocities of passive joints $$\dot{\psi_i}$$ and $$\dot{\xi_i}$$?