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We have the following parallel robot architecture:

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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 $\dot{\xi_i}$?

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