In order to study constraints imposed on kinematics of the Crab pulsar's jet we consider motion of particles along co-rotating field lines in the magnetosphere of the Crab pulsar. It is shown that particles following the co-rotating magnetic field lines may attain velocities close to observable values. In particular, we demonstrate that if the magnetic field lines are within the light cylinder, the maximum value of the velocity component parallel to the rotation axis is limited by 0.5c. This result in the context of the X-ray observations performed by Chandra X-ray Observatory seems to be quite indicative and useful to estimate the density of field lines inside the jet. Considering the three-dimensional (3D) field lines crossing the light cylinder, we found that for explaining the force-free regime of outflows the magnetic field lines must asymptotically tend to the Archimedes' spiral configuration. It is also shown that the 3D case may explain the observed jet velocity for appropriately chosen parameters of magnetic field lines.