Based on the contact mechanics,tribology and the pseudo static theory of angular contact bearing,the theoretical computational formulae of the friction torque of solid lubrication angular contact ball bearings are obtained. Based on this,the relationship between the friction torque of spacecraft driving mechanism shafting is studied and the theoretical analysis and experimental verification for the friction torque are presented after fully considering the boundary conditions on the shafting. The result shows that the friction torque of the angular contact coated solid lubricating film increases with the increase of axial preload and the friction torque of shafting increases with the increase of tightening torque after it reaches the critical value. Furthermore the theoretical and experimental values keep consistent. So theoretical computational formulae of friction torque based on pseudo static theory is suitable for the solid lubrication angular contact bearing and spacecraft driving mechanism shafting at low speed.