Upward Impending Motion

Consider a square-threaded screw jack. Applying a force at its handle results in a torsional moment, which causes upward impending motion of the screw. This is achieved by overcoming the static friction between the threads of the screw and the jack.

Consider the completely unraveled thread as a block in contact with the groove of the jack and draw its free-body diagram.

The torsional moment produces a horizontal force that pushes the movable thread up the fixed incline of the jack thread, and the load applies an axial force on the thread.

The groove exerts a reaction force on the screw thread. This reaction has both normal and frictional components, which are related through the coefficient of friction.

The angle of static friction for impending motion equals the tan inverse of the coefficient of friction.

Now, apply the equilibrium equations for the forces along the horizontal and vertical axes.

Rearranging the equations in terms of the reaction force and equating them determines the moment equilibrium equation for the upward impending motion.