8.9:
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.
8.9:
Upward Impending Motion
A square-threaded screw jack is a mechanical device widely used for lifting heavy loads or applying considerable force. Its operation is based on converting the force applied at its handle into a torsional moment, causing the upward impending motion of the screw. This movement is accomplished by overcoming the static friction between the threads of the screw and the jack.
To better comprehend how a screw jack functions, consider the completely unraveled thread as a block in contact with the groove of the jack. By drawing a free-body diagram of this scenario, we can analyze the forces acting on the system.
The torsional moment produced by the applied force at the handle generates a horizontal force that pushes the movable thread up the fixed incline of the jack thread. Simultaneously, the load being lifted applies an axial force on the thread.
The groove of the jack exerts a reaction force on the screw thread. This reaction force comprises both normal and frictional components, which are related through the coefficient of friction. The angle of static friction for impending motion can be determined by finding the inverse tangent of the coefficient of friction.
With this information, apply the equilibrium equations for the forces along the horizontal and vertical axes.
These equations allow the analysis of the relationship between the applied force, the reaction forces, and the resulting motion of the screw jack.
Rearranging the equations in terms of the reaction force and equating them provides the moment equilibrium equation for the upward impending motion.
By solving this moment equilibrium equation, one can determine the minimum force required at the handle to initiate the upward motion of the screw jack. This calculation enables the optimization of the design and operation of the screw jack for various applications, ensuring that it can effectively lift heavy loads or apply large forces as needed.
Suggested Reading
- Hibbeler, R.C. (2016). Engineering Mechanics: Statics. Fourteenth Edition, New Jersey: Pearson. Pp. 432-433.
- Meriam, J.L., Kraige, L.G. and Bolten, J.N.(2016). Engineering Mechanics: Statics and Dynamics. Eighth Edition, Singapore: John Wiley & Sons. Pp. 355-356.
- Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. and Self, B.P. (2016). Vector Mechanics For Engineers. Eleventh Edition, New York: McGraw-Hill Education. Pp. 451.