Name: screw jack force and friction analysis
Uploaded: 2023-09-22T11:49:29.000Z
Duration: 1 min 21 s
Channel: JoVE

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.

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.
<img alt="Static equilibrium diagram, inclined plane, force vectors, angle θ, frictional force F&lt;sub&gt;s&lt;/sub&gt;." src="/files/ftp_upload/14319/14319_PT_Figure_1v2.svg" style="text-align: center; height: 300px;" data-altupdatedat="1761830439000" data-alt="Figure 1">
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.
<img alt="static equilibrium formula, ϕs=tan⁻¹μs, trigonometric relation, diagram" src="/files/ftp_upload/14319/14319_PT_Equation_1.png" style="text-align: center; height: 18px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
With this information, apply the equilibrium equations for the forces along the horizontal and vertical axes.
<img alt="Timeline diagram of a musical piece with notes and rests; sheet music reading analysis." src="/files/ftp_upload/14319/14319_PT_Equation_2v2.svg" style="text-align: center; height: 28px;" data-altupdatedat="1761830439000" data-alt="Equation 2">
<img alt="Static equilibrium diagram; ΣFx=0; illustrates balanced forces setup with labeled vectors." src="/files/ftp_upload/14319/14319_PT_Equation_3v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation 3">
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.
<img alt="Static equilibrium concept with human figures on a seesaw diagram, illustrating balance principles." src="/files/ftp_upload/14319/14319_PT_Equation_4v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation 4">
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.

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 ...

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Friction

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screw jack force and friction analysis

A square-threaded screw jack lifts heavy loads by turning handle force into a twisting moment. Its upward motion depends on overcoming static friction between the screw threads and the jack. To study this motion, the thread can be treated as if it were a block on the groove of the jack after the thread is completely unraveled.

A free-body diagram helps show the forces acting on this simplified system. The force at the handle creates a horizontal force that pushes the movable thread up the fixed incline of the jack thread. At the same time, the load acts downward as an axial force on the thread.

The groove of the jack also pushes back on the screw thread with a reaction force. That reaction force has both normal and frictional parts, and they are linked by the coefficient of friction. The angle of static friction for impending motion is found by taking the inverse tangent of the coefficient of friction.

With these force relationships, equilibrium equations can be written for the horizontal and vertical directions. These equations describe how the applied force, the reaction forces, and the motion of the screw jack are connected. Rearranging the equations in terms of the reaction force and setting them equal leads to the moment equilibrium equation for upward impending motion.

Solving that moment equilibrium equation gives the minimum force needed at the handle to start the screw jack moving upward. This result is useful for understanding how the jack is designed and operated. It also helps the jack lift heavy loads or apply large forces when needed.

Screw Jack Force and Friction Analysis

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key terms and concepts

Explore how a square-threaded screw jack uses force, friction, and equilibrium equations to lift loads and find the minimum handle force needed.

Screw Jack Force and Friction Analysis | JoVE K12

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Screw Jack Force and Friction Analysis

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