Formula to calculate force as a function of angle

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SUMMARY

The formula to calculate the force required to push a rotating arm attached to a shaft is derived from the principles of torque and geometry. Given a load of 1 Nm torque and a rotating arm width of 1 cm, the force can be expressed as a function of the angle of the shaft, which rotates from -45 to +45 degrees. At 0 degrees, the distance from the shaft center to the closest point of contact is 3 cm, necessitating a hyperbolic function to represent the force as the angle changes. A diagram illustrating these relationships is essential for clarity.

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What formula can I use to calculate the force I need to apply to a sliding arm that makes a point contact along the edge of a rotating arm attached to a shaft driving a load in order to push the rotating arm to rotate the shaft? The rotating arm is 1 cm wide. The load at the shaft is 1 Nm torque. The shaft rotates from -45 through +45 degrees. The sliding arm is perpendicular to the edge of the rotating arm when the shaft is at 0 degrees. At that angle, the distance between the center of the shaft and the point along the center line of the rotating arm closest to the point of contact between the two arms is 3 cm. I would like to calculate force as a function of the angle of the shaft. I imagine it is some type of hyperbolic function offset by ½ the width of the rotating arm. Thanks!
 
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A diagram is needed.
 

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