Max Horizontal Force: Calculate with Cam Setup & Motor Torque

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The discussion centers on calculating the maximum horizontal force produced by a cam setup on a pushrod, with known motor torque and RPM while ignoring friction. The user reports that testing indicates the setup can generate approximately 150 pounds of force using 84 lb*in of torque, which seems excessively high. There is confusion regarding the expected force in the X direction, as it should theoretically be less than the total torque based on the distance from the torque application point to the pushrod contact point. The user clarifies that the angle of rotation should be measured from the torque application center, not the cam center. The inquiry seeks insights into whether the observed force output aligns with expected mechanical principles.
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I am having to figure out the maximum horizontal force our cam is able to produce on a pushrod that slides back and forth through bushings. I have attached a picture showing the basic setup.

The motor torque, and RPM's are known and for this estimate I am ignoring frictional forces.

I'm not sure if I'm making this out to be way more complicated than it should be, any help would be appreciated.
 

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I'm still having trouble with this problem because testing shows this setup (picture attached) can produce up to ~150lb. of force using 84 lb*in of torque. This seems way too high--shouldn't it only be able to produce near that amount of force in the X direction when phi=90 and the entire force from the torque is directed that way?

I would have assumed the force in the X direction would be a fraction of the total torque based on the distance between the center and where the cam touches the pushrod.

Any thoughts?
[EDIT]
the angle of rotation phi should be off of the center of where the torque is applied, not the center of the cam.
 

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