Max Horizontal Force: Calculate with Cam Setup & Motor Torque

[jeffc0987]

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.

 

[jeffc0987]

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.