Calculate torque for a cam

Does this help?

Take the [Angle] that's most prejudicial to opposing F, and consider the lever arm to the camshaft centre. It looks like my screen grab is the worst case scenario, but with the changing lever arm to point of contact, you should really repeat this for sever angles of cam rotation. I'm sure there's software for this, but it can be done graphically by hand by plotting a surface development of the cam profile against shaft rotation, say 0 - 180 degrees. Repeat the calculation every 15 degrees and Fanny's your Aunt.

One thing. You can't possibly have a fully algebraic solution unless you have an equation for the profile of the cam as you won't be able to determine [Angle] other than by numerical /graphical means. I might be tempted to scan the cam profile and use a graphics package to segment and develop the cam profile. Or use a rule.