Maximum allowable value of a force

[Mohmmad Maaitah]

Homework Statement

Obtain a formula for the maximum permissible force
P(allow) based upon an allowable compressive stress in
the connecting rod.

Relevant Equations

None

This really confused how is it that when Cosα is minimum P is maximum? shouldn't it be the oppose?
Problem statement (IGNORE):

The piston in an engine is attached to a
connecting rod AB, which in turn is connected to a crank arm
BC (see figure). The piston slides without friction in a cylinder
and is subjected to a force P (assumed to be constant) while
moving to the right in the figure. The connecting rod, which has
diameter d and length L, is attached at both ends by pins. The
crank arm rotates about the axle at C with the pin at B moving
in a circle of radius R. The axle at C, which is supported by
bearings, exerts a resisting moment M against the crank arm

SOLUTION (MANUAL):
The maximun allowable force P occurs when cos(α) has its
smallest value, which means that α has its largest value.

 

[berkeman]

(just a thought, but...) When does the resisting moment M exert the most force on the connecting rod?

 

[haruspex]

(just a thought, but...) When does the resisting moment M exert the most force on the connecting rod?

There is also compression in the crank arm.

This really confused how is it that when Cosα is minimum P is maximum? shouldn't it be the oppose?

P does not have a maximum or minimum during operation; we are told it is constant. We are asked for the maximum allowable value of that constant. For that, we need to find the maximum compression in the rod for a given P.
If we take the piston to be massless and the compression in the rod is $F$, what equation relates $P, F$ and $\alpha$?

 

[Lnewqban]

This really confused how is it that when Cosα is minimum P is maximum? shouldn't it be the oppose?

Could you explain your reasoning?

 

[haruspex]

Could you explain your reasoning?

I think one can guess what @Mohmmad Maaitah 's reasoning is. If you take F as given, P is maximised when $\cos(\alpha)$ is maximised. But that is not the question.

 

[Lnewqban]