5IMPENDING MOTION TO LEFTE1 1F FABGFCRFC ␪␪CRDFACCCONSIDER FORCE F A...

1-5

Impending motion to leftE1 1f fABGF

_cr

FC ␪␪

cr

DF

_acc

Consider force F at G, reactions at B and D. Extend lines of action for fully-developed fric-

tion D E and B E to find the point of concurrency at E for impending motion to the left. The

critical angle is θ cr . Resolve force F into components F acc and F _cr . F acc is related to mass and

acceleration. Pin accelerates to left for any angle 0 < θ < θ cr . When θ > θ cr , no magnitude

of F will move the pin.

Impending motion to rightE⬘ ⭈EdF⬘F

_cr

⬘ ␪⬘␪

cr

⬘CF⬘

acc

Consider force F at G, reactions at A and C. Extend lines of action for fully-developed fric-

tion AE and C E to find the point of concurrency at E for impending motion to the left. The

critical angle is θ _cr . Resolve force F into components F _acc and F _cr . F _acc is related to mass

and acceleration. Pin accelerates to right for any angle 0 < θ < θ _cr . When θ > θ _cr , no mag-

nitude of F will move the pin.

The intent of the question is to get the student to draw and understand the free body in

order to recognize what it teaches. The graphic approach accomplishes this quickly. It is im-

portant to point out that this understanding enables a mathematical model to be constructed,

and that there are two of them.

This is the simplest problem in mechanical engineering. Using it is a good way to begin a

course.

What is the role of pin diameter d?

Yes, changing the sense of F changes the response.