# Self Locking Brake Question

I've been staring at this problem for statics for quite a while now and I just don't understand it. The question states:

"The brake is to be designed to be self locking, that is, it will not rotate when no load P is applied to it when the disk is subjected to a clockwise couple moment $$M_0$$.

It then say to determine the distance $$d$$ that allows this to happen, assuming that the coefficient for static friction at $$B$$ is $$\mu_s = 0.44$$.

I don't understand at all how the length of $$d$$ correlates to anything, especially since a moment about $$A$$ from $$P$$ would not be affected by it at all. I know that I need to have some sort of FBD, but my mind is just blanking right now. If someone could provide even just that I would be very grateful. Thanks!

• it should probably say determine the minimum distance Nov 25, 2023 at 20:06
• That is to say "The disk will not rotate" even when no load is applied at P., which is to say, the disk will not rotate unless the brake is deliberately unloaded at P, which is to say, the brake is self-locking (if d is big enough) Nov 26, 2023 at 22:31

The moment imparts horizontal force F at the contact with the brake. $$F=M/R=M/1=M$$ This force requires a friction horizontal force in the opposite direction to lock the wheel.

Let's call the angle between AB and horizon $$\theta$$. $$F_{friction}= F/0.44=2.27F$$

$$cos(\theta)=2.27 F,$$ $$\theta= arccos 2.27 F$$ We calculate hypotenuse AB by the $$secant\theta$$ formula.

$$d=AB*sin\theta$$

I don't understand at all how the length of d correlates to anything, especially since a moment about A from P would not be affected by it at all.

I offer the modified image to prompt some further thought.

The brake is to be designed to be self locking, that is, it will not rotate when no load P is applied to it when the disk is subjected to a clockwise couple moment M0.

Have you transcribed the bold part correctly. It seems oddly worded.

• Yeah I copy-pasted the exact text from my homework... I'm glad that I'm not the only one confused on the wording lol Nov 25, 2023 at 16:55

The rotating wheel with torque $$M_0$$ will impart a force equal to $$\frac{M_0}{r}$$, where r is the radius of the wheel.
Upon contact with the braking bar, the wheel will geneare a horizontal force with direction and towards the right.

This means it generates a CCW rotation on the bar which is proportional to d. The greater the distance d, the greater the moment about point A.

Additionally as the moment increases the vertical reaction between the rotating wheel and the bar increases (thus in turn increasing the maximum friction force between the two). If you don't have a large enough d, then vertical reaction is not large enough to generate a friction force large enough to block the wheel.

In order to solve this you need to write down a) the relationship between the force generated by the torque and the maximum friction force b) the equilibrium of bending moments about A.

Another hint: Since its a self locking brake the P force can be zero, and can be neglected in this problem.

The result should provide you minimum distance d which should be a function of

• the static coefficient and
• L: the horizontal distance between point A and the point of contact