How does a single pivot side-pull caliper bicycle brake work?

Question

How does a single pivot side-pull caliper bicycle brake work? The brake cable only pulls on one of the arms, so what is causing the force on the other arm? I understand that it is a normal force due to the cable housing, but why is this force developed?

EDIT

I'll elaborate on my questions a bit. Let $A$ be the point where the cable is attached, $B$ be the point where the housing pushes on the other arm, $P$ be the point of pivot, $C$ be the point where the first arm touches the rim and $D$ be the point where the second arm touches the rim. $APC$ is then the arm pulled on by the cable and $BPD$ is the arm potentially pushed by the housing.

Let's say the cable pulls at $A$ with some tension force $T$. A normal force $N$ from the wheel must then push on $C$, in order for the torque with respect to $P$ to be zero. We have $N = (|AP|_x/|CP|_yS) $, if $x$ and $y$ are in the horizontal and vertical direction respectively, and $T$ is vertical and $N$ horizontal.

The force $N$ gives a lateral force on the rim and a torque on the wheel. They could be balanced by a normal force of the same magnitude at the other brakepad. By symmetry, $B$ would then have to be pushed by a force of magnitude $T$.

But couldn't they also be balanced at the hub? Does it have to do with the construction of the wheel, i.e. because it's spoked? If the wheel were in the form of a solid cylinder (which would of course be very impractical!), would the situation be different?

^{image source wikipedia}

Answer 1

Inside The pivot there is a spring holding the 2 arms apart. This adds a torque to the arm and keeps the cable under tension.

In normal state the brake pads are not in contact with the rim.

When the cyclist starts pulling $A$ and $B$ will start to move together until one of the pads contacts the rim. This will then prevent that arm from moving further and apply a little bit of drag on the rim.

Further pulling on the cable will still try and move the pads together but not only 1 arm can move because the other is blocked by the rim.

Once both pads are in contact with the rim any tension that isn't compensated for by the spring will put force on the pads squeezing the rim and applying the breaking force.

The force applied by both brakepads don't need to be equal. The arms are very rarely perfectly centered and balanced and the brake line will also apply a bit of force putting things further off balance. Any sideways force can indeed be compensated for by the hub.

If you look at a bicycle wheel head-on you will see that where the spokes are attached to the hub is much wider than the single line where they are attached on the rim. This creates a triangle shape that can compensate for the sideways force on the wheel and prevents buckling in turns. Any sideways force on the rim will result in a upwards force on one side of the hub and a downwards force on the other.

When dealing with force diagrams you have to take into account all forces which can be quite the rabbit hole in complex situations.

Answer 2

The brake cable doesn't apply a force to the arms. It reduces the size of the gap between the arms, and therefore between the two brake pads.

The cyclist can only to apply a force to the brake lever because the wheel rim prevents the arms moving together. If the bike wheel is removed, it requires very little force to pull the brake lever as far as it can move.

Since the brake assembly can pivot around the point where it is attached to the bike frame, by symmetry the force applied to brake pad on each side will be equal and opposite. The two arms and the pivot form a symmetrical lever arrangement.

Answer 3

I taught about it a lot and I think I have come to an answer . the housing of the cable is actually a tube, that tube pushes down the lever . suppose the pad break from the other side of the wheel is already pressing the rim so now when you pull- the magic starts to happen - the lever from the side of the cable is pushed down by the cablehouse . now when you squeeze the break - where does the cable come from ? (the cable that is attached to the lever doesn't move, so how come you succeed pulling the cable ? ) answer--> the cablehouse is curved - is not a strait line between the break handle and the lever.if the cable was bear with no cablehouse you would think that there is a lot of redundant cable .now you are pulling that "redundant" cable - now the cable house dosnt have enough space so it pushes the lever- its like trying to insert a 25 cm spring(not streched spring )to a 20 cm gap.the string has a "belly" trying to push the spring to make it without a belly will cause a pressure on the gap to open . I hope this is helpfull ....yoav Israel

Answer 4

"The brake cable only pulls on one of the arms, so what is causing the force on the other arm?".

The cable shortens when the brake is applied, so both arms are pulled:

The "A" moves up, the "B" moves down, resulting in "C" and "D" moving towards each other. The movement of "C" and "D" isn't always exactly even or synchronized, but once one side touches the rim there's nowhere else to go, and the other side moves and both clamp each side of the rim.

Answer 5

The problem in understanding why the B part is being pulled towards the A part lies mostly in the image from Wikipedia. It shows only the brakes and the arms, but not the whole cable and housing from the arms to the lever.

If you go and see a real bicycle, you will notice that there is always a curve in the cable and housing, of 90 degrees, or more sometimes. This curve is maintained by the brake noodle. It is because of this curve only that the B part is pulled towards the A part. (The housing of the cable is able to take on compression forces, and also tension forces. The compression forces are the ones that matter for this effect)

The cable is in tension and it exerts a force along its path. If you analyze the forces acting on the curved part (Free body diagram), than you will see that the resultant force has a component in the direction of the A part. Because the housing is able to take compression loads, and because of the noodle that keeps the shape curved, the cable-housing structure is being pulled to the A part.

I thought about it myself, and only thanks to a video mentioning this break noodle, it hit me that there is a curve there...

Edit: Now I see that Yoav wrote the same thing before me... I agree with his answer.

Answer 6

This is my understanding of how the inner and outer parts of a bicycle brake cable work to push and pull on the two separate parts of a single-pivot, side pull brake caliper (only cable parts shown):-

1. When the cable is slack (brake off).

2. Brake applied, pulling one side of caliper in contact with hub, causing inner cable to go taut. This forces the outer cable jacket to also become taut and attempt to straighten (shortest route). This makes the cable cover a greater distance than when relaxed, and thus forces the other (push) side of the caliper in contact with the hub.

Answer 7

Force diagrams often gloss over complications that are assumed to be common knowledge. Here I will be annotating the full system with multiple step interpolations, but for now without force arrows. A single-pivot side-pull caliper brakes is composed of the following elements, pictured below:

• brake line
• brake line housing (aka noodle)
• brake line puller (ie, a handle)
• left caliper (green) attached to pivot point
• right caliper (red) attached to pivot point
• spring, which pushes the calipers apart
• wheel/tire

Let's simplify the model by removing the spring and truncating the right caliper (red). We also assume the rigidity of the brake line and the brake line housing is enough to support the left caliper (green), which without the spring would otherwise fall into the tire. When the handle and brake line are pulled, it is intuitive that only the right caliper (red) contracts.

Let's now incorporate the complete right caliper (red) so that only the spring is missing. At first and until the tire is contacted, only the right caliper (red) contracts. Just as before. However with the right caliper (red) locked into place and unable to further close, continued pulling of the handle forces the brake line taut, reducing the length of brake line which runs between the L2-L3 points. Since the brake line housing cannot contract or collapse it forces the left caliper (green) shut, balancing the force diagram.

Now really, the left caliper (green) isn't fixed and would collapse into the tire. So we introduce a spring to force the calipers apart when the handle and brake line are no longer being pulled. We would also like the calipers to be balanced - to make contact with the tire at the same time and with equal force. Fortuitously, the spring has just that effect. Recall that the force to compress a spring grows linearly with distance. In our previous model, regardless of the force applied along the brake line, once the brake makes contact with the tire the right caliper (red) will not move. In other words, upon contact there is an equal and opposite force. With the spring installed this force grows linearly rather than instantaneously. As before, tension between the L2-L3 points is counteracted by the cable housing, forcing the left caliper (green) shut.

The trick is balance the brakes so the calipers close equally. We have two variables: the spring stiffness and the length of the brake line housing. I've never balanced these brakes but I imagine that the spring cannot be tightened. Which leaves the length of housing; I imagine that properly balancing such brakes is difficult. For finer adjustments and as with many bicycle systems, the length of the housing can be adjusted by screw. Refer to the original image: