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The Geometry of Cantilever Brakes
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by Sheldon "Theory" Brown

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This article is one of several on this site about cantilever brakes. If you are just looking for practical instruction on how to get your cantilever brakes working properly, you might want to start out with my introductory article on Cantilever Adjustment. This article is a bit more of a theoretical examination of the fine points of cantilever brake geometry.

Cantilever Brake Setup

In 1980 and earlier, cantilever brakes were weird, exotic equipment, found mainly on expensive tandems and very high-end touring bikes. They were even rarer than triple chainwheels! Times have changed, and equipment that was once available only to knowledgeable, well-heeled fanatics is now found even on department-store bikes.

Nevertheless, there still remains a bit of mystery to cantilever brakes. The purpose of this article is to clear up this mystery, and to help you do a better job of setting up cantilevers by understanding the nitty-gritty details of the geometry that makes them work.

In particular, it addresses the question of how long to make the transverse cable, or, to put it another way, how low to mount the cable yoke. With most cantilevers, the mechanic has considerable latitude in setting up this cable system, and it makes a real difference in the performance of the brakes what he or she does, especially with the newer "low-profile" cantilevers.

 Mechanical Advantage

You cannot understand bicycle brakes unless you understand mechanical advantage!

"Mechanical advantage", or "leverage" is the ratio between how much you get out of a linkage and how much you put in. Mechanical advantage may be looked at as a ratio of forces or as a ratio of distances. Imagine a simple lever with a pivot (fulcrum) 1/3 of the way along it:

mechanical advantage
Side B of the lever is twice as long as side A so the mechanical advantage is 2:1 (or 1:2, depending on which way you look at it!)

Side B will move 2 times as far as side A, but you will have to push on Side A with 2 times the force to lift a weight on Side B.

The crucial point is that changing the leverage (for instance by moving the pivot) will affect both the force and the distance at the same time, since they are two sides of the same coin. You cannot increase the force ratio without reducing the distance ratio.

In the case of bicycle brakes, the mechanical advantage of the system represents the ratio between the amount of force that presses the brake shoes against the rim and the amount of force that the rider's fingers have to apply to the brake levers to create this braking force. If a particular braking system has a mechanical advantage of 8, then squeezing the brake lever with 10 pounds of force will cause the brake shoes to apply 80 pounds of force against the rim. (Actually, somewhat less than 80 pounds would be delivered, due to frictional losses, but for purposes of this article, friction within the brake mechanisms is not important and will be ignored.)

Mechanical advantage can also be viewed as a ratio of distances, rather than forces. A brake with high mechanical advantage will apply a lot of force to the brake shoe for a small amount of finger pressure on the lever; the other side of the coin is that a system with high mechanical advantage will require the hand lever to move a long way to move the brake shoes a short distance toward the rim. If you have too much mechanical advantage, the brake lever will bump up against the handlebar before the brake shoe has moved far enough to engage the rim. If you tighten such a brake up enough to avoid bottoming out the lever, the brake shoes may not retract far enough when the brake is released, and may still drag on the rim.

With caliper brakes, the mechanical advantage is basically fixed by the manufacturer. You cannot change it except by replacing the calipers or the levers or the wheels. (Installing smaller wheels requires you to lower the brake shoes, increasing the effective reach of the calipers, and reducing the mechanical advantage accordingly. For instance, substituting 622 mm (700C) wheels on a bike built for 630 mm (27 inch) wheels will degrade the braking.)

The new direct-pull cantilevers, such as Shimano's "V" brakes, also have a fixed mechanical advantage. Since their pivots are below the level of the rim, smaller wheels give more mechanical advantage, rather than less as with caliper brakes. Traditional cantilever brakes, however, allow the mechanic to adjust the mechanical advantage to a considerable extent, mainly by adjusting the length of the transverse cable and the height of the cable yoke.

"Feel" vs. Function

With automobile brakes, a nice "hard" pedal feel is a sign that the brakes are in good condition. A soft, "spongy" feel at the brake pedal is a sign of trouble, perhaps air in the hydraulic lines. This is not the case with bicycle brakes. A hard, crisp feel to the brakes on a bicycle may be a sign that the brakes don't have much mechanical advantage. You squeeze them until the brake shoes hit the rim, then they stop. Brakes with a high mechanical advantage will feel "spongy" by comparison, because the large amount of force they deliver to the brake shoes will squash the shoes against the rim, deforming them temporarily under pressure. You can feel this deformation in your fingers. The brakes with the rock-hard feel may seem nice on the work stand or the showroom floor, but when it comes to making the bike actually stop, the spongy set-up will do the job better, with less finger pressure and greater margin for safety in wet conditions.

Definitions

For purposes of this article, I have defined 1 distance, 2 arms, and 3 angles as shown in the illustration.
 

Pivot-Cable distance (PC)

The shortest distance from the center of the pivot to the line of the transverse cable.
In the case of low-profile brakes, this is the shortest distance from the pivot to the imaginary line extending from the transverse cable.

 

Shoe arm (PS)

Runs from the center of the pivot to the part of the brake shoe that contacts the rim.

 

Anchor arm (PA)

Runs from the center of the pivot to the attachment point for the end of the transverse cable.

 

Yoke angle

The angle of the transverse cable from the horizontal.

 

Anchor angle

The angle between the end of the transverse cable and the anchor arm.

 

Cantilever angle

The angle between the shoe arm and the anchor arm.
cantilever schematic

Types of Cantilevers

Conventional cantilevers fall into three types, defined by their cantilever angle: Variant cantilevers have their own categories:

Mechanical Advantage of Cantilevers

Three separate factors determine the mechanical advantage of any particular cantilever braking system. The total mechanical advantage of the system is the product of all three multiplied together:
  1. The first factor is the brake lever itself. The lever's mechanical advantage is determined by the distance from the lever's pivot to the cable end, and by the effective length of the brake lever from its pivot to where the rider's fingers grip it. Typical mountain-bike type brake levers give a mechanical advantage of around 3 1/2, old-style drop-bar levers around 4, and "æro" drop-bar levers around 4 1/2. Levers for direct-pull ("V-type") brakes are around 2.

    Shimano ("Servo-Wave" ®) and Odyssey both make mountain-bike type levers with a variable mechanical advantage that increases as the lever is pulled.

Two distinct aspects of the cantilever system determine its mechanical advantage:
  1. The individual cantilever's mechanical advantage is the ratio between the pivot-cable distance (PC) and the pivot-shoe distance (PS) . The pivot-cable distance (PC) is at its greatest when the anchor angle is 90 degrees, so that PC and PA are the same. Some authorities recommend adjusting the length of the transverse cable accordingly, but I believe that this is an over-simplification. With wide- and medium-profile cantilevers, the mechanical advantage of the cantilever unit increases as it travels inward, increasing as the brake shoes wear down. With narrow-profile cantilevers, the mechanical advantage tends to decrease as the cantilever travels inward. The mechanical advantage of a typical cantilever is generally between 1 and 2. Medium-profile cantis tend to have more of this type of mechanical advantage.
  2. A larger contribution to the mechanical advantage of a well-adjusted cantilever brake, especially a low-profile one, comes from the transverse cable. The mechanical advantage is strictly determined by the "yoke angle ". The formula is:
    Mechanical Advantage = 1/sin yoke angle
    For readers without slide rules I have calculated a few examples: [How quaint :-) John Allen]
  3. Yoke Angle
    (Degrees)
    Mechanical
    Advantage
    90° 1
    80° 1.015
    70° 1.063
    60° 1.15
    50° 1.31
    40° 1.55
    30° 2
    20° 2.92
    10° 5.76
    11.47
    Infinity!
    A 90 degree yoke angle would result from an infinitely long transverse cable, such that each side of the cable was running vertically down from the cable yoke.

    A 0 degree yoke angle would represent the shortest possible transverse cable, running in a perfect straight line along the top of the cable yoke.

    As you can see from the table, the shorter and straighter the transverse cable, the more difference it makes. This effect is what makes it possible to make a low-profile brake with good stopping power.

Special Considerations for Low-Profile Cantilevers

The small cantilever angle of narrow-profile brakes causes the anchor arm (PA) to be nearly vertical, especially on mountain bikes that have wide-set pivot bosses and narrow rims. Traditional good practice had been to slide the brake shoe holders all the way into the eyebolts, so that the back of the shoe butts up against the cantilever arm. This is not the case with the newer low-profile models.

With low-profile cantilevers,, the shoe needs to be extended inward from the arm, increasing the effective cantilever angle . The unsupported length of shaft connecting the brake shoe to the arm may cause an increased tendency to squeal, but that is one of the inherent trade-offs of low-profile brakes.

Many newer cantilevers replace the separate transverse cable and yoke with "link wire." This is a cable carrier that has a length of narrow housing running from the yoke to the anchor arm. The primary cable runs through this housing, and forms half of the transverse cable. There is a guide line printed on the round yoke, which is intended to be lined up with the exposed side of the transverse cable.

Link wires are commonly available in five lengths:

Code Length DESCRIPTION
S 63 mm
A 73 mm
B 82 mm
C 106 mm
D 93 mm

If you substitute a conventional yoke and separate transverse cable, you may be able to increase the mechanical advantage slightly on a particular bicycle. In general, the stock set up works about as well as possible, but only if you use the Shimano guide.

Since the yoke angle is so critical to the mechanical advantage, the mechanical advantage gets less and less as the brake is engaged, and as the brake shoes wear down. The short transverse cables necessary to get high mechanical advantage from low-profile cantilevers exaggerate this effect, because the yoke angle gets larger for a given amount of upward travel of the yoke. Thus, low-profile cantilevers should be set up with minimum pad clearance if you want to get high mechanical advantage when the brake is actually engaged.

Direct-pull ("V-type") CantileversDirect Pull V-Brake

The latest thing in cantilevers is the direct-pull cantilever, popularly known by Shimano's trademark "V-Brake". These resemble very tall, low-profile cantilevers, but they do not have a separate transverse cable. They are a side-pull, rather than center-pull design. One arm has the housing stop, and the inner cable runs from the top of that arm to an anchor bolt on the top of the opposite arm. Direct-pull cantilevers have a very high mechanical advantage, which makes them unsuitable for use with conventional levers. If you do use conventional levers with direct-pull cantilevers, braking may be too abrupt. The excessive mechanical advantage of this combination will either cause the brake shoes to rub on the rim when they are at rest, or the brake lever will bottom out against the handlebar, depending on the cable adjustment.

Also see my article about direct-pull cantilevers

There are a few new aftermarket gadgets that permit you to use conventional brake levers with direct-pull brakes. These generally use eccentric or doubled pulleys to cause them to pull farther (but less hard) than the incoming cable pulls.

V-Daptor
The unit illustrated above is a World Class "V-Daptor." In this case, it has been installed on a conventional Shimano LX cantilever, thus converting a traditional center-pull cantilever into a direct-pull unit. This is a handy way to improve braking on many touring bikes and tandems, but there is not usually enough clearance to let this modification work with fat mountain-bike tires--for them, you need a purpose-built direct-pull brake.

Parallel-Push Linkage

v-type brake
Shimano's XTR and XT V-Brakes feature a special parallelogram linkage. This serves two purposes:
  1. It causes the brake shoes to remain at the same angle to the rim throughout the stroke, and throughout the service life of the pad.
  2. It causes the direction of motion of the brake shoes to be close to horizontal, rather than the usual slanted arc centered on the pivot boss. This is a major advantage for those who use very fat tires on narrow rims, because it prevents the shoe from rising up and damaging the sidewall of the tire on release, and also prevents having the brake shoes dive under the rim as they wear down.
Unfortunately, the extra pivots considerably complicate the mechanism, and this has caused maintenance problems and excessive squeal in practice.

Mechanical Advantage--How Much is Enough?

Generally, more mechanical advantage is better than less, but it is possible to overdo it.

There is a direct trade-off between how much force you get and how far the parts travel. Given a mechanical advantage of 8, pulling the brake lever in by 16 millimeters will only move the brake shoes 2 millimeters closer to the rim. The more mechanical advantage you have, the closer the brake shoes will be to the rim at their rest position. This is not a problem with a perfectly true wheel, but can cause the brake shoes to rub too easily on rims that have seen better days.

There is a case to be made for less than maximum mechanical advantage on the front brakes of bikes that are aimed at less experienced riders, lest they lock up the front wheel and hurt themselves.

With a brake set up for maximum mechanical advantage, the shorter transverse cable has a shallower yoke angle. This may make it difficult or impossible to unhook the transverse cable for wheel removal. For some riders, it may be a worthwhile trade-off to give up some braking power for the sake of easier wheel removal.

On touring bikes with high-mechanical-advantage "æro" brake levers, excessive mechanical advantage may cause the brake to run out of lever travel, so that the lever hits against the handlebar. Shimano makes an extra-wide cable yoke for such applications, but you can achieve the same effect by lengthening the transverse cable, unless the bike has such a small frame that you run out of room.

Wide yoke

Getting the Most out of your Cantilevers

Aside from the issue of mechanical advantage, there are other ways to improve your cantilever braking.

If you reduce flex in the system, you can set the brake for more mechanical advantage without running out of lever travel. I would suggest the following:

Cantilever Brake Compatibility/Interchangeability
Cantilever
Type
Frame
Pivot Studs
Levers Cable Routing
Direct Pull
V-Brake ®
Below the Rim Long Pull
Low Tension
Cable comes in from the side.

Lower housing stop is part of the cantilever

Traditional
Center Pull
Standard
Short Pull
High Tension
Cable runs down the bicycle's center line.

Lower rear housing stop on frame,
either special braze-on ,
or mounted to the seatpost bolt.

Front housing stop on headset ,
fork or handlebar stem .

U-Brake
Cantilever
Above the Rim
Roller-Cam
Cantilever

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