If you know the concept, skip this.
If you don't, then the transmission angle is something you probably are familiar without knowing. You have no doubt tried to move an object that was somehow constrained. An object that could not move freely, but was attached to something: the handle of a crank, a curtain on a rail, a supermarket trolley on wheels that do not turn, a sliding door.
In all of these cases, the object may not be able to move in the direction of your pushing or pulling.
Let's take the case of the sliding door as an example:
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If you take the moving panel by the handle and pull in the direction in which the door can slide, it is easy to move it. |
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But if you push or pull it at right angles to the panel, then it won't move at all. |
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If you pull at an angle in between these extremes, the panel will slide more or less easily. |
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The door panel is constrained: it can only slide in one direction. The force we apply can be misaligned with that direction. In the image the angle µ is the angle between these two important directions: that of the possible motion and that of the applied force.
The smaller µ is, the better the door will slide, and it will not slide at all if µ = 90° The angle µ is the supplement of the transmission angle: it specifies how efficiently the force will do its work. (note that it's (90°-µ) that is called the transmission angle, but these are theoretical details). For this example, µ should be small. |
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In the case of a crank we should apply the force at right angles to the crank's spoke.
The pedals of a bicycle are cranks. Depending on the position of the pedals it will be more or less easy to start biking: position (b) is good, but position (a) is uncomfortable because your feet apply their force perpendicular to the direction in which the pedal can move and hence the transmission is very inefficient. |
(a): the force is straight down (red arrow) but the pedal can only move forward (green arrow) |
(b): the force is still straight down, but it is now aligned with the pedal's possible motion and the transmission is therefore best. |
| Starting in position (b) has the disadvantage that you can apply force only until the pedal is down, i.e. at most a quarter turn. So in practice you will choose a position somewhat higher, say at 45° up, even though the transmission angle is then not perfect: at least you will be able to push a little longer and get more speed. | |
