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11.1 SIMPLE GEAR TRAINS
À pWhen we want to increase/reduce angular displacements/velocities/etc. we can use simple gear trains.
As we have seen before, gears typically have an input to output ratio. The relationship below is for simple gear trains - only one gear on each axis.
We can deal with compound gear trains (multiple gears on each axis) by using product of driven and driving teeth.
11.1.1 Examples - Fixed Axis Gears
(|A simple gear train has only one gear on each axis.
A compound gear train has multiple gears on the same axis. Consider the truck transmission example from Shigley and Uicker,
We may also consider an in-line gear train. These can be used for items such divide by twelve and sixty in clocks,
Quite often we will have a particular speed ratio in mind. We can convert this to teeth numbers by finding a suitable fractional value,
The gear train in the previous example might look something like,
11.1.2 Examples - Moving Axis Gears
(|In some cases gears move relative to each other. This can be used to generate some interesting alternatives.
11.1.2.1 - Epicyclic Gear Trains
´ ð´ 0Epicyclic gears have many applications, such as automatic transmissions in automobiles.
In these trains the gears typically orbit each other.
Consider the basic epicyclic gear train,
We can represent these gears using a notation developed by Levai. Consider the basic epicyclic gear,
When designing with these gears, we can consider different control modes possible. In the case above we could connect the gear `4' to a ring gear (internal gear) and make a simple multispeed transmission.
Some of the other possible gear train types include variations on the number of planets.
Consider the compact planetary gear shown below,
We can also construct an epicyclic gear using bevel gears. This is called Humpage's reduction gear.
11.1.2.2 - Differentials
´ ð´ 0Differential mechanisms allow us to effectively do subtraction or averaging.
If we want to determine the difference between two linear motions we could a mechanism like the one shown below,
An angular differential is shown below using bevel gears,
************** include image here
In one type of automotive differential the housing above is driven, and both the output shafts turn. This allows a small difference in wheel speed. Without this simple action like turning corners would exert large forces on the tires and drive train. This is also why one of the drive wheels can spin while the other is fixed.
Various vehicles can disengage the differential for offroad conditions (where tires can slip), while others have mechanisms to balance torque to the wheels when an excessive difference in speed is detected.
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