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contact point improves mobility greatly. Three wheels can be laid out in several ways. Five varieties are pictured in the following figures. The most common and easiest to implement, but with, perhaps, the least mobility of the five three-wheeled types, is represented by a child s tricycle. On the kid-powered version, the front wheel provides both propulsion and steers. Robots destined to be used indoors, in a test lab or other controllable space, can use this simple layout with ease, but it has extremely poor mobility. Just watch any child struggling to ride their tricycle on anything but a flat smooth road or sidewalk. Powering only one of the three wheels is the major cause of this problem. Nevertheless, there have been many successful indoor test platforms that use this layout precisely because of its simplicity. In order to improve the mobility and stability of motorcycles, the three wheeled All Terrain Cycle (ATC) was developed. This vehicle demonstrates the next step up in the mobility of three wheeled vehicles. The rear two wheels are powered through a differential, and the front steers. This design is still simple, but although ATCs seemed to have high mobility, they did not do well in forest environments filled with rocks and logs, etc. The ATC was eventually outlawed because of its major flaw, very poor stability. Putting the single wheel in front lead to reduced resistance to tipping over the front wheel. This is also the most common form of accident with a child s tricycle. Increasing the stability of a tricycle can be easily accomplished by reversing the layout, putting the two wheels in front. This layout works fine for relatively low speeds, but the geometry is difficult to control when turning at higher speeds as the forces on the rear steering wheel tend to make the vehicle turn more sharply until eventually it is out of control. This can be minimized by careful placement of the vehicle s center of gravity, moving it forward just the right amount without going so far that a hard stop flips the vehicle end over end. A clever version of this tail dragger-like layout gets around the problem of flipping over by virtue of its ability to flip itself back upright simply by accelerating rapidly. The vehicle flips over because there is no lever arm to resist the torque in the wheels. Theoretically, this could be done with a tricycle also. At low speeds, this layout has similar mobility to a tail dragger and, in fact, they are very similar vehicles. Steering with the front wheels on a reversed tricycle removes the steering problem, but adds the complexity of steering and driving both wheels. This layout does allow placing more weight on the passive rear wheel, significantly reducing the flipping over tendencies, and mobility is moderately good. The layout is still dragging around a passive wheel, however, and mobility is further enhanced if this wheel is powered.
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Figure 4-6 Reversed tricycle, differential steer
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Figure 4-7 front steer
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Reversed tricycle,
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Figure 4-8 Reversed tricycle, all drive, all steer
The most complicated and highest mobility three-wheeled layout is one where all wheels are powered and steered. This layout is extremely versatile, providing motion in any direction without the need to be moving; it can turn in place. This ability is called holonomic motion and is very useful for mobile robots because it can significantly improve mobility in cluttered terrain. Of the vehicles discussed so far, all, except the front steer reversed tricycle, can be made holonomic if the third wheel lies on the circumference of the circle whose center is midway between the two opposing wheels, and the steering or passive wheel can swing through 180 degrees. To be truly holonomic, even in situations where the vehicle is enclosed on three sides, like in a dead-end hallway, the vehicle itself must be round. This enables it to turn at any time to find a path out of its trap. See Figure 4-8. Before we investigate four-wheeled vehicles, there is a mechanism that must be, at least basically, understood the differential. The differential (Figure 4-9) gets its name from the fact that it differentiates the rotational velocity of two wheels driven from one drive shaft. The most basic differential uses a set of gears mounted inside a larger gear, but on an axis that lies along a radius of the larger gear. These gears rotate with the large gear, and are coupled to the axles through crown gears on the ends of the axles. When both wheels are rolling on relatively high fric-
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