Gears
The primary uses of gears is the transmission of force, changing the direction of a force in a machine and creating more power or speed in a machine. The pointed part of the gears are referred to as teeth and are the pieces used to transmit forces from one gear to the next or to another piece of machinery. Gears are able to increase speed by pairing a larger gear with more teeth with a smaller gear with less teeth. However, the larger gear will be applying more force than the smaller gear. The ratio of the number of teeth on the gears is called the gear ratio.
Gears come in many different types including spur, helical, worm, rack and pinion, and bevel. The necklace above is based on the simplest type, a spur gear. Helical gears are similar but have a slanted edge to their teeth. The angle allows for easier and quieter engagement of the gears. Worm gears are much different than spur of helical gears. A worm gear is a screw-like gear put up against a spur gear. The long screw turning results in the spur gear spinning. Worm gears are very high torque but have a low speed.
Gears have been around all the way back to the 4th century in China and have been an important part of history. Gears have been a part of everything from clocks to grain mills.
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Mohr's Circle
Mohr’s circle, named for Christian Mohr, is a way many engineers show normal and shear stress visually. Mohr’s circle can be applied to both 2D and 3D stress by changing the number of circles drawn in the plot. Two dimensional plots use one circle while three dimensional plots require three circles.
Stress is technically defined as the force applied divided by the cross sectional area seeing the force. For example, if you applied a force to a single spaghetti noodle it will easily break in half. The cross sectional area of the single noodle is very small and a high stress occurs causing the noodle to break. Now imagine you apply the same force to a whole handful of spaghetti noodles. Most likely the noodles will not break, but why? The cross sectional area has drastically increased, which means the stress in each noodle has decreased. The stress felt by each noodle has not reached its failure point.
For two and 3 dimensional stress, the plot is created by calculating the principal stresses and using the Mohr’s circle equations for each type of stress case. The Mohr’s circle represents the combinations of normal and shear stress acting on a plane rotated about the center from the original plane. The angle the plane is rotated correlates to the angle the points are located on the Mohr’s circle. The normal and shear stress are the x and y axis so each point set of the circle represents a different normal and shear stress combination.
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