#GEAR TOOTH GEOMETRY CALCULATOR FULL#
a decimal number - expressing the gear ratio as a decimal number gives us a quick idea about how much the input gear has to be turned for the output gear to complete one full revolution.a fraction or a quotient - where, if possible, we simplify the fraction by dividing both the numerator and the denominator by their greatest common factor.The gear ratio, just like any other ratios, can be expressed as: Gear ratio = input gear teeth number / output gear teeth number Gear ratio = (input gear teeth number * (gear thickness + teeth spacing)) / (output gear teeth number * (gear thickness + teeth spacing))īut, since the thickness and spacing of the gear train's teeth must be the same for the gears to engage smoothly, we can cancel out the gear thickness and teeth spacing multiplier in the above equation, leaving us with the equation below: We can express the gear's circumference by multiplying the sum of a tooth's thickness and the spacing between teeth by the number of teeth the gear has: Doing so is similar to considering the circumferences of the gears. Similarly, we can calculate the gear ratio by considering the number of teeth on the input and output gears. gear ratio = (radius of input gear)/(radius of output gear).gear ratio = (diameter of input gear)/(diameter of output gear).Simplifying this equation, we can also obtain the gear ratio when just the gears' diameters or radii are considered: Gear ratio = (π * diameter of input gear)/(π * diameter of output gear) We can determine the circumference of a specific gear in the same way we calculate the circumference of a circle. We calculate the gear ratio between two gears by dividing the circumference of the input gear by the circumference of the output gear. The gear ratio helps us in determining the number of teeth each gear needs to produce a desired output speed/ angular velocity, or torque. The gear ratio is the ratio of the circumference of the input gear to the circumference of the output gear in a gear train. To help you visualize this, here is an illustration of the different types of gears and their input-to-output gear relationships: The resulting movement of the output gear could be in the same direction as the input gear, but it could be in a different direction or axes of rotation depending on the type of gears in the gear train. In a two-gear system, we can call these gears the driving gear and the driven gear, respectively. The final gear that the input gear influences is known as the output gear. We can also call it the driving gear since it initiates the movement of all the other gears in the gear train. The gear that initially receives the turning force, either from a powered motor or just by hand (or foot in the case of a bike), is called the input gear. In a gear train, turning one gear also turns the other gears. We call this system of gears a gear train. The transfer of movement happens when two or more gears in a system mesh together while in motion. Gears come in different shapes and sizes (even if the most common are involute gears), and these differences describe the translation or transfer of the rotational movement. A gear is a toothed wheel that can change the direction, torque, and speed of rotational movement applied to it.
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