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For the close-ratio transmission, first gear has a 4:1 ratio or 4, and second gear has a ratio of 3:1 or 3, so the progression between gears is 4 / 3 , or 133%. Since 133% is less than 200%, the transmission with the smaller progression between gears is considered close-ratio.
Worm-and-gear sets are a simple and compact way to achieve a high torque, low speed gear ratio. For example, helical gears are normally limited to gear ratios of less than 10:1 while worm-and-gear sets vary from 10:1 to 500:1. [45] A disadvantage is the potential for considerable sliding action, leading to low efficiency. [46]
Analysis assumes a common gear design modulus. The planetary gears (blue) turn in a ratio determined by the number of teeth in each gear. Here, the ratio is − + 27 / 18 , or − + 3 / 2 ; meaning that each planet gear turns at 3 / 2 the rate of the sun gear, in the opposite direction. An outer ring gear is not shown.
The speed ratio for a pair of meshing gears can be computed from ratio of the radii of the pitch circles and the ratio of the number of teeth on each gear, its gear ratio. Two meshing gears transmit rotational motion. The velocity v of the point of contact on the pitch circles is the same on both gears, and is given by = =, where input gear A ...
The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (pitch angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers .
Classical mechanics utilises many equations—as well as other mathematical concepts—which relate various physical quantities to one another. These include differential equations, manifolds, Lie groups, and ergodic theory. [4] This article gives a summary of the most important of these.
Depending on the gear ratio of the bicycle, a (torque, angular speed) input pair is converted to a (torque, angular speed) output pair. By using a larger rear gear, or by switching to a lower gear in multi-speed bicycles, angular speed of the road wheels is decreased while the torque is increased, product of which (i.e. power) does not change.
The capstan equation [1] or belt friction equation, also known as Euler–Eytelwein formula [2] (after Leonhard Euler and Johann Albert Eytelwein), [3] relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan).