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Belt Problem
The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius ''r''1 and ''r''2 whose centers are separated by a distance ''P''. The solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congruent angles. Solution Clearly triangles ACO and ADO are congruent right angled triangles, as are triangles BEO and BFO. In addition, triangles ACO and BEO are similar. Therefore angles CAO, DAO, EBO and FBO are all equal. Denoting this angle by \varphi (denominated in radians), the length of the belt is :CO + DO + EO + FO + \text CD + \text EF \,\! :=2r_1\tan(\varphi) + 2r_2\tan(\varphi) + (2\pi-2\varphi)r_1 + (2\pi-2\varphi)r_2 \,\! :=2(r_1+r_2)(\tan(\varphi) + \pi- \varphi) \,\! This exploits the convenience of denominating angles in radians that the length of an arc = the radius × the measure of the angle facing the arc. To find \varp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belt Problem V2
Belt may refer to: Apparel * Belt (clothing), a leather or fabric band worn around the waist * Championship belt, a type of trophy used primarily in combat sports * Colored belts, such as a black belt or red belt, worn by martial arts practitioners to signify rank in the kyū ranking system Geology * A synonym for orogen (e.g. orogenic belt) * Greenstone belt * A large-scale linear or curved array of belt of igneous rocks (e.g. Transscandinavian Igneous Belt) * A large-scale linear or curved array of mineral deposits (e.g. Bolivian tin belt) * Metamorphic belt :* Paired metamorphic belts Mechanical and vehicular * Belt (mechanical), a looped strip of material used to link multiple rotating shafts * Conveyor belt, a device for transporting goods along a fixed track * Belt manlift, a device for moving people between floors in a building or grain elevator. * Seat belt, a safety device in automobiles and on the plane * Timing belt, part of an internal combustion engine * Serpenti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle
In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two rays lie in the plane (geometry), plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. ''Angle'' is also used to designate the measurement, measure of an angle or of a Rotation (mathematics), rotation. This measure is the ratio of the length of a arc (geometry), circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factory
A factory, manufacturing plant or a production plant is an industrial facility, often a complex consisting of several buildings filled with machinery, where workers manufacture items or operate machines which process each item into another. They are a critical part of modern economic production, with the majority of the world's goods being created or processed within factories. Factories arose with the introduction of machinery during the Industrial Revolution, when the capital and space requirements became too great for cottage industry or workshops. Early factories that contained small amounts of machinery, such as one or two spinning mules, and fewer than a dozen workers have been called "glorified workshops". Most modern factories have large warehouses or warehouse-like facilities that contain heavy equipment used for assembly line production. Large factories tend to be located with access to multiple modes of transportation, some having rail, highway and water loading ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated
Automation describes a wide range of technologies that reduce human intervention in processes, namely by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines. Automation has been achieved by various means including mechanical, hydraulic, pneumatic, electrical, electronic devices, and computers, usually in combination. Complicated systems, such as modern factories, airplanes, and ships typically use combinations of all of these techniques. The benefit of automation includes labor savings, reducing waste, savings in electricity costs, savings in material costs, and improvements to quality, accuracy, and precision. Automation includes the use of various equipment and control systems such as machinery, processes in factories, boilers, and heat-treating ovens, switching on telephone networks, steering, and stabilization of ships, aircraft, and other applications and vehicles with reduced human i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luggage
Baggage or luggage consists of bags, cases, and containers which hold a traveler's personal articles while the traveler is in transit. A modern traveler can be expected to have packages containing clothing, toiletries, small possessions, trip necessities. On the return trip, travelers may have souvenirs and gifts. For some people, luggage and the style thereof is representative of the owner's wealth and status. Luggage is constructed to protect the items during travel either with a hard shell or a durable soft material. Luggage often has internal subdivisions or sections to aid in securing items. Handles are typically provided to facilitate carrying, and some luggage may have wheels and/or telescoping handles or leashes to make moving them easier. Baggage (not luggage), or ''baggage train'', can also refer to the train of people and goods, both military and of a personal nature, which commonly followed pre-modern armies on campaign. Overview Luggage has changed over time. Hist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Airport
An airport is an aerodrome with extended facilities, mostly for commercial air transport. Airports usually consists of a landing area, which comprises an aerially accessible open space including at least one operationally active surface such as a runway for a plane to take off and to land or a helipad, and often includes adjacent utility buildings such as control towers, hangars and terminals, to maintain and monitor aircraft. Larger airports may have airport aprons, taxiway bridges, air traffic control centres, passenger facilities such as restaurants and lounges, and emergency services. In some countries, the US in particular, airports also typically have one or more fixed-base operators, serving general aviation. Operating airports is extremely complicated, with a complex system of aircraft support services, passenger services, and aircraft control services contained within the operation. Thus airports can be major employers, as well as important hubs for tourism ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conveyor Belt
A conveyor belt is the carrying medium of a belt conveyor system (often shortened to belt conveyor). A belt conveyor system is one of many types of conveyor systems. A belt conveyor system consists of two or more pulleys (sometimes referred to as drums), with a closed loop of carrying medium—the conveyor belt—that rotates about them. One or both of the pulleys are powered, moving the belt and the material on the belt forward. The powered pulley is called the drive pulley while the unpowered pulley is called the idler pulley. There are two main industrial classes of belt conveyors; Those in general material handling such as those moving boxes along inside a factory and bulk material handling such as those used to transport large volumes of resources and agricultural materials, such as grain, salt, coal, ore, sand, overburden and more. Overview Conveyors are durable and reliable components used in automated distribution and warehousing, as well as manufacturing and produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bicycle Gearing
Bicycle gearing is the aspect of a bicycle drivetrain that determines the relation between the cadence, the rate at which the rider pedals, and the rate at which the drive wheel turns. On some bicycles there is only one gear and, therefore, the gear ratio is fixed, but most modern bicycles have multiple gears and thus multiple gear ratios. A shifting mechanism allows selection of the appropriate gear ratio for efficiency or comfort under the prevailing circumstances: for example, it may be comfortable to use a high gear when cycling downhill, a medium gear when cycling on a flat road, and a low gear when cycling uphill. Different gear ratios and gear ranges are appropriate for different people and styles of cycling. A cyclist's legs produce power optimally within a narrow pedalling speed range, or cadence. Gearing can be optimized to use this narrow range as efficiently as possible. As in other types of transmissions, the gear ratio is closely related to the mechanical ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aeroplane
An airplane or aeroplane (informally plane) is a fixed-wing aircraft that is propelled forward by thrust from a jet engine, propeller, or rocket engine. Airplanes come in a variety of sizes, shapes, and wing configurations. The broad spectrum of uses for airplanes includes recreation, transportation of goods and people, military, and research. Worldwide, commercial aviation transports more than four billion passengers annually on airliners and transports more than 200 billion tonne-kilometersMeasured in RTKs—an RTK is one tonne of revenue freight carried one kilometer. of cargo annually, which is less than 1% of the world's cargo movement. Most airplanes are flown by a pilot on board the aircraft, but some are designed to be remotely or computer-controlled such as drones. The Wright brothers invented and flew the first airplane in 1903, recognized as "the first sustained and controlled heavier-than-air powered flight". [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pulley Problem
The belt problem is a mathematics problem which requires finding the length of a crossed belt that connects two circular pulleys with radius ''r''1 and ''r''2 whose centers are separated by a distance ''P''. The solution of the belt problem requires trigonometry and the concepts of the bitangent line, the vertical angle, and congruent angles. Solution Clearly triangles ACO and ADO are congruent right angled triangles, as are triangles BEO and BFO. In addition, triangles ACO and BEO are similar. Therefore angles CAO, DAO, EBO and FBO are all equal. Denoting this angle by \varphi (denominated in radians), the length of the belt is :CO + DO + EO + FO + \text CD + \text EF \,\! :=2r_1\tan(\varphi) + 2r_2\tan(\varphi) + (2\pi-2\varphi)r_1 + (2\pi-2\varphi)r_2 \,\! :=2(r_1+r_2)(\tan(\varphi) + \pi- \varphi) \,\! This exploits the convenience of denominating angles in radians that the length of an arc = the radius × the measure of the angle facing the arc. To find \varphi we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc (geometry)
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's ''Elements'': "The urvedline is €¦the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which €¦will leave from its imaginary moving some vestige in length, exempt of any width." This definition of a curve has been formalized in modern mathematics as: ''A curve is the image of an interval to a topological space by a continuous function''. In some contexts, the function that defines the curve is called a ''parametrization'', and the curve is a parametric curve. In this article, these curves are sometimes called ''topological curves'' to distinguish them from more constrained curves such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, \theta = \frac, where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly \frac radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, which i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
