Capstan Equation
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Capstan Equation
The capstan equation or belt friction equation, also known as Euler-Eytelwein's formula (after Leonhard Euler and Johann Albert Eytelwein), relates the hold-force to the load-force if a flexible line is wound around a cylinder (a bollard, a winch or a capstan). Because of the interaction of frictional forces and tension, the tension on a line wrapped around a capstan may be different on either side of the capstan. A small ''holding'' force exerted on one side can carry a much larger ''loading'' force on the other side; this is the principle by which a capstan-type device operates. A holding capstan is a ratchet device that can turn only in one direction; once a load is pulled into place in that direction, it can be held with a much smaller force. A powered capstan, also called a winch, rotates so that the applied tension is multiplied by the friction between rope and capstan. On a tall ship a holding capstan and a powered capstan are used in tandem so that a small force c ...
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Capstan Equation Diagram
Capstan may refer to: *Capstan (band), an American post-hardcore band *Capstan (cigarette), a brand of British cigarette * Capstan (nautical), a rotating machine used to control or apply force to another element * Capstan (tape recorder), rotating spindles used to move recording tape through the mechanism of a tape recorder *Capstan equation, formula to describe hold-force in relation to load-force for flexible lines around a cylinder *Horse capstan, a device similar to a windlass used in mining; also called a whim *Slingsby Capstan, a British two-seat glider of the 1960s *Capstan (software), audio restoration program by Celemony which eliminates wow and flutter See also * *Rack and pinion A rack and pinion is a type of linear actuator that comprises a circular gear (the '' pinion'') engaging a linear gear (the ''rack''). Together, they convert rotational motion into linear motion. Rotating the pinion causes the rack to be driven ...
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Elasticity (physics)
In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to ''plasticity'', in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied. Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of ...
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Belt Friction
Belt friction is a term describing the friction forces between a belt and a surface, such as a belt wrapped around a bollard. When a force applies a tension to one end of a belt or rope wrapped around a curved surface, the frictional force between the two surfaces increases with the amount of wrap about the curved surface, and only part of that force (or resultant belt tension) is transmitted to the other end of the belt or rope. Belt friction can be modeled by the Belt friction equation. In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a system determine how many times the belt or rope must be wrapped around a curved surface to prevent it from slipping. Mountain climbers and sailing crews demonstrate a working knowledge of belt friction when accomplishing tasks with ropes, pulleys, bollards and capstans. Equation The equation used ...
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Geodesic Curvature
In Riemannian geometry, the geodesic curvature k_g of a curve \gamma measures how far the curve is from being a geodesic. For example, for 1D curves on a 2D surface embedded in 3D space, it is the curvature of the curve projected onto the surface's tangent plane. More generally, in a given manifold \bar, the geodesic curvature is just the usual curvature of \gamma (see below). However, when the curve \gamma is restricted to lie on a submanifold M of \bar (e.g. for curves on surfaces), geodesic curvature refers to the curvature of \gamma in M and it is different in general from the curvature of \gamma in the ambient manifold \bar. The (ambient) curvature k of \gamma depends on two factors: the curvature of the submanifold M in the direction of \gamma (the normal curvature k_n), which depends only on the direction of the curve, and the curvature of \gamma seen in M (the geodesic curvature k_g), which is a second order quantity. The relation between these is k = \sqrt. In particular g ...
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Orthotropic Material
In material science and solid mechanics, orthotropic materials have material properties at a particular point which differ along three orthogonal axes, where each axis has twofold rotational symmetry. These directional differences in strength can be quantified with Hankinson's equation. They are a subset of anisotropy, anisotropic materials, because their properties change when measured from different directions. A familiar example of an orthotropic material is wood. In wood, one can define three mutually perpendicular directions at each point in which the properties are different. It is most stiff (and strong) along the grain, because most cellulose fibrils are aligned that way. It is usually least stiff in the radial direction (between the growth rings), and is intermediate in the circumferential direction. This anisotropy was provided by evolution, as it best enables the tree to remain upright. Because the preferred coordinate system is cylindrical-polar, this type of orthotrop ...
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Serpentine Belt
A serpentine belt (or drive belt) is a single, continuous belt used to drive multiple peripheral devices in an automotive engine, such as an alternator, power steering pump, water pump, air conditioning compressor, air pump, etc. The belt may also be guided by an idler pulley and/or a belt tensioner (which may be spring-loaded, hydraulic, or manual). To allow the belt to pass over more than three pulleys with a large enough wrap angle to avoid slipping, idler pulleys which press against the back of the belt are included, forcing the belt into a serpentine shape. To accommodate this bidirectional flexing while remaining strong enough to transfer the total force required by multiple loads, a serpentine belt is almost always of multi-groove (multi-vee, poly-v, or multi-rib) construction. Variations On some engine designs, the "back" (smooth side) of the belt may drive some accessories. This is typically limited to components requiring less torque or where a large angle of wrap i ...
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V-belt
A belt is a loop of flexible material used to link two or more rotating shafts mechanically, most often parallel. Belts may be used as a source of motion, to transmit power efficiently or to track relative movement. Belts are looped over pulleys and may have a twist between the pulleys, and the shafts need not be parallel. In a two pulley system, the belt can either drive the pulleys normally in one direction (the same if on parallel shafts), or the belt may be crossed, so that the direction of the driven shaft is reversed (the opposite direction to the driver if on parallel shafts). The belt drive can also be used to change the speed of rotation, either up or down, by using different sized pulleys. As a source of motion, a conveyor belt is one application where the belt is adapted to carry a load continuously between two points. History The mechanical belt drive, using a pulley machine, was first mentioned in the text the ''Dictionary of Local Expressions'' by the Han Dynast ...
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V-belt
A belt is a loop of flexible material used to link two or more rotating shafts mechanically, most often parallel. Belts may be used as a source of motion, to transmit power efficiently or to track relative movement. Belts are looped over pulleys and may have a twist between the pulleys, and the shafts need not be parallel. In a two pulley system, the belt can either drive the pulleys normally in one direction (the same if on parallel shafts), or the belt may be crossed, so that the direction of the driven shaft is reversed (the opposite direction to the driver if on parallel shafts). The belt drive can also be used to change the speed of rotation, either up or down, by using different sized pulleys. As a source of motion, a conveyor belt is one application where the belt is adapted to carry a load continuously between two points. History The mechanical belt drive, using a pulley machine, was first mentioned in the text the ''Dictionary of Local Expressions'' by the Han Dynast ...
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Anchor
An anchor is a device, normally made of metal , used to secure a vessel to the bed of a body of water to prevent the craft from drifting due to wind or current. The word derives from Latin ''ancora'', which itself comes from the Greek ἄγκυρα (ankȳra). Anchors can either be temporary or permanent. Permanent anchors are used in the creation of a mooring, and are rarely moved; a specialist service is normally needed to move or maintain them. Vessels carry one or more temporary anchors, which may be of different designs and weights. A sea anchor is a drag device, not in contact with the seabed, used to minimise drift of a vessel relative to the water. A drogue is a drag device used to slow or help steer a vessel running before a storm in a following or overtaking sea, or when crossing a bar in a breaking sea.. Overview Anchors achieve holding power either by "hooking" into the seabed, or mass, or a combination of the two. Permanent moorings use large masses (common ...
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Tail
The tail is the section at the rear end of certain kinds of animals’ bodies; in general, the term refers to a distinct, flexible appendage to the torso. It is the part of the body that corresponds roughly to the sacrum and coccyx in mammals, reptiles, and birds. While tails are primarily a feature of vertebrates, some invertebrates including scorpions and springtails, as well as snails and slugs, have tail-like appendages that are sometimes referred to as tails. Tailed objects are sometimes referred to as "caudate" and the part of the body associated with or proximal to the tail are given the adjective "caudal". Function Animal tails are used in a variety of ways. They provide a source of locomotion for fish and some other forms of marine life. Many land animals use their tails to brush away flies and other biting insects. Most canines use their tails to comunicate mood and intention . Some species, including cats and kangaroos, use their tails for balance; and some, such ...
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