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Involute Gear
The involute gear profile is the most commonly used system for gearing today, with cycloid gearing still used for some specialties such as clocks. In an involute gear, the profiles of the teeth are ''involutes of a circle.'' The involute of a circle is the spiraling curve traced by the end of an imaginary taut string unwinding itself from that stationary circle called the base circle, or (equivalently) a triangle wave projected on the circumference of a circle. Advantages and design The involute gear profile, sometimes credited to Leonhard Euler, was a fundamental advance in machine design, since unlike with other gear systems, the tooth profile of an involute gear depends only on the number of teeth on the gear, pressure angle, and pitch. That is, a gear's profile does not depend on the gear it mates with. Thus, n and m tooth involute spur gears with a given pressure angle and pitch will mate correctly, independently of n and m. This dramatically reduces the number of shapes o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Involute Spur Gears Meshing
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. The evolute of an involute is the original curve. It is generalized by the roulette family of curves. That is, the involutes of a curve are the roulettes of the curve generated by a straight line. The notions of the involute and evolute of a curve were introduced by Christiaan Huygens in his work titled '' Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae'' (1673), where he showed that the involute of a cycloid is still a cycloid, thus providing a method for constructing the cycloidal pendulum, which has the useful property that its period is independent of the amplitude of oscillation. Involute of a parameterized curve Let \vec c(t),\; t\in _1,t_2 be a re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gear
A gear or gearwheel is a rotating machine part typically used to transmit rotational motion and/or torque by means of a series of teeth that engage with compatible teeth of another gear or other part. The teeth can be integral saliences or cavities machined on the part, or separate pegs inserted into it. In the latter case, the gear is usually called a cogwheel. A cog may be one of those pegsDefinition of "cog" in the ''Oxford Learner's Dictionary'' online. Accessed on 2024-07-29.Definition of "cog" in the ''Merriam-Webster Dictionary'' online. Accessed on 2024-07-29. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cycloid Gear
A cycloidal gear is a toothed gear with a cycloidal profile. Such gears are used in mechanical clocks and watches, rather than the involute gear form used for most other gears. Cycloidal gears have advantages over involute gears in such applications in being able to be produced flat (making them easier to polish, and thereby reduce friction), and having fewer points of contact (both reducing friction and wear). Their gear tooth profile is based on the epicycloid and hypocycloid curves, which are the curves generated by a circle rolling around the outside and inside of another circle, respectively. Characteristics When two toothed gears mesh, an imaginary circle, the ''pitch circle'', can be drawn around the centre of either gear through the point where their teeth make contact. The curves of the teeth outside the pitch circle are known as the ''addenda'', and the curves of the tooth spaces inside the pitch circle are known as the ''dedenda''. An addendum of one gear rests ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Involute
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the Locus (mathematics), locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. The evolute of an involute is the original curve. It is generalized by the Roulette (curve), roulette family of curves. That is, the involutes of a curve are the roulettes of the curve generated by a straight line. The notions of the involute and evolute of a curve were introduced by Christiaan Huygens in his work titled ''Horologium Oscillatorium, Horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae'' (1673), where he showed that the involute of a cycloid is still a cycloid, thus providing a method for constructing the cycloidal pendulum, which has the useful property that its period is independent of the amplitude of oscillation. Involute of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and Mathematical notation, notation, including the notion of a mathematical function. He is known for his work in mechanics, fluid dynamics, optics, astronomy, and music theory. Euler has been called a "universal genius" who "was fully equipped with almost unlimited powers of imagination, intellectual gifts and extraordinary memory". He spent most of his adult life in Saint Petersburg, Russia, and in Berlin, then the capital of Kingdom of Prussia, Prussia. Euler is credited for popularizing the Greek letter \pi (lowercase Pi (letter), pi) to denote Pi, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spur Gear
Spur gears or straight-cut gears are the simplest type of gear. They consist of a cylinder or disk with teeth projecting radially. Viewing the gear at 90 degrees from the shaft length (side on) the tooth faces are straight and aligned parallel to the axis of rotation. Looking down the length of the shaft, a tooth's cross section is usually not triangular. Instead of being straight (as in a triangle) the sides of the cross section have a curved form (usually involute and less commonly cycloidal) to achieve a constant drive ratio. Spur gears mesh together correctly only if fitted to parallel shafts. No axial thrust is created by the tooth loads. Spur gears are excellent at moderate speeds but tend to be noisy at high speeds. Spur gear can be classified into two pressure angles, 20° being the current industry standard and 14½° being the former (often found in older equipment). Spur gear teeth are manufactured as either involute In mathematics, an involute (also known as an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angle Of Pressure
In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight lines at a point. Formally, an angle is a figure lying in a plane formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle. More generally angles are also formed wherever two lines, rays or line segments come together, such as at the corners of triangles and other polygons. An angle can be considered as the region of the plane bounded by the sides. Angles can also be formed by the intersection of two planes or by two intersecting curves, in which case the rays lying tangent to each curve at the point of intersection define the angle. The term ''angle'' is also used for the size, magnitude or quantity of these types of geometric figures and in this context an angle consists of a number and unit of measurement. Angular measure or measure of angle are sometimes used to distinguish between the measurement and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backlash (engineering)
In mechanical engineering, backlash, sometimes called lash, play, or slop, is a Engineering tolerance, clearance or lost motion in a mechanism caused by gaps between the parts. It can be defined as "the maximum distance or angle through which any part of a mechanical system may be moved in one direction without applying appreciable force or motion to the next part in mechanical sequence."p. 1-8 An example, in the context of gears and gear trains, is the amount of clearance between mated gear teeth. It can be seen when the direction of movement is reversed and the slack or lost motion is taken up before the reversal of motion is complete. It can be heard from the railway couplings when a train reverses direction. Another example is in a valve train with mechanical tappets, where a certain range of lash is necessary for the valves to work properly. Depending on the application, backlash may or may not be desirable. Some amount of backlash is unavoidable in nearly all reversing me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limited-slip Differential
A limited-slip differential (LSD) is a type of differential gear train that allows its two output shafts to rotate at different speeds but limits the maximum difference between the two shafts. Limited-slip differentials are often known by the generic trademark Positraction, a brand name owned by General Motors and originally used for its Chevrolet branded vehicles. In an automobile, such limited-slip differentials are sometimes used in place of a standard differential, where they convey certain dynamic advantages, at the expense of greater complexity. Early history In 1932, Ferdinand Porsche designed a Grand Prix racing car for the Auto Union company. The high power of the design caused one of the rear wheels to experience excessive wheel spin at any speed up to . In 1935, Porsche commissioned the engineering firm ZF to design a limited-slip differential to improve performance. The ZF "sliding pins and cams" became available, and one example was the Type B-70 used during t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
