![Two involute gears, the left driving the right: Blue arrows show the contact forces between them (1) downward force applied by the left gear and (2) upward resistance by the right gear. The force line (or line of action) runs along the long leg of dashed blue line which is a tangent common to both base circles. The involutes here are traced out in converse fashion: points of contact move along the stationary force-vector "string" as if it was being unwound from the left rotating base circle, and wound onto the right rotating base circle. In this situation, there is no force, and so no contact needed, along the opposite [lower left to upper right] common tangent (not shown). In other words, if the teeth were slightly narrower while everything else remained the same there would be a gap above each tooth on the left gear, because downward force is being applied by it. Involute wheel.gif](http://upload.wikimedia.org/wikipedia/commons/c/c2/Involute_wheel.gif)
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.
The involute gear profile, sometimes credited to Leonhard Euler, [1] 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 of gears that need to be manufactured and kept in inventory.
In involute gear design, contact between a pair of gear teeth occurs at a single instantaneous point (see figure at right) where two involutes of the same spiral hand meet. Contact on the other side of the teeth is where both involutes are of the other spiral hand. Rotation of the gears causes the location of this contact point to move across the respective tooth surfaces. The tangent at any point of the curve is perpendicular to the generating line irrespective of the mounting distance of the gears. Thus the line of the force follows the generating line, and is thus tangent to the two base circles, and is known as the line of action (also called pressure line or line of contact). When this is true, the gears obey the fundamental law of gearing: [2]
The angular velocity ratio between two gears of a gearset must remain constant throughout the mesh.
This property is required for smooth transmission of power with minimal speed or torque variations as pairs of teeth go into or come out of mesh, but is not required for low-speed gearing.
Where the line of action crosses the line between the two centres, it is called the pitch point of the gears, where there is no sliding contact.
The distance actually covered on the line of action is then called line of contact. The line of contact begins at the intersection between the line of action and the addendum circle of the driven gear and ends at the intersection between the line of action and the addendum circle of the driving gear. [3]
The pressure angle is the acute angle between the line of action and a normal to the line connecting the gear centers. The pressure angle of the gear varies according to the position on the involute shape, but pairs of gears must have the same pressure angle in order for the teeth to mesh properly, so specific portions of the involute must be matched.
While any pressure angle can be manufactured, the most common stock gears have a 20° pressure angle, with 14½° and 25° pressure angle gears being much less common. [4] Increasing the pressure angle increases the width of the base of the gear tooth, leading to greater strength and load carrying capacity. Decreasing the pressure angle provides lower backlash, smoother operation and less sensitivity to manufacturing errors. [5]
Most common stock gears are spur gears, with straight teeth. Most gears used in higher-strength applications are helical involute gears where the spirals of the teeth are of different hand, and the gears rotate in opposite direction. Also there are various researches on gears with a teeth with non-involute curve profile. [6] [7] [8]
Only used in limited situations are helical involute gears where the spirals of the teeth are of the same hand, and the spirals of the two involutes are of different "hand" and the line of action is the external tangents to the base circles (like a normal belt drive whereas normal gears are like a crossed-belt drive), and the gears rotate in the same direction, [9] such as can be used in limited-slip differentials [ clarification needed ] [10] [11] because of their low efficiencies, and in locking differentials when the efficiencies are less than zero.
A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth, which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic principle behind the operation of gears is analogous to the basic principle of levers. A gear may also be known informally as a cog. Geared devices can change the speed, torque, and direction of a power source. Gears of different sizes produce a change in torque, creating a mechanical advantage, through their gear ratio, and thus may be considered a simple machine. The rotational speeds, and the torques, of two meshing gears differ in proportion to their diameters. The teeth on the two meshing gears all have the same shape.
A rack and pinion is a type of linear actuator that comprises a circular gear engaging a linear gear. Together, they convert between rotational motion and linear motion. Rotating the pinion causes the rack to be driven in a line. Conversely, moving the rack linearly will cause the pinion to rotate. A rack-and-pinion drive can use both straight and helical gears. Though some suggest helical gears are quieter in operation, no hard evidence supports this theory. Helical racks, while being more affordable, have proven to increase side torque on the datums, increasing operating temperature leading to premature wear. Straight racks require a lower driving force and offer increased torque and speed per fraction of gear ratio which allows lower operating temperature and lessens viscal friction and energy use. The maximum force that can be transmitted in a rack-and-pinion mechanism is determined by the torque on the pinion and its size, or, conversely, by the force on the rack and the size of the pinion.
Hobbing is a machining process for gear cutting, cutting splines, and cutting sprockets using a hobbing machine, a specialized milling machine. The teeth or splines of the gear are progressively cut into the material by a series of cuts made by a cutting tool called a hob.
In mathematics, an involute 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.
In geometry, a tractrix is the curve along which an object moves, under the influence of friction, when pulled on a horizontal plane by a line segment attached to a pulling point that moves at a right angle to the initial line between the object and the puller at an infinitesimal speed. It is therefore a curve of pursuit. It was first introduced by Claude Perrault in 1670, and later studied by Isaac Newton (1676) and Christiaan Huygens (1693).
A non-circular gear (NCG) is a special gear design with special characteristics and purpose. While a regular gear is optimized to transmit torque to another engaged member with minimum noise and wear and with maximum efficiency, a non-circular gear's main objective might be ratio variations, axle displacement oscillations and more. Common applications include textile machines, potentiometers, CVTs, window shade panel drives, mechanical presses and high torque hydraulic engines.
Edwin R. Fellows was an American inventor and entrepreneur from Torrington, Connecticut who designed and built a new type of gear shaper in 1896 and, with the mentoring of James Hartness, left the Jones & Lamson Machine Company to co-found the Fellows Gear Shaper Company in Springfield, Vermont, which became one of the leading firms in the gear-cutting segment of the machine tool industry. Fellows' machines made a vital contribution to the mass production of effective and reliable gear transmissions for the nascent automotive industry. By the conclusion of World War II, Fellows Gear Shaper Company machines were in defense contractor plants, manufacturing geared components for aircraft engines, tanks, instruments, cameras, fuses and other war-time materiel.
A gear train or gear set is a machine element of a mechanical system formed by mounting two or more gears on a frame such that the teeth of the gears engage.
A worm drive is a gear arrangement in which a worm meshes with a worm wheel. The two elements are also called the worm screw and worm gear. The terminology is often confused by imprecise use of the term worm gear to refer to the worm, the worm wheel, or the worm drive as a unit.
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, and having fewer points of contact.
Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing faces of the gears themselves are conically shaped. Bevel gears are most often mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well. The pitch surface of bevel gears is a cone, known as a pitch cone. Bevel gears transfer the energy from linear to vertical power, making it very useful in machines widely used in mechanical settings.
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 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 the sides of the cross section have a curved form 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.
In mechanical engineering, backlash, sometimes called lash, play, or slop, is a 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.
Pressure angle in relation to gear teeth, also known as the angle of obliquity, is the angle between the tooth face and the gear wheel tangent. It is more precisely the angle at a pitch point between the line of pressure and the plane tangent to the pitch surface. The pressure angle gives the direction normal to the tooth profile. The pressure angle is equal to the profile angle at the standard pitch circle and can be termed the "standard" pressure angle at that point. Standard values are 14.5 and 20 degrees. Earlier gears with pressure angle 14.5 were commonly used because the cosine is larger for a smaller angle, providing more power transmission and less pressure on the bearing; however, teeth with smaller pressure angles are weaker. To run gears together properly their pressure angles must be matched.
A duplex worm or dual lead worm is a worm gear set where the two flanks are manufactured with slightly different modules and/or diameter quotients. As a result of this, different lead angles on both tooth profiles are obtained, so that the tooth thickness is continuously increasing all over the worm length, while the gap between two threads is decreasing. This allows control of backlash.
The profile angle of a gear is the angle at a specified pitch point between a line tangent to a tooth surface and the line normal to the pitch surface. This definition is applicable to every type of gear for which a pitch surface can be defined. The profile angle gives the direction of the tangent to a tooth profile.
A spiral bevel gear is a bevel gear with helical teeth. The main application of this is in a vehicle differential, where the direction of drive from the drive shaft must be turned 90 degrees to drive the wheels. The helical design produces less vibration and noise than conventional straight-cut or spur-cut gear with straight teeth.
In engineering, a mechanism is a device that transforms input forces and movement into a desired set of output forces and movement. Mechanisms generally consist of moving components which may include:
In mechanical engineering, kinematic synthesis determines the size and configuration of mechanisms that shape the flow of power through a mechanical system, or machine, to achieve a desired performance. The word synthesis refers to combining parts to form a whole. Hartenberg and Denavit describe kinematic synthesis as
...it is design, the creation of something new. Kinematically, it is the conversion of a motion idea into hardware.