Pressure angle in relation to gear teeth, also known as the angle of obliquity, [1] 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 (which is normal to the tooth surface) 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. [2] 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. [3]
The pressure angle is also the angle of the sides of the trapezoidal teeth on the corresponding rack. The force transmitted during the mating of gear teeth acts along the normal. This force has components along the pitch line and the other along the line perpendicular to the pitch line. The force along the pitch line which is responsible for power transmission is proportional to the cosine of pressure angle. The one which exerts thrust (perpendicular to the pitch line) is proportional to the sine of pressure angle. So it is advised to keep the pressure angle low.
Just as there are three types of profile angle, there are three types of corresponding pressure angle: the transverse pressure angle, the normal pressure angle, and the axial pressure angle. [4]
A cam is a rotating or sliding piece in a mechanical linkage used especially in transforming rotary motion into linear motion. It is often a part of a rotating wheel or shaft that strikes a lever at one or more points on its circular path. The cam can be a simple tooth, as is used to deliver pulses of power to a steam hammer, for example, or an eccentric disc or other shape that produces a smooth reciprocating motion in the follower, which is a lever making contact with the cam. A cam timer is similar, and were widely used for electric machine control before the advent of inexpensive electronics, microcontrollers, integrated circuits, programmable logic controllers and digital control.
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 rotational power. While doing so, they can change the torque and rotational speed being transmitted and also change the rotational axis of the power being transmitted. The teeth on the two meshing gears all have the same shape.
In geometry, a normal is an object that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the line perpendicular to the tangent line to the curve at the point.
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.
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.
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 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.
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 change the axis of rotation of rotational power delivery and are 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.
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 Gears and gear trains; Belts and chain drives; cams and followers; Linkages; Friction devices, such as brakes or clutches; Structural components such as a frame, fasteners, bearings, springs, or lubricants; Various machine elements, such as splines, pins, or keys.
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.