Robotic Mechanisms – GEARS and GEARING 51030

A gear is a wheel with evenly sized and spaced teeth machined or formed around its perimeter. Gears are used in rotating machinery not only to transmit motion from one point to another, but also for the mechanical advantage they offer. Two or more gears transmitting motion from one shaft to another is called a gear train, and gearing is a system of wheels or cylinders with meshing teeth. Gearing is chiefly used to transmit rotating motion but can also be adapted to translate reciprocating motion into rotating motion and vice versa.

Gears are versatile mechanical components capable of performing many different kinds of power transmission or motion control.

Examples of these are:

• Changing Rotational Speed
• Changing Rotational Direction
• Changing the angular orientation of rotational motion
Multiplication or division of torque or magnitude of rotation
• Converting rotational to linear motion, and its reverse
Offsetting or changing the location of rotating motion



The teeth of a gear can be considered as levers when they mesh with the teeth of an adjoining gear. However, gears can be rotated continuously instead of rocking back and forth through short distances as is typical of levers. A gear is defined by the number of its teeth and its diameter. The gear that is connected to the source of power is called the driver, and the one that receives power from the driver is the driven gear. It always rotates in a direction opposing that of the driving gear; if both gears have the same number of teeth, they will rotate at the same speed. However, if the number of teeth differs, the gear with the smaller r number of teeth will rotate faster. The size and shape of all gear teeth that are to mesh properly for working contact must be equal.

Simple Gear Trains

A gear train made up of multiple gears can have several drivers and several driven gears. If the train contains anodd number of gears, the output gear will rotate in the same direction as the input gear, but if the train contains an even number of gears, the output gear will rotate opposite that of the input gear. The number of teeth on the intermediate gears does not affect the overall velocity ratio, which is governed purely by the number of teeth on the first and last gear.

In simple gear trains, high or low gear ratios can only be obtained by combining large and small gears. In the simplest basic gearing involving two gears, the driven shaft and gear revolves in a direction opposite that of the driving shaft and gear. If it is desired that the two gears and shafts rotate in the same direction, a third idler gear must be inserted between the driving gear and the driven gear. The idler revolves in a direction opposite that of the driving gear.


Compoung Gear Trains

More complex compound gear trains can achieve high and low gear ratios in a restricted space by coupling large and small gears on the same axle. In this way gear ratios of adjacent gears can be multiplied through the gear train.

Figure below shows a set of compound gears with the two gears B and D mounted on the middle shaft. Both rotate at the same speed because they are fastened together. If gear A (80 teeth) rotates at 100 rpm clockwise, gear B (20 teeth) turns at 400 rpm counterclockwise because of its velocity ratio of 1 to 4. Because gear D (60 teeth) also turns at 400 rpm and its velocity ratio is 1 to 3 with respect to gear C (20 teeth), gear C will turn at 1200 rpm clockwise. The velocity ratio of a compound gear train can be calculated by multiplying the velocity ratios for all pairs of meshing gears.

For example, if the driving gear has 45 teeth and the driven gear has 15 teeth, the velocity ratio is 15/45  1/3.

Torque on Gears

Gear Classification

Go to Robotic Mechanisms – TYPES of GEARS 51034 Page

Gear Tooth Geometry

Gear Terminology

Addendum: The radial distance between the top land and the pitch circle. This distance is measured in inches or millimeters.
Addendum Circle: The circle defining the outer diameter of the gear.
Circular Pitch: The distance along the pitch circle from a point on one tooth to a corresponding point on an adjacent tooth. It is also the sum of the tooth thickness and the space width. This distance is measured in inches or millimeters.
Clearance: The radial distance between the bottom land and the clearance circle. This distance is measured in inches or millimeters.

Contact Ratio: The ratio of the number of teeth in contact to the number of teeth not in contact.
Dedendum: The radial distance between the pitch circle and the dedendum circle. This distance is measured in inches or millimeters.
Dedendum Circle: The theoretical circle through the bottom lands of a gear.
Depth: A number standardized in terms of pitch. Full-depth teeth have a working depth of 2/P. If the teeth have equal addenda (as in standard interchangeable gears), the addendum is 1/P. Full-depth gear teeth have a larger contact ratio than stub teeth, and their working depth is about 20 percent more than stub gear teeth. Gears with a small number of teeth might require undercutting to prevent one interfering with another during engagement.
Diametral Pitch (P): The ratio of the number of teeth to the pitch diameter. A measure of the coarseness of a gear, it is the index of tooth size when U.S. units are used, expressed as teeth per inch.

Pitch: A standard pitch is typically a whole number when measured as a diametral pitch (P). Coarse pitch gears have teeth larger than a diametral pitch of 20 (typically 0.5 to 19.99). Fine-pitch gears usually have teeth of diametral pitch greater than 20. The usual maximum fineness is 120 diametral pitch, but involute-tooth gears can be made with diametral pitches as fine as 200, and cycloidal tooth gears can be made with diametral pitches to 350.

Pitch Circle: A theoretical circle upon which all calculations are based.
Pitch Diameter: The diameter of the pitch circle, the imaginary circle that rolls without slipping with the pitch circle of the mating gear, measured in inches or millimeters.
Pressure Angle: The angle between the tooth profile and a line perpendicular to the pitch circle, usually at the point where the pitch circle and the tooth profile intersect. Standard angles are 20° and 25°. It affects the force that tends to separate mating gears. A high pressure angle decreases the contact ratio, but it permits the teeth to have higher capacity and it allows gears to have fewer teeth without undercutting.

Gear Dynamics Terminology

Backlash: The amount by which the width of a tooth space exceeds the thickness of the engaging tooth measured on the pitch circle. It is the shortest distance between the noncontacting surfaces of adjacent teeth.
Gear Efficiency: The ratio of output power to input power taking into consideration power losses in the gears and bearings and from windage and the churning of the gear lubricant.
Gear Power: A gear’s load and speed capacity. It is determined by gear dimensions and type. Helical and helical-type gears have capacities to approximately 30,000 hp, spiral bevel gears to about 5000 hp, and worm gears to about 750 hp.
Gear Ratio: The number of teeth in the larger gear of a pair divided by the number of teeth in the pinion gear (the smaller gear of a pair). It is also the ratio of the speed of the pinion to the speed of the gear. In reduction gears, the ratio of input speed to output speed.
Gear Speed: A value determined by a specific pitchline velocity. It can be increased by improving the accuracy of the gear teeth and the balance of all rotating parts.
Undercutting: The recessing in the bases of gear tooth flanks to improve clearance.

Gear Terms

Alloy Steel A steel containing another material that is added intentionally to improve certain properties of the metal.
Aluminum Alloy A silvery white metal that is soft, light, and has a high strength-to-weight ratio.
Automatic Transmission A complex transmission that does not require the operator to shift gears in order to change the speed and torque of mechanical energy.
Axis An imaginary straight line that passes through the center of an object. A gear may have an opening at its axis through which a shaft can be inserted.
Belt Drive System A system consisting of a belt and at least two fixed pulleys that is used to transmit motion.
Bevel Gear A type of gear with cone-shaped teeth cut at an angle. Bevel gears are often used in angular gear trains.
Breakage The fracture of part or all of a gear tooth caused by excess load and gear stress.
Carbon Steel Steel that is made up of iron and carbon, without any additional materials.
Chain Drive System A system consisting of a chain and sprockets that is used to transmit motion.
Conical Cone-shaped, with a cylindrical base and pointed tip. The teeth of some bevel gears are conical.
Corrode To deteriorate the useful properties in a material due to oxidation.
Corrosion The gradual chemical attack on a material by atmosphere, moisture, or other agents. Some chains are designed to resist corrosion.
Cylindrical Configuration A worm gear drive configuration that uses a cylindrical worm to mesh with a cylindrical helical gear. Cylindrical configurations offer high speed reduction ratios but can be used only with light loads.
Double Helical Gear A type of helical gear with two sets of teeth cut at opposing angles, separated by a groove that runs around the center of the gear. Double helical gears are used to provide smoother operation and avoid side loads.
Double-Enveloping Configuration A worm gear drive configuration that uses an hourglass-shaped worm with curved teeth to wrap around part of the worm gear. This configuration provides the highest amount of tooth contact and can carry the greatest amount of load.
Drip-Feed System A type of lubricant delivery system that includes a small reservoir of lubricant connected to pipes that distribute the lubricant to machine parts.
Drive Gear The gear that receives energy from a power source, such as an electric motor. A drive gear transmits power to a meshing driven gear to perform work.
Driven Gear The gear that receives motion from the drive gear on a machine. Driven gears often turn tools or components.
Efficiency A measure of the work output of a system versus the total work supplied to it.
Enclosed Gear Drive A system of assembled gears encased by a housing that transmits mechanical energy from a prime mover to an output device, also known as a gearbox.
Epicyclic Gear Train A gear train that consists of one or more outer gears rotating around a central gear. Epicylic gear trains are also known as planetary gear trains.
Ferrous Metals Metals that contain iron. Ferrous metals are commonly used to make gears.
Gear A round or cylindrical mechanical component with teeth, used to transmit power. Gears are designed to intersect with one another and can alter the speed, torque, or direction of mechanical energy.
Gear Train A system of gears used to transmit rotary motion from one part of a mechanical system to another.
Gearbox An enclosed system of assembled gears that transmits mechanical energy from a prime mover to an output device, also known as an enclosed gear drive.
Gradual Wear A type of gear failure that involves the removal of material from the surfaces of the gear teeth. Gradual wear can be reduced through the use of lubricants.
Hardness A material’s ability to resist penetration, indentation, or scratching. Hard materials tend to be very strong and resistant to wear.
Helical Gear A type of gear with slanted teeth. Helical gears are quieter than spur gears, but they are more expensive and produce side loads.
Helix Angle The angle between the axis of a helical gear and an imaginary line that is tangent to the gear tooth. Helix angles can vary in size from 0° to 90 degrees.
Herringbone Gear A type of gear that has angled teeth in the shape of a letter “V.” Herringbone gears resist side loading but are expensive to produce.
Idler Gear A gear that is used to keep the direction of motion consistent between a drive gear and a driven gear.
Input Shaft The rotating shaft that receives power from the power source and introduces it into a mechanical system.
Internal Gear A circular gear with teeth that face inward, used to mesh with planet gears in a planetary gear train. Also known as a ring gear.
Involute Curve The path determined by tracing a point on a line that is unwound from a circle.
Left-Hand Helical Gear A helical gear with teeth that lean to the left when the gear is placed on a flat, horizontal surface.
Linear Motion Motion that takes place along a straight line.
Lockout/Tagout A method of protecting employees from accidental machine startup through proper locking and labeling of machines that are undergoing maintenance.
Lubricant A substance used to reduce friction between two surfaces in relative motion. Oil and grease are common industrial lubricants.
Lubrication The act of applying lubricant to machines. Lubrication reduces friction and wear between mechanical components.
Mechanical Advantage The difference between the applied force and the work accomplished. Mechanical advantage allows machines to perform more work with less effort.
Meshing The action of interlocking with another object. Meshing gears are used to transmit mechanical energy.
Miter Gear A type of bevel gear used in pairs with intersecting shafts at 90° angles. Both the driving gear and driven gear in a miter gear pair have the same diameter, same number of teeth, and a mechanical advantage of 1.
Nip Point The point where two gears mesh, which can pinch or crush fingers or other body parts.
Nonferrous Metals Metals that do not intentionally contain iron.
Nonmetallic Materials Materials that are not made of metal, such as wood and plastic. Nonmetallic materials can be used to make gears, though they are not as common.
Open Gearing Gears in an unassembled form.
Output Shaft The rotating shaft that receives power from the mechanical system and transfers it to the output source.
Personal Protective Equipment Safety equipment that a person wears or uses to prevent injury in the workplace. Personal protective equipment is abbreviated as PPE.
Pinion A circular gear used in a rack and pinion system to produce linear motion. As the pinion turns, the flat rack slides in a linear direction.
Pitch A property used to classify gears. Pitch usually refers to the number of gear teeth in one inch of the gear’s pitch diameter.
Pitch Diameter The diameter of a gear’s pitch circle. A gear’s pitch diameter can be determined by measuring from the top of one gear tooth to the bottom of the opposite gear tooth.
Pitting The corrosion of a metal that takes place in specific locations on a workpiece or component.
Planet Arm A moveable arm that rotates around the sun gear on which planet gears can be mounted.
Planet Gear An outer gear in a planetary gear train that rotates around the sun gear. A planet gear can be mounted on a moveable planet arm that also rotates around the sun gear.
Planetary Gear Train A gear train that consists of one or more outer gears rotating around a central gear. Planetary gear trains are also known as epicyclic gear trains.
Plastic Flow A gear failure condition in which the gear teeth deform due to heavy loads.
Pressure Angle The angle made by the sides of a gear tooth as they incline toward the top of the gear.
Rack A flat bar with teeth used in a rack and pinion system to produce linear motion. As the circular pinion turns, the rack slides in a linear direction.
Rack And Pinion A pair of gears used to convert rotary motion into linear motion. A rack and pinion consists of a circular gear, or pinion, that meshes with a flat-toothed bar, or rack.
Right Angle An angle that measures exactly 90 degrees.
Right-Hand Helical Gear A helical gear with teeth that lean to the right when the gear is placed on a flat, horizontal surface.
Ring Gear A circular gear with teeth that face inward, used to mesh with planet gears in a planetary gear train. Also known as an internal gear.
Rotary Motion Spinning or turning motion that takes place around an axis, without a change in linear position.
Shaft In a mechanical system, a cylindrical bar used to support rotating components or to transmit power or motion by rotation.
Side Load A force that occurs when gears are meshed together at an angle. Side load can lead to deflection and wear.
Single-Enveloping Configuration A worm gear drive configuration that uses a gear with curved teeth to wrap around part of the worm. This configuration provides more contact between the worm and worm gear teeth and can carry more load.
Skew Tooth Gear A type of bevel gear with teeth that are straight and cut at an angle to the axis of the gear shaft. Skew tooth gears can carry more load than straight bevel gears and are generally made in large sizes.
Spalling A severe form of pitting that occurs when large pits develop over a considerable area of the gear.
Speed The amount of distance an object travels in a given period of time. Speed is used to measure both linear and rotational movement.
Speed Increasers A gearbox used to increase the speed of mechanical energy while decreasing the torque. Speed increasers are not used as often as speed reducers.
Speed Reducer A gearbox used to reduce the speed of mechanical energy while increasing the torque. Worm gear drives are often used in speed reducers.
Speed Reduction A process during which the speed of mechanical energy is reduced during power transmission. Speed reduction increases the torque of mechanical energy and is often accomplished with a worm gear drive.
Spiral Angle The angle at which spiral bevel gear teeth are set from the gear shaft axis. The spiral angle of most bevel gears is 35 degrees.
Spiral Bevel Gear A type of bevel gear with conical and curved teeth, designed for smooth operation. The teeth of spiral bevel gears have a spiral angle.
Splash Lubrication A type of lubrication used in enclosed gear drives. In splash lubrication, the gear tooth dips into a tray of lubricant and transfers the lubricant to the meshing gear as it rotates.
Spur Gear A type of gear that has straight, flat-topped teeth set parallel to the shaft. Spur gears are the most common type of gears used in industry.
Stainless Steel An alloy steel that is designed to resist corrosion.
Straight Bevel Gear The basic bevel gear, which has tapered teeth that are widest at their outer part. Straight bevel gears are cost-effective when transmitting power between shafts at right angles.
Sun Gear The central gear in a planetary gear train around which the planet gears rotate.
Surface Fatigue A gear failure condition in which small pieces of metal have been removed from the gear, leaving indentations, or pits, in the surface.
Titanium Alloy A metal containing titanium, which is a silver-gray, strong, and lightweight metal known for its corrosion resistance.
Torque A force that produces rotation. Gears can transmit high levels of torque.
Toughness The ability of a material to withstand forces or sudden impacts that attempt to break it.
Wear The gradual removal of material on a surface caused by contact between microscopic peaks on surfaces in motion.
Worm A cylindrical, screw-shaped shaft that is used with a worm gear to transmit motion.
Worm Gear A gear with teeth that mesh with the screw-like threads of a worm to transmit motion.
Worm Gear Drive A gear drive consisting of a long, cylindrical device with a spiraling groove that intersects with the teeth of a wheel-like gear. A worm gear drive is used to transmit motion between nonintersecting perpendicular shafts, and the cylindrical “worm” is always the drive gear.
Wrap Point An exposed rotating shaft with the potential to become caught on clothing, pulling a person toward the machinery and potentially causing injury.
Zerol Bevel Gear A type of bevel gear with curved teeth and a 0° spiral angle. Zerol bevel gears provide smooth and quiet operation, but they produce side loads.


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