# 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

## TEETH of a GEAR

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 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.