1. GEARS AND CAMS
C H A P T E R S E V E N T E E N

2. OBJECTIVES
1. Define the characteristics of a spur gear, worm gear, and bevel gear.
2. Calculate the gear ratio and rpm of two mating gears, given the
pitch diameters.
3. Define the principal spur gear terms.
4. Draw a spur gear.
5. Describe the relationship between a cam profile and a
displacement diagram.
6. Draw a cam profile, given a displacement profile drawing.
7. List the types of cam followers.

3. UNDERSTANDING GEARS
Friction Gears and Toothed Gears
The friction wheels can transmit motion and power from one shaft to another parallel shaft. However, friction wheels are subject to slipping, and a great deal of pressure is required between them to create the necessary frictional force; therefore, they are usually used for low-power applications, such as CD ROM drives. Spur gears have teeth on the cylindrical surfaces that fit together and transmit the same motion and power without slipping and with reduced bearing pressures.

4. Spur Gear Definitions and Formulas
Proportions and shapes of gear teeth are well standardized, and the terms illustrated are common to all spur gears.
(Courtesy of Big Sky Laser.)

5. CONSTRUCTING A BASE CIRCLE
The involute tooth form depends on the pressure angle, which was ordinarily 14.5° and is now typically 20° or 25°. This pressure angle determines the size of the base circle; from this the involute curve is generated.

6. THE INVOLUTE TOOTH SHAPE
If the exact shape of the tooth is desired, the portion of the profile from the base circle to the addendum circle can be drawn as the involute of the base circle.

7. SPACING GEAR TEETH
Space the teeth around the periphery by laying out equal angles. The number of spaces should be 2N, twice the number of teeth, to make the space between teeth equal to the tooth thickness at the pitch circle.
The Divide command in the AutoCAD software is very handy for dividing a circle or other geometry into any number of equal divisions. You can also use it to insert a block at the same time. A polar array is another useful tool for creating gears.

8. RACK TEETH
Gear teeth formed on a flat surface are called a rack. In the involute system, the sides of rack teeth are straight and are inclined at an angle equal to the pressure angle.
To mesh with a gear, the linear pitch of the rack must be the same as the circular pitch of the gear, and the rack teeth must have the same height proportions as the gear teeth.

9. WORKING DRAWINGS OF SPUR GEARS
Because the teeth are cut to standard shape, it is not necessary to show individual teeth on the drawing. Instead, draw the addendum and root circles as phantom lines and the pitch circle as a centerline.

10. SPUR GEAR DESIGN
Spur gear design normally begins with selecting pitch diameters to suit the required speed ratio, center distance, and space limitations. The size of the teeth (the diametral pitch) depends on the gear speeds, gear materials, horsepower to be transmitted, and the selected tooth form.

11. WORM GEARS Worm gearing offers a large speed ratio, since with one
revolution a single-thread worm advances the worm wheel only one tooth and a space.

12. WORKING DRAWINGS OF WORM GEARS
On detail drawings, the worm and gear are usually drawn separately, although their dimensioning depends on the production method, it is standard practice to dimension the blanks on the views and give the cutting data in a table.

13. BEVEL GEARS
Bevel gears are used to transmit power between shafts whose axes intersect.
Bevel Gears. (Courtesy of Stock Drive Products/ Sterling Instruments.)
The analogous friction drive would consist of a pair of cones with a common apex at the point where their axes intersect.

14. BEVEL GEAR DEFINITIONS AND FORMULAS
Because the design of bevel gears is very similar to that of spur gears, many spur gear terms are applied with slight modification to bevel gears. Just as in spur gears, the pitch diameter D of a bevel gear is the diameter of the base of the pitch cone, the circular pitch p to the teeth is measured along this circle and the diametral pitch P is also based on this circle.

15. WORKING DRAWINGS OF BEVEL GEARS
Like those for spur gears, working drawings of bevel gears give only the dimensions
of the gear blank. Data
necessary for cutting the
teeth are given in a note
or table. A single sectional
view will usually provide all
necessary information.

16. CAMS
Cams can produce unusual and irregular motions that would be difficult to produce otherwise.
A shaft rotating at uniform speed carries an irregularly shaped disk called a cam; a reciprocating member, called the cam follower, presses a small roller against the curved surface of the cam. (The roller is held in contact with the cam by gravity or a spring.) Rotating the cam causes the follower to reciprocate with a cyclic motion according to the shape of the cam profile.

17. CAM PROFILES The disk cam rotating counterclockwise
on its shaft raises and lowers the roller
follower, which is constrained to move
along the straight line AB.
With the follower in its lowest or initial position, the center of the roller is at A, and OA is the radius of the base circle.

18. OFFSET AND PIVOTED CAM FOLLOWERS
If the follower is offset, an offset circle is drawn with center O and radius equal to the amount of offset. As the cam turns, the
extended centerline of the follower will
always be tangent to this offset circle.
The equiangular spaces are stepped off
on the offset circle, and tangent lines are
then drawn from each point on the offset
Circle.

19. CYLINDRICAL CAMS
When the follower movement is in a plane parallel to the camshaft, some form of cylindrical cam must be employed.
… the follower rod moves vertically parallel to the cam axis as the attached roller follows the groove in the rotating cam cylinder.

20. GEARS USING AUTODESK INVENTOR DESIGN ACCELERATOR
When you know the design requirements for a gear pair, you can use a CAD package, such as Autodesk Inventor, to automatically generate the 3D models from the information. It can be very time-consuming to create drawings of gears and cams by hand, whereas using CAD frees you to spend more time on
other aspects of your designs.
(Autodesk screen shots reprinted with the permission of Autodesk, Inc.)