Sites:

## 7.1 INVOLUTE FUNCTION CALCULATIONS

Involute functions are used in some of the equations required to perform involute gear design. These functional values of the involute curve are easily calculated with the aid of the pocket calculator. Refer to the following text for the procedure required to calculate the involute function.

The Involute Function: inv = tan arc . The involute function is widely used in gear calculations. The angle for which involute tables are tabulated is the slope of the involute with respect to a radius vector R (see Fig. 7.1).

Figure 7.1: Involute geometry.

Involute Geometry (See Fig. 7.1). The involute of a circle is defined as the curve traced by a point on a straight line which rolls without slipping on the circle. It is also described as the curve generated by a point on a nonstretching string as it is unwound from a circle. The circle is called the base circle of the involute. A single involute curve has two branches of opposite hand, meeting at a point on the base circle, where the radius of curvature is zero. All involutes of the same base circle are congruent and parallel, while involutes of different base circles are geometrically similar.

Figure 7.1 shows the elements of involute geometry. The generating line was originally in position G 0, tangent to the base circle at P 0. The line then rolled about the base circle through the...

##### Products & Services
Gear Cutters and Hobs
Gear cutters and hobs are tools for machining gear-tooth profiles.
Gearboxes and gearheads, also called gear reducers or speed reducers, are power transmission devices that use a gear arrangement in an enclosed housing to transfer energy, increase torque and reduce speed from one device to another. Gearboxes may also be referred to as gear reducers or speed reducers.
Spline Shafts
A spline shaft has either grooves or tongues machined along its length. The mating bearings run along either the groove or tongue, providing high rigidity. There are two main types of spline shafts, parallel key spline shafts and involute spline shafts.
Fixed Gages
Fixed gages are designed to access a specific attribute based on comparative gaging. These gages are used for quickly assessing approximate size in a go / no-go manner.
Bevel and Miter Gears

Bevel gears are gears designed to transmit motion between intersecting axes. Perpendicular arrangements are most common, but bevel gears can be manufactured for nearly any angle. The teeth bearing surface of the gear, or surface pitch, is conically shaped or tapered. Miter gears are bevel gears manufactured in a 1:1 ratio, with the same number of teeth on mating gears and with perpendicular axes.

##### Topics of Interest

8.1 RATCHETS AND RATCHET GEARING A ratchet is a form of gear in which the teeth are cut for one-way operation or to transmit intermittent motion. The ratchet wheel is used widely in machinery and...

15.1 INTRODUCTION Involute gears, spur and helical ones, are widely used in reducers, planetary gear trains, transmissions, and many other industrial applications. The level of sophistication in the...

13.1 INTRODUCTION The predecessor of involute gearing is the cycloidal gearing that has been broadly used in watch mechanisms. Involute gearing has replaced cycloidal gearing in many areas but not...

19.6 GENERATION AND GEOMETRY OF ZI (INVOLUTE) WORMS Surface Equations The worm surface is generated by a straight line that performs a screw motion and is tangent to the helix M o M on the base...

16.1 INTRODUCTION Involute helical gears are widely applied in the industry for transformation of rotation between parallel and crossed axes. Figure 16.1.1 shows an involute helical gear drive with...

Product Announcements