FORMULAS

Sine bars or sine plates usually have a length of 5 inches or 10 inches. These standard lengths are commonly used by the tool maker or inspector. The sine bar or sine plate is used for accurately setting up work for machining or for inspection. Gage blocks are usually used for establishing the height.

Rule for determining the height of the sine bar setting for a given angle: multiply the sine of the angle by the length of the sine bar. The sine of the angle is taken from the tables of trigonometric functions.

Problem: What would be the height to set a sine bar for establishing an angle of 230 41′? Solution: The sine of 23’41’ is 0.40168. Multiply this by 5 because a 5-inch sine bar is used; 5 x 0.40168 = 2.0084, which is the height to set the sine bar.

RULES FOR FIGURING TAPERS

TO FIND GIVEN RULE

Taper per inch Taper per foot Divide the taper per foot by 12.

Taper per foot Taper per inch Multiply the taper per inch by 12.

Taper per foot End diameters and length of taper in inches Subtract small diameter from large, divided by length of taper, and multiply quotient by 12.

Diameter at small end in inches Large diametre, length of taper in inches, and taper foot Divide taper per foot by 12, multiply by length of taper, and subtract from large diameter.

Diameter at large end in inches Small diameter, length of taper in inches, and taper per foot Divide taper per foot by 12, multiply by length of taper, and add results to small diameter.

Distance between two given diameters in inches Taper per foot and two diameters in inches Subtract small diameter from large, divide remainder by taper per foot and multiply quotient by 12.

Amount of taper in a certain length given in inches Taper per foot Divide taper per foot by 12 and multiply by given length of tappered part

To find the circumference of a circle Pi x D or D/0.3183.

To find the diameter of a circle 0.31831 x C or C/Pi

To find the area of a circle Pir2.

To find size of round stock needed to machine a hexagon, D = 1.1547 x distance across the flats

To find size of round stock needed to machine a square, D = 1.4142 x distance across the flats

To find the area of a square, square one side

To find the area of a rectangle, multiply length times width

To find the volume of a cube, multiply length times width times depth

To find the volume of a square prism, multiply length times width times depth

To find the volume of a cylinder, multiply Pi times radius squared times height

To find the area of a triangle, multiply base times height divided by 2

To find the area of a ring, subtract the area of inside diameter from the area of the outside diameter.