A sine bar consists of a hardened, precision ground body with two precision ground cylinders fixed at the ends. The distance between the centers of the cylinders is precisely controlled, and the top of the bar is parallel to a line through the centers of the two rollers. The dimension between the two rollers is chosen to be a whole number (for ease of later calculations) and forms the hypotenuse of a triangle when in use.

When a sine bar is placed on a level surface the top edge will be parallel to that surface. If one roller is raised by a known distance, usually using gauge blocks, then the top edge of the bar will be tilted by the same amount forming an angle that may be calculated by the application of the sine rule.

• The hypotenuse is a constant dimension—(100 mm or 10 inches in the examples shown).
• The height is obtained from the dimension between the bottom of one roller and the table's surface.
• The angle is calculated by using the sine rule. Some engineering and metalworking reference books contain tables showing the dimension required to obtain an angle from 0-90 degrees, incremented by 1 minute intervals.

${\displaystyle \sin \left(angle\right)={perpendicular \over hypotenuse}}$

Angles may be measured or set with this tool.

Principle

For example, to measure the angle of a wedge, the wedge is placed on the upper surface of sine bar. With use of slip gauge blocks, the taper surface of wedge is made parallel to the surface plate using dial gauge. The sine of the angle of inclination of the wedge is the ratio of the height of the gauge blocks used and the distance between the centers of the cylinders.

NOTE:

• Proof of any angle can be traced to
  • dividing the circle
  • the sine principle
• Sine principle uses the ratio of two sides of a right triangle in deriving a given angle
  • any scale may be employed, as the ratio of the sides is used
• Dividing the circle is based upon the fact that the circle can be divided into any equal number of parts
  • the accuracy of the circular division is proven when the circle is closed.

Types

The simplest type consists of a lapped steel bar, at each end of which is attached an accurate cylinder, the axis of cylinder being mutually parallel and parallel to the upper surface of the bar. In the advanced type some holes are drilled in the body of the bar to reduce the weight and facilitate handling.

Sine centre

A special type of sine bar is sine centre which is used for conical objects having male and female parts. It cannot measure the angle more than 45 degrees

Sine table

A sine table (or sine plate) is a large and wide sine bar, typically equipped with a mechanism for locking it in place after positioning, which is used to hold workpieces during operations.

Compound sine table

It is used to measure compound angles of large workpiece. In this case, two sine tables are mounted one over the other at right angles. The tables can be twisted to get the required alignment.