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 In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse e ...

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 block Gauge blocks (also known as gage blocks, Johansson gauges, slip gauges, or Jo blocks) are a system for producing precision lengths. The individual gauge block is a metal or ceramic block that has been precision ground and lapped to a specific ...

s, 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 In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, \frac \,=\, \frac \,=\, \frac \,=\, 2R, where , and are ...

. * 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 (a

trigonometric function In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in a ...

from mathematics). 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.

\sin \left(angle \right) =

Angles may be measured or set with this tool.

Principle

Angles are measured using a sine bar with the help of gauge blocks and a dial gauge or a

spirit level A spirit level, bubble level, or simply a level, is an instrument designed to indicate whether a surface is horizontal (level) or vertical ( plumb). Different types of spirit levels may be used by carpenters, stonemasons, bricklayers, ...

. The aim of a measurement is to measure the surface on which the dial gauge or spirit level is placed horizontally. For example, to measure the angle of a

wedge A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converti ...

, the wedge is placed on a horizontal table. The sine bar is placed over the inclined surface of the wedge. At this position, the top surface of the sine bar is inclined the same amount as the wedge. Using gauge blocks, the top surface is made horizontal. 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.

Types

The simplest type consists of a

lapped Lapping is a machining process in which two surfaces are rubbed together with an abrasive between them, by hand movement or using a machine. Lapping often follows other subtractive processes with more aggressive material removal as a first step ...

steel bar, at each end of which is attached an accurate cylinder, the axes of the cylinders 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 center which is used for conical objects having male and female parts. It cannot measure the angle more than 60 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.

References

Metalworking measuring instruments {{Commons category, Sine bars