Understanding Angle Measuring Devices in Measurement

In various fields like engineering, manufacturing, and drafting, accurately measuring and setting angles is crucial. Different tools are used for different measurement purposes, including measuring angles, lengths, or transferring dimensions. Let's examine the given options to identify which one is specifically used for measuring angles.

Analyzing the Options

Let's look at the function of each tool provided in the options:

• Trammel: A trammel is a tool used primarily for drawing large circles or arcs. It consists of a beam with two adjustable points that can be set to a desired radius. It is also used for transferring large distances. It is not an angle measuring device.
• Hermaphrodite calipers: These calipers have one leg pointed like a divider and the other leg shaped like a caliper leg (with a curved foot). They are used for scribing lines parallel to an edge or for finding the center of round bars. They are not an angle measuring device.
• Divider: A divider is a tool with two pointed legs, joined at a pivot. It is used for transferring distances, stepping off equal divisions along a line or curve, or scribing circles and arcs of smaller radii compared to a trammel. It is not an angle measuring device.
• Sine bar: A sine bar is a precision measuring instrument used to measure or set angles accurately. It works based on the trigonometric principle of sine. It is typically used in conjunction with gauge blocks (slip gauges) to create a specific angle relative to a surface plate. The height of the gauge blocks placed under one roller, divided by the length of the sine bar (distance between roller centers), gives the sine of the angle.

Based on the functions described, the sine bar is the only device among the given options that is used for measuring or setting angles.

How a Sine Bar Measures Angles

A sine bar consists of a hardened and ground steel bar with two precision rollers of equal diameter fixed at the ends. The distance between the centers of these rollers is the nominal length of the sine bar (e.g., 100 mm, 200 mm, 10 inches). To measure an angle, the sine bar is placed on a flat surface plate. The workpiece whose angle is to be measured is placed on top of the sine bar. Gauge blocks are then carefully inserted under one of the rollers until the top surface of the sine bar (or the workpiece resting on it) is parallel to the surface plate. The parallelism is usually checked using a dial indicator or other sensitive comparison instrument.

The angle (\(\theta\)) is calculated using the formula:

\[ \sin(\theta) = \frac{\text{Height of Gauge Blocks (H)}}{\text{Length of Sine Bar (L)}} \]

Where:

• \(H\) is the total height of the gauge blocks used.
• \(L\) is the distance between the centers of the sine bar rollers.

From this, the angle can be found using \( \theta = \arcsin\left(\frac{H}{L}\right) \). This method allows for very precise angle measurements.

Conclusion

Among the given options – Trammel, Hermaphrodite calipers, Divider, and Sine bar – only the Sine bar is designed and used as an angle measuring device, especially for achieving high precision.

Revision Table: Workshop Measuring Tools

Additional Information: Precision Angle Measurement

While a protractor is a common tool for angle measurement, precision tasks in manufacturing require more accurate methods. Tools like sine bars, angle gauges, and autocollimators are used for higher precision angle measurement. The sine bar, particularly when used with certified gauge blocks and a sensitive indicator on a stable surface plate, can measure angles with very high accuracy, often within seconds of arc. The accuracy depends on the quality of the sine bar, the surface plate, the gauge blocks, and the technique used for checking parallelism.

Other methods for precision angle measurement include:

• Bevel Protractor: More accurate than a simple protractor, often with a vernier scale for increased precision.
• Angle Gauges: Sets of precision blocks manufactured to specific angles, used for setting or checking angles by wringing combinations together.
• Autocollimator: An optical instrument used to measure small angular differences with very high precision.

Understanding the appropriate tool for a given measurement task is essential in engineering and manufacturing.