Question

Which of the following parameters is NOT the essential requirement for accuracy of the measurement with the sine bar?

• A. Flatness of upper surface, equality of size and roundness of rollers
• B. Exact distance between the roller axes and mutual parallelism
• C. Parallelism between top surface and bottom surface
• D. Parallelism of the roller axes to the upper surface

Hint:

The accuracy of a sine bar depends entirely on the geometry of its upper surface, the equality and roundness of the two rollers, and the exact distance ($L$) between their centers. Any reference to a flat "bottom surface" is irrelevant to its function.

Answer 1

The Correct Option is C

Concept: A sine bar is a precision linear metrology tool used to measure unknown angles or set workpieces at specific inclinations. Its operation is based on the trigonometric sine rule applied to a right-angled triangle: \[ \sin(\theta) = \frac{h}{L} \quad \Rightarrow \quad \theta = \sin^{-1}\left(\frac{h}{L}\right) \] Where:

• \( L \) is the precise distance between the centers of the two pivoting rollers.

• \( h \) is the height of the slip gauge block stack.

• \( \theta \) is the inclination angle being measured.

Step 1: Identify the critical geometric features required for precision accuracy. For the trigonometric relationship to hold true, several manufacturing criteria are necessary: 1. The upper gauging surface must be perfectly flat (Flatness of upper surface). 2. The two rollers must have identical diameters and be perfectly cylindrical (equality of size and roundness of rollers). 3. The distance \( L \) between the roller centers must be known precisely and their axes must be parallel (Exact distance between the roller axes and mutual parallelism). 4. The axes of the rollers must be parallel to the upper workspace gauging plane (Parallelism of the roller axes to the upper surface).

Step 2: Determine which feature is not required. A sine bar consists of an upper gauging plane and two lower cylindrical rollers resting on a reference surface plate or slip gauges. It does not have a separate functional "bottom surface" parallel to its top face; instead, the bottom boundary consists of the tangent lines along the undersides of the two rollers. Therefore, parallelism between the top surface and a bottom surface is not a relevant or essential parameter for its measurement accuracy.