A sine bar is used for angle measurement by creating a precise angle using gauge blocks and trigonometric principles. When placed on a flat surface, and one roller is raised by a known distance (height) using gauge blocks, the sine bar's top surface forms an angle with the base. This angle can then be calculated using the sine function.
Here's a breakdown of the process:
1. Setup:
- The sine bar is placed on a precision surface plate.
- Gauge blocks are carefully selected and stacked to achieve a specific height.
- One roller of the sine bar is placed on top of the gauge block stack, while the other roller remains on the surface plate.
2. Angle Creation:
- Raising one roller by a specific height (h) relative to the other creates an angle (θ) between the surface plate and the sine bar's top surface.
3. Angle Calculation:
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The sine of the angle (sin θ) is calculated by dividing the height of the gauge block stack (h) by the distance between the centers of the sine bar rollers (L):
sin θ = h / L
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Therefore, the angle θ can be determined using the inverse sine function:
θ = arcsin (h / L)
4. Measurement Application:
- Once the sine bar is set to the desired angle, it can be used for various angle measurement or inspection tasks. For example:
- Checking the angle of a machined part.
- Setting up a workpiece at a specific angle for machining.
Example:
Let's say you have a 5-inch sine bar (L = 5 inches) and you use a gauge block stack of 1.25 inches (h = 1.25 inches).
sin θ = 1.25 / 5 = 0.25
θ = arcsin (0.25) ≈ 14.48 degrees
Therefore, the sine bar is set at approximately 14.48 degrees.
Key Considerations:
- Accuracy: The accuracy of the angle measurement depends heavily on the accuracy of the gauge blocks and the precision of the sine bar itself.
- Sine Bar Length: Standard sine bars come in lengths such as 5 inches and 10 inches, but custom sizes are also available. The length of the sine bar impacts the accuracy of the angle setting; longer bars typically provide higher accuracy.
- Surface Plate: A high-quality surface plate is essential to ensure a stable and accurate base for the sine bar and gauge blocks.
- Roller Diameter: While not directly used in the calculation, the consistency of the roller diameters is crucial for accurate setup.
In summary, a sine bar allows for precise angle creation and measurement by using gauge blocks to establish a known height difference and then applying the sine function to calculate the resulting angle.
