Although CMM measuring machines took away many of the traditional use cases of the sine bar, It is still the most accurate method to measure the angle of a ground surface.

Likewise, the sine vice is still a very effective holding device to grind an inclined plane at a precise angle on a manual surface grinder.

## Sine Bar Calculator

(The calculator can be used also for sine plates and sine vises)

## Sine Bar Formulas

(The below formulas are valid also for sine plates and sine vises)

$$\large \Theta = \arcsin \left ( {\frac{H}{L}} \right )$$
$$\large L = H \times \sin{\theta }$$

Explanation: The formulas are straightforward and are a result of the fact that the sine bar forms a right triangle:

• The Sine Bar length (L) is measured between the center of the cylinders and forms the triangle’s hypotenuse.
• The Sine Bar height (H) is the height of the stack of the gauge blocks placed under the cylinder and constitutes the triangle’s opposed leg.
• The angle (Theta) results from these two basic properties.

## Sine Bar Principales

### How does it work?

Sine bar is a simple yet very accurate method to measure the angle of a part. It is built from a precision ground plate sitting on two precision ground cylinders, where the distance between the cylinders is a known whole number. (like 5″ or 100 mm)

You need a Sine bar from a reputable manufacturer that guarantees the device’s accuracy across the board to get a precise result. The overall accuracy is a combination of several factors:

• The accuracy and uniformity of the two cylinders (C1 and C2).
• The exact distance between the two-cylinder centers (Usually equal a whole number like 5 inches or 100 mm).
• The flatness of the top surface (A)
• The parallelism between the top surface (A) and the theoretical plane connecting the cylinder center lines (L).
• The accuracy of the gauge block stack (H).

### Measuring the angle of a small component:

• Calculate the needed height of the gauge block stack to level the plane horizontaly.
$$\large H = L \times \sin \left ( \Theta \right )$$
• Check the parallelism of the top surface with a dial indicator.
• If it is not close enough to zero, add or decrease the height of the stack.
• Repeat this step until reaching zero (or near zero) parallelism.
• Measure the total gauge block stack height.
• L is known from the Sinebar model.
• Calculate the actual angle:
$$\large \Theta = \arcsin \left ( {\frac{H}{L}} \right )$$

### Measuring the angle of a large size component:

• L is known from the Sinebar model.
• Measure H1 & H2 with a Dial Height Gauge.
• Calculate the angle:
$$\large \Theta = \arcsin \left ( {\frac{H2\,-\, H1}{L}} \right )$$

## Types of Sine bars

### Sine Bar

Used to measure the angle of a flat area on a workpiece.

### Sine center

This sub-type of a sine bar is used to measure the angle on cylindrical parts.

### Sine Plate

A holding device used to hold a large workpiece at a precise angle to perform milling or grinding operations. The clamping of the components can be magnetic or mechanical.

### Sine Vice

This sub-type of a sine plate holds small components at a precise angle for machining (usually surface grinding).

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