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How to Use a Compound Sine Plate

Guide · Updated October 28, 2026

A compound sine plate tilts on two axes, each set by its own gage block stack. It holds parts on a magnetic or plain top for grinding or inspecting features at two angles at once.

Build both stacks

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Step by step

  1. Find the plate length: Check the roll center distance stamped on the plate (often 5 in); every stack uses it.
  2. Calculate the stacks: Stack = L × sin θ for each axis.
  3. Set the lower axis: Set the base axis stack first.
  4. Set the upper axis: Set the second axis stack.
  5. Clamp: Lock both axes.
  6. Check: Indicate or use a protractor to check.
  7. Grind or inspect: Proceed.

Worked example

5.000 in plate. First axis 10°: 5 × sin 10° = 5 × 0.173648 = 0.8682 in. Second axis 15°: 5 × 0.258819 = 1.2941 in. Build 0.8682 and 1.2941 in stacks.

Compound angles

The two plate angles are not always the drawing angles. When a drawing gives a true angle measured in an inclined plane, work out the two plate settings with proper compound-angle trig (see Machinery's Handbook) before building stacks.

Worked example: checking the setting

After setting the 10° axis on a 5.000 in plate with a 0.8682 in stack, sweep a test indicator along the top over 4.000 in of travel on a height stand. The top should rise 4.000 × tan 10° = 4.000 × 0.17633 = 0.7053 in, more than most indicators read, so instead check the part: place a 1-2-3 block on the plate and check its top with a sine bar set to the same angle, or measure the ground angle afterward with a sine bar and gage blocks on the surface plate.

How stack error affects angle

On a 5 in plate, the angle changes by about Δh ÷ (L × cos θ) radians. At 10°, a 0.0002 in stack error gives 0.0002 ÷ (5 × 0.9848) = 0.0000406 rad, about 8.4 arc seconds. At 60°, the same error gives 0.0002 ÷ (5 × 0.5) = 0.00008 rad, about 16.5 arc seconds, so steep angles are more sensitive.

Order of setup

Set and lock the lower (base) axis first, then the upper axis. Wring each stack, seat it squarely under the correct roll, and lower the plate gently onto it. Check both stacks are still seated before clamping.

Accuracy

Clean rolls and stacks, use a grade of gage block suited to the job, and keep the plate at room temperature.

Common problems

Wrong angle: stack under the wrong roll or in the wrong axis. Rocking: dirt or burrs under a roll. Drift while grinding: clamp not locked or magnetic top not switched fully on. Angle off by a set amount: a compound angle taken straight from the drawing without conversion.

Tips

FAQ

What is a compound sine plate?

A sine plate that tilts on two axes.

How do I calculate the stack?

L × sin θ for each axis.

What is the 10° stack on a 5 in plate?

0.8682 in.

Order of setup?

Lower axis first.

Are plate angles the drawing angles?

Not always; convert compound angles first.

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