How do you measure angles with a dial indicator?

One of the design criteria for TS-Aligner Jr. was that it perform all of the functions of TS-Aligner. This presented quite a problem when it came to the task of affordable but accurate angle measurement. Some alignment jigs ignore angle measurement completely. Others use simple protractors with very limited accuracy. And, a few rely on the accuracy of their machined edges to give you a rough indication of a few fixed angles. None of these solutions are acceptable for TS-Aligner Jr. because they offer no capability beyond what most woodworkers can already do. It just doesn't make sense to ask people to spend their hard earned money on a solution that they already have or can purchase for much less. Why spend $140 on a jig that does no more than the head on a combination square? Why spend $230 on a jig that offers no more accuracy than an adjustable plastic triangle?

So, I invented a new angle measurement device specifically for TS-Aligner Jr. I called it the Angle Attachment Gage and it's an exclusive feature that you'll find only on TS-Aligner Jr. It applies the full accuracy of the dial indicator to the task of measuring angles.

The photo above shows TS-Aligner Jr. using the Angle Attachment Gage to measure the angle of a blade tilt. Using the chart provided in the User's Guide, the dial indicator reading is translated directly into an angle. The resulting measurement is far more accurate and reliable than any other home shop alignment jig can claim.

How it works

The Angle Attachment Gage relies on simple High School Trigonometry for all it's work.  In a right triangle, one of the angles is 90 degrees and the other two angles can be calculated if the length of the two sides (A and B) are known. The photo above shows how the Angle Attachment Gage is precisely machined to construct this right triangle geometry so that side A is measured by the dial indicator and side B is fixed at a precise distance. When the length of side A is measured to be exactly the same as side B then the angle is 45 degrees. When the length of side A is measured to be exactly zero, then the angle is 90 degrees. Angles in between are easily calculated using the following formula:

Angle = Arc Tan(length of side A)

A quick reference table is included on the back cover of the User's Guide so that angles can be easily determined without the need to do any calculations. Since it's easier to measure how far the dial indicator plunger is pushed in (rather than the length of side A), the table uses the following formula:

Reading on the indicator = 1 - Tan(angle desired)

So, the reading is 0.000" for 45 degrees (plunger barely pushed in) and 1.000" (plunger pushed in almost all the way) for 90 degrees (actually zero degrees).

How accuracy is ensured

There are some significant possibilities for error in the Angle Attachment Gage but careful design decisions have helped to eliminate them.

1. Contact with the surface being measured must maintain the constant spacing for side B regardless of the angle being measured. This is accomplished by using indicator tips that have identical points on their ends.

2. The plunger on the dial indicator must travel in a line that is parallel with the table surface. Tilt of the dial indicator is therefore controlled by a set screw that contacts the back of the dial indicator. This set screw is calibrated at our factory and can also be calibrated by the user. Complete instructions are included.

3. Compensation must be made for any error in the full scale accuracy of the dial indicator.

4. Compensation must be made for any slight variations in parts and machining.

These last two items are real problems. I solved them by using a calibration procedure that relies on the accuracy of a precisely ground 45 degree steel angle block. This procedure depends on the fact that a right triangle whose hypotenuse is 45 degrees will have sides of equal length (an isosceles right triangle). The tilt of the dial indicator is set so that an accurate 45 degree reference gives a reading of exactly "Zero" on the dial indicator. At the same time, an accurate 90 degree reference must read exactly "One Inch" on the dial indicator. This creates the geometry of an isosceles right triangle.  It doesn't matter if the actual distance of side B is exactly one inch.  The accuracy of the dial indicator doesn't matter either so long as it consistently divides the distance on side A of that triangle into 1000 parts. But, the angle must be 45 degrees and the "Zero" and "One Inch" points must be set accurately.  The calibration procedure ends up tilting the dial indicator very slightly to compensate for any irregularities in the machining of the parts (including the stylus points) and the accuracy of the dial indicator.

The calibration method is limited to the amount of error that it can compensate for. So, precise machining and good quality dial indicators are still necessary. The resulting angle measurement accuracy obtained is quite surprising.

The angle attachment gauge provides the best angle measurement at the lowest possible cost. And, you'll find it only on TS-Aligner Jr.

 

Last revised: January 21, 2006.