How
do you measure angles with a dial indicator?
One of the design criteria
for TSAligner Jr. was that it perform all of the functions of TSAligner.
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 TSAligner 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 TSAligner Jr. I called it the
Angle Attachment Gage and it's an exclusive feature that you'll find
only on TSAligner Jr. It applies the full accuracy of the dial indicator
to the task of measuring angles.
The photo above shows TSAligner
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.

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.

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.

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

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 TSAligner Jr.