The DILAGON: a DIY laser goniometer

[Cyrano]

For your budget-conscious measurement needs, I introduce the DIY Laser Goniometer, aka DILAGON. 

Materials needed:

Laser pointer
Articulated/adjustable stand or holder for the laser pointer
Printer paper (letter size)
Tape
Scissors
sheet of thin, rigid material (e.g. stiff cardboard), 165 mm x 85 mm
optional: thermal laminating pouch for letter-size paper

Tools needed:

PDF-capable computer & printer
Scissors
single-sided tape
double-sided tape
optional: thermal laminating machine (or use of laminating service at a local office-supply store)

How to build the DILAGON: 

(1) Print the attached PDF on letter-sized paper.

(2) Optional: laminate the print. This will make the DILAGON more sturdy, and also make it easier to align the laser for measurements. 

(3) Cut out the DILAGON.

(4) Fold the DILAGON into its 3-dimensional shape, and tape the edges to secure its form.  

(5) Tape the DILAGON to the rectangular piece of rigid material. 

The result looks like this:





How to use the DILAGON: 

(1) Set the laser pointer in its holder:



(2) Aim the laser pointer at the DILAGON. Align the beam so as to be horizontal at the level of the protractor scale, and in the plane defined by the horizontal and vertical center lines of the DILAGON. This is easily done by aiming the laser at the front of the horizontal center line, then adjusting the laser's pitch to bring the laser spot upwards, until the beam is hitting the protractor scale. When the beam is properly aligned, the laser spot will track along the horizontal and vertical center lines.

Laser spot hitting near the front of the horizontal center line, and reflecting off the shiny lamination to hit the vertical center line:



Laser pitch adjusted to bring the laser spot upwards, tracking on the vertical center line until it reaches the measurement position on the protractor scale: 



(3) Hold the knife vertically with its tip resting on the front edge scale of the DILAGON, and its edge facing right. Position the knife so that its edge is just interrupting the laser beam, and note the distance between the tip and the origin of the measurement scale. In this case, the knife tip is 9 mm away from the origin: 



(4)  Hold the knife vertically with its edge facing forward, and its tip resting on the horizontal center line of the DILAGON at the distance noted in the previous step. 

* Adjust the knife's roll until the reflected laser pattern on the protractor scale is of equal brightness on either side of zero. 

* Adjust the knife's yaw until the two reflected spots nearest zero (corresponding to the blade's primary bevel) are symmetrical around zero. 

When roll and yaw are properly adjusted, the reflected laser spots furthest from zero indicate the angles of the edge apex:

[grepper]

That's cool Mr. Cyrano.  Any pointers on a good fine focusing, reasonably priced laser pointer?   The PDF for the gauge is cool too.

I've looked at the CATRA goniometer an number of times, but just couldn't justify pulling the trigger due to the cost.

[KnifeGrinders]

Call me retard, but i've read the instructions 3 times and can't understand how the scale is calibrated?
A prerequisite for calibration is that the laser pointer is at the same distance to the knife edge, but as per the instructions the edge position is floating?!
I would never doubt Cyrano's higher cognitive functions, I'd rather doubt mine - can someone push me in the right direction please?

[Cyrano]

... A prerequisite for calibration is that the laser pointer is at the same distance to the knife edge ...

Jan's diagram illustrates the geometry at work. Visualize sliding the laser left and right, and you'll see alpha is independent of the distance between the laser pointer and the knife edge: 



Measuring alpha requires a fixed distance in the plane of measurement between the knife edge and the measurement scale. The DILAGON achieves this via the 2-step procedure of measuring the offset in the plane of measurement between the knife tip and the knife edge, then positioning the tip back from the origin of the protractor by the measured offset. 

While this procedure establishes the correct distance between the knife edge and the measurement scale of the DILAGON, it does not ensure the edge is optimally aligned in the laser beam. Alignment is done by freehand adjustment of the knife's roll and yaw, neither of which should have a significant effect on the accuracy of the measurement.

[KnifeGrinders]

I understand this, thank you - the knife edge is in the constant position in relation to the scale.
Still I cannot understand how you calibrated the scale for the reflection to show the correct angle.
You were to use some standard "corner" or "wedge" of a known angle to establish that constant distance between the knife edge and the scale at which the laser reflects the correct angle on the scale, weren't you?

[Cyrano]

The scale is a semicircle centered at the knife edge.  Correct angle markings require only that the scale compass 180 degrees, is divided into equal segments, and is centered around zero. 

As the reflected spots are the result of twice the edge angle (angle of incidence + angle of reflection,) compassing 180 degrees translates into scale markings which compass 90 degrees: -45 degrees at the left end of the scale, and +45 degrees at the right end of the scale.

[Cyrano]

From several comparisons of DILAGON readings to microscopic examination, I estimate my DILAGON measurements are accurate and precise to c. 1 degree for well-behaved edges. 

This knife was sharpened yesterday with a Tormek T-8 set for 15 degrees. It read 15 degrees on the DILAGON:

[KnifeGrinders]

Appreciate your taking time to explain - I must have had a slippage of brain cogs yesterday.
The knife edge is to be positioned at the diameter of the semicircle, and since we use the semicircle the scale itself does not require calibration as in case of a straight scale.

CATRA's Hobbigoni laser protractor design limits blade width to 42 mm, while yours can be used to check edge angle on wider blades.

[Cyrano]

... The knife edge is to be positioned at the diameter of the semicircle, and since we use the semicircle the scale itself does not require calibration as in case of a straight scale ...

A straight scale would not require calibration in the sense of using some physical object as a standard. Straight or circular, as long as the knife edge is positioned at a known and fixed point, a scale can be created. A straight scale would need to be sized appropriately for the intended distance to the knife edge -- but that is true for a circular scale, too. 

This diagram represents a fold-up template similar to the DILAGON.pdf file posted earlier in this thread -- but instead of a semicircular scale, this version uses a straight scale. To make this template into a goniometer, one would simply fold the diagram along the central horizontal line: 
 

[Jan]

Mr. Cyrano, in my understanding the angles shown in your straight scale by green lines are 2*alfa (double the bevel angle) while in the semi-circular DILAGON scale the figures are bevel angles alfa in degrees.

Jan