A rotary table with a set of division plates allows accurate placement of features upon a workpiece.

This is especially useful when cutting gears on a mill for instance.

Most division plates will come with a table providing the number of turns and holes to evenly
divide the 360 degree rotation into the desired number of divisions.

Sometimes, as it was in my case, this table may be found to hold non usable data, or simply
incorrect data.

The correct values can however be readily determined when the number of turns of the
hand wheel to create a complete 360 degree rotation of the table is known.

My rotary table takes 90 full turns of the hand wheel to rotate the table a full 360 degrees.
This is usually specified as a 90:1 ratio.

Calculating a division

A usable division plate can be deduced by the simple formula of:

               Turns Ratio     
           Number of Divisions

Simplification of this fraction may reveal a number of holes more suited to those available.
The following examples all assume a 90:1 ratio table.

eg 1:  10 Divisions

         10 divisions:    =>   ⁹⁰⁄₁₀   = 9
                    

As the result is a whole number, we simply need to crank the hand wheel 9 complete turns
for each division.
No specific division plate is required to achieve the desired result.

eg 2:  21 Divisions

         21 divisions:    =>   ⁹⁰⁄₂₁   =   4 + ⁶⁄₂₁
 

In this instance, the result is not a whole number.
Notice the remainder is left as a fraction as a decimal result is of no assistance when determining
which division plate we can use.

We can simplify the fractional part by dividing both the numerator and denominator by 3, leaving ²⁄₇.

Thus to perform a set of 21 divisions, you will need to crank the hand wheel 4 full turns, plus a
further ²⁄_7’s of a turn.

By using a division plate, we can readily crank the hand wheel by exactly ²⁄_7’s of a turn without any
concern of how many decimal degrees that may be.

Ideally you would choose a 7 hole plate and mount that to the rotary table, but it’s extremely
unlikely a plate with so few holes will be available.
Never fear, a plate that has a multiple of 7 holes can be used, such as a 49 hole circle, or even
21 as per the original divisor.

In either case, the number of holes to be skipped needs be proportionally scaled to suit.
ie:
     21 hole plate:  7 x 3 ⇒ ²⁄₇ × ³⁄₃ =  ⁶⁄ ₂₁
     or
     49 hole plate:  7 x 7 ⇒ ²⁄₇ × ⁷⁄₇ = ¹⁴⁄₄₉

As counting off holes is a very tedious and error prone process, sector arms are used to assist in
quickly and accurately locating the next indexing location during the fractional movement.

Each sector arm is beveled on opposing edges.
All indexing should take place between these beveled edges.

Before commencing work, the sector arms are adjusted so the beveled edges will encompass the
required movement.
Despite not needing to count holes during the indexing process, you must always count full turns.

Note: the number of holes visible between the arms will be one more than required for the fractional movement.
eg: Think of the case where no holes were to be skipped over.
     Each arm could be set to be directly adjacent to each side of a hole.
     Despite no movement taking place, a single hole would be visible between the arms.

The following diagram makes this clearer by setting the starting hole to be number zero.

Note that the number of visible holes between the beveled edges is 7 or 15, one more than the required
movement of 6 or 14.

Setting the Sector Arms in practice:

1. Install the correct division plate.
2. Install and align the hand crank so the indexing pin will readily drop into the correct circle of holes.
3. With the indexing pin in any hole, align the sector arm with the bevel to its right hand edge to the
   immediate left of the indexing pin.
   The darker areas in the diagram indicate the beveled edges.
4. Count off the required number of holes, the occupied hole being ignored (zero).
5. Align the second sector arm’s bevel adjacent to the right hand edge of the ending hole.
6. Lock the sector arms together.
7. Recheck the total number of holes visible between the arms, there should be one more than
   the required number of holes to skip. (Occupied hole plus the number to move by).

To perform the actual indexing operation:

1. Move the sector arms as a pair so the leftmost beveled edge rests against the left side of the indexing pin.
2. Unlock the rotary table’s clamps.
3. Pull the indexing pin clear of the hole and sector arms and crank 4 complete turns.
   Take care to not disturb the sector arm position as you crank the table.
4. Keep cranking till the indexing pin covers the hole adjacent to the rightmost beveled edge.
5. Drop the index pin into the end hole.
6. Tighten the rotary table’s clamps, preventing unwanted movement.
7. Repeat from step one until all indexing operations are complete.

To eliminate backlash, always rotate in a consistent direction, and avoid overshooting.
If you do overshoot, wind back at least half a turn, then approach the end hole from the correct direction.

eg 3:  13 Divisions

         13 divisions:    =>   ⁹⁰⁄₁₃   =   6 + ¹²⁄₁₃
 

Once again, the result is not a whole number.

Thus to perform a set of 13 divisions, you will need to crank the hand wheel 6 full turns, plus a
further ¹²⁄_13’s of a turn.

As 13 is a prime number no further simplification of this fraction is possible.

Ideally you would choose a 13 hole plate, and mount it to the rotary table.
However it is far more likely a 39 hole plate will exist (ie: ¹²⁄₁₃ × ³⁄ ₃ = ³⁶⁄₃₉) so we’ll continue with
that sized plate.

When setting the sector arms in this specific case, using the method in the previous example
will not be possible as the arms will mechanically clash well before you get to the 36th hole.
Instead this is handled by setting the arms to span the holes in a reverse direction,
ie 36 holes is actually 3 holes short of a full 39 hole revolution.

This time you’d align the beveled edge to rest against the right hand side of the indexing pin.
The other arm is then set to expose the required number of holes to the left of the starting
point, PLUS ONE.
ie: 4 holes will be visible between the beveled edges.

You will still crank the hand wheel as before, but now you will leave and return to the constraints
of the sector arms; start by crossing the start arm, cranking about and finishing at the hole immediately
after crossing the end arm.