A dividing head uses a 40:1 worm and worm wheel so that one turn of the crank rotates the spindle 1/40th of a turn, 9 degrees, and a hole plate on the crank shaft counts the fractions of a turn; to divide into N parts, turn the crank 40/N times for each division. Which N a head can reach depends on which hole circles its plate carries, because the fractional part of 40/N must fit a circle.
Part of Precision Tool Making
A worm-gear indexing device that rotates a workpiece through any chosen equal division, used for cutting gear teeth, drilling hole circles and engraving scales.
The Worm Reduction Also Divides The Plate’s Errors By Forty
The head combines two ideas. The worm gear gives a large fixed reduction, 40:1 in the carrier’s design, so that one full revolution of the worm shaft turns the spindle 360 / 40 = 9 degrees (Worm Gears). The dividing plate on the worm shaft then counts fractions of a revolution with a spring pin entering one hole of a circle.
The reduction does a second job: any error in how far the crank is turned is divided by 40 at the spindle. A plate hole mis-positioned by 0.5 degree of crank rotation (an assumed figure) becomes 0.5 / 40 = 0.0125 degree at the spindle. What the reduction does not hide is error in the worm wheel itself or backlash in the mesh.
What You Need
- A worm and wheel of 40:1, cut and fitted so they turn smoothly (Worm Gears)
- A spindle with a chuck or centres, mounted in a rigid base
- A dividing plate with circles of 24, 30, 36, 48 and 60 holes, and a spring-loaded indexing pin (Dividing Plate)
- A pair of sector arms, or a note of holes counted, to mark the fraction
Method: Index To N Divisions
Step 1: Compute 40/N as whole turns plus a fraction.
Step 2: Choose a hole circle whose hole count is divisible by the fraction’s denominator.
Step 3: Turn the crank the whole turns and then the fractional number of holes.
Step 4: Always approach from the same direction so backlash in the worm is taken up the same way every time.
Step 5: Cut or drill, then index to the next position.
Step 6: Check closure. After N divisions the crank has turned exactly 40 times and the spindle exactly once. If the work does not return to its start mark, the error is in the setup, not in the arithmetic.
Worked Example
The carrier’s example is 7 divisions. 40 / 7 = 5 5/7, so 5 whole turns plus 5/7 of a turn; on a 21-hole circle 5/7 = 15/21, so advance 15 holes. Note that a 21-hole circle is not among the plate’s usual rows of 24, 30, 36, 48 and 60, so a seven-division job needs that extra circle.
Other divisions with the five usual circles:
| Divisions | 40/N | Turn |
|---|---|---|
| 9 | 4 4/9 | 4 turns and 16 holes on the 36 circle |
| 15 | 2 2/3 | 2 turns and 16 holes on the 24 circle |
| 25 | 1 3/5 | 1 turn and 18 holes on the 30 circle |
| 30 | 1 1/3 | 1 turn and 8 holes on the 24 circle |
| 60 | 2/3 | 16 holes on the 24 circle |
Checking one: 9 divisions, 4 turns and 16/36 of a turn = 4.444 turns; 9 x 4.444 = 40.0 turns. Divisions such as 11 and 13 cannot be reached with these circles, since none of 24, 30, 36, 48 or 60 is a multiple of 11 or 13; they need a circle of 11 or 13 holes or a multiple.
Common Mistakes
- Overshooting the hole and backing up. Backlash then enters the setting; go round again.
- Counting the hole the pin is in. Count the spaces moved.
- Assuming every N is reachable. Work out which circle serves before cutting.
- Trusting the head without a closure check. Make N moves and see whether the spindle returns to its start mark.
Safety
A head holds work against a cutter
The workpiece on a dividing head sits under a milling cutter or drill. Clamp the head and the work, lock the spindle before cutting, keep hands clear of the cutter, and know where the machine’s stop is and how long it takes to coast down.
What’s Next
- Learn next: Gear Cutting - using the head to cut teeth
- Combine with: Dividing and Indexing - the circle-closure check