Gear Cutting

Part of Simple Machines

Practical methods for cutting wooden and metal gear teeth without specialized machinery.

Why This Matters

Gears allow you to transmit rotary power between shafts, change speeds, change directions, and trade speed for torque or torque for speed. A water wheel spinning at 10 rpm can drive a grinding stone at 100 rpm through a 10:1 gear ratio. A slow but powerful windmill can drive a fast but light pump through appropriate gearing. Without gears, every machine component must spin at the same speed as the power source — a severe limitation.

The challenge with gears is accuracy. Two gears mesh at their tooth surfaces, and if the teeth are unevenly spaced or poorly shaped, the gears will bind, vibrate, wear rapidly, and transmit power inefficiently. Professional gear cutting requires specialized machines. Hand cutting requires patience and systematic technique.

This article focuses on what is actually achievable without machine tools: wooden spur gears for mills and slow-speed machinery, simple metal gears for moderate-precision applications, and the lantern gear as the practical alternative when precision is limited. These methods were used in water mills and windmills for centuries before precision machine tools existed.

Understanding Gear Geometry

Before cutting, understand the key dimensions.

Tooth pitch (circular pitch): The distance from one tooth center to the next, measured along the pitch circle (the imaginary circle at mid-tooth height where the two gears theoretically contact). All calculations start with this.

Pitch circle diameter:

Pitch circle diameter = Number of teeth × Circular pitch / π

Tooth height (addendum + dedendum):

• Addendum (tooth above pitch circle) = 0.318 × pitch
• Dedendum (tooth below pitch circle) = 0.368 × pitch
• Total tooth height = 0.686 × pitch

For a 20 mm circular pitch:

• Addendum = 6.4 mm
• Dedendum = 7.4 mm
• Total tooth height = 13.7 mm

Tooth width at pitch circle: Approximately half the pitch (10 mm for 20 mm pitch)

The tooth profile: Ideally an involute curve (the shape traced by a point on a string unwinding from a cylinder). In practice, for wooden gears at low speed, a simplified profile (straight or slightly curved flanks) works adequately if the pitch accuracy is good.

Marking Out the Gear

Step 1: Prepare the Blank

1. Cut the gear blank from well-seasoned hardwood to the calculated outside diameter (pitch circle diameter + 2 × addendum)
2. Face both sides flat — uneven thickness causes the gear to run out-of-flat
3. Find and mark the center precisely
4. If you have a lathe, turn the blank to true round (even modest run-out causes binding)
5. Drill the bore hole at exact center — the bore must be concentric with the tooth circle

Step 2: Mark the Pitch Circle

Set a compass or dividers to the pitch circle radius. Scribe the pitch circle on the flat face of the gear blank. This circle is your reference — all tooth positions are measured from it.

Step 3: Divide the Circumference

This is the critical step. Each tooth must be exactly equally spaced, or the gear will bind at the unevenly-spaced teeth.

Method 1 — Dividing by stepping with dividers:

1. Set dividers to the circular pitch (the tooth center-to-center distance)
2. Step around the pitch circle, marking each tooth center
3. After going all the way around, you should return exactly to your starting mark
4. If you are off, adjust the dividers slightly and repeat

This method accumulates error — small errors in divider setting compound over many teeth. For a 30-tooth gear, even a 0.5% error in setting means the last tooth is off by 30 × 0.5% × pitch = 0.15 × pitch — significant. Recheck frequently.

Method 2 — Using a geometric division: For gears with a number of teeth that can be divided geometrically:

• 4, 8, 16 teeth: bisect repeatedly
• 6, 12, 24 teeth: divide circle into sixths (each sixth = 60 degrees)
• 3, 9, 18 teeth: divide by thirds (120 degrees)
• Numbers like 13, 17, 19 (primes) are very difficult — use the stepping method

Method 3 — Using a paper template: For careful work, draw the full gear tooth layout on paper, cut it out as a template, and prick each tooth center through the template onto the gear blank. A paper template can be drawn with accurate geometry tools (compass, protractor, ruler) to higher precision than divider stepping.

Step 4: Mark the Tooth Outlines

For each tooth position:

1. Mark the tooth center on the pitch circle
2. Mark the addendum circle (the outer edge of teeth)
3. Mark the root circle (the bottom of the gaps between teeth)
4. Draw the tooth outline between adjacent tooth centers

For simplified tooth profile: draw straight sides on each tooth, slightly tapering from base to tip. The base width is the pitch minus appropriate clearance; the tip width is approximately 60% of the base width.

Cutting Wooden Gear Teeth

Tools Required

• Rip saw or frame saw for rough cuts
• Coping saw or scroll saw for curved work
• Chisels (1 cm, 1.5 cm widths)
• Shoulder plane or router plane for bottoms of tooth gaps
• Rasps and files for shaping
• Dividers and marking gauge

The Cutting Process

Step 1: Cut the gaps between teeth.

The wood removed between teeth defines the teeth. Cut two lines at the sides of each gap, then remove the waste.

1. Using a fine-tooth saw, cut along the side lines of each gap to the root circle depth
2. Work carefully — cut slightly outside the line and refine later
3. For the best results, cut all left-side lines of gaps around the full gear first, then cut all right-side lines

Step 2: Remove the waste.

Between the two cuts defining each gap, chop out the waste wood:

1. Chisel across the grain at the root circle depth to sever the wood fibers at the bottom of the gap
2. Pare down from the surface, working in layers toward the root
3. Use a shoulder plane or router plane to get the gap bottom flat and at the exact root depth

Step 3: Shape the tooth flanks.

The raw cut faces are flat, which is close enough for slow-speed wooden gears. Optionally, use a curved chisel (gouge) to add slight concave curvature to the tooth flanks for better mesh — this approximates the involute profile.

Step 4: Check the tooth spacing and profile.

Make a test gauge from a thin metal strip — bend it to the tooth and gap profile you want. Check each tooth against the gauge. File or pare any teeth that deviate.

Step 5: Final smoothing.

Use a file or sandstone to smooth all tooth surfaces. Sharp burrs and tool marks concentrate stress and cause premature wear.

Cutting Metal Gear Teeth

For wrought iron or soft steel gears, the marking process is the same but the cutting tools differ.

Cutting Iron Teeth

1. Mark the gear blank with a scribe (steel scribing tool) rather than pencil
2. Use a hacksaw for the gap side cuts
3. Use cold chisels and a hammer to remove the waste
4. File the tooth surfaces smooth with a metal file
5. Test the mesh by trying the gear against its mating partner by hand — feel for binding and tight spots, file those spots

Allowance for forge-fitting: If the gear is forge-shaped (hammer forged rather than machined), add 0.5-1 mm to all clearances. Forged surfaces are less precise than machined ones and need more play.

Pegged Metal Teeth (Simpler Alternative)

Instead of cutting teeth from solid metal, peg iron teeth into a wooden wheel body:

1. Cut a wooden gear disc slightly smaller than needed
2. Drill equally spaced holes around the rim at the required pitch
3. Forge iron pegs (rectangular cross-section, shaped like a tooth) and drive them into the holes
4. The iron pegs act as teeth, meshing with the wooden teeth of the mating gear

This hybrid approach provides iron wear surfaces on the most-stressed parts while allowing the less-skilled operation of wooden gear cutting for the majority of the work.

The Lantern Gear Alternative

If tooth-cutting precision is beyond your current capability, build a lantern gear system instead.

Lantern gear construction:

1. Two parallel wooden discs, 30-50 cm diameter
2. Equally spaced round pegs (2-3 cm diameter hardwood dowels) connecting the two discs around their perimeter
3. The pegs act as “teeth” that mesh with a rack or face gear

Mating gear (face gear/crown gear): The lantern gear meshes with a face gear — a flat gear with teeth cut into its face (not its edge). The face gear teeth are simple rectangular slots cut into a flat board or disc. The lantern pins pass through these slots as the gears rotate.

Advantages: Much easier to make than involute spur gears. Tolerates larger dimensional errors. Self-correcting (a loose pin can be replaced easily).

Disadvantages: Less efficient than spur gears, noisier, higher wear rate. But perfectly adequate for mill applications where durability matters more than efficiency.

Lantern gears powered water mills and windmills across Europe and Asia for centuries. They are a proven, practical solution for low-precision manufacture.

Testing and Adjusting

After completing the gear, test it before installation.

Mesh test: Turn the two gears against each other slowly by hand. They should roll smoothly through every tooth combination. Any binding indicates a tight spot — locate it by marking teeth with charcoal and looking for rub marks, then file the tight tooth.

Backlash check: There should be a small amount of play between meshing teeth (backlash). Too little = binding. Too much = noisy and imprecise. For wooden gears, 0.5-1 mm of backlash at the pitch circle is appropriate.

Run-in period: New wooden gears wear in during the first hours of operation. Run them at light load initially, then gradually increase to full load. Apply tallow or oil to the teeth every 30-60 minutes during the first day of operation.