I'm fascinated by the history of technology too. Gears go back a long time, and the sophistication of the 2000 year old Antikythera Mechanism surprised everybody!

However, for centuries the main use of gear wheels was in windmills and watermills grinding flour. Millwrights were agricultural, metal expensive, and so the wheels and teeth were both made of wood.

At first simple round rods, later more accurately shaped teeth. Early gear makers didn't understand the mathematics, but overtime wear tends to shape the teeth more-or-less correctly, and fairly good gears can be made by rule of thumb methods.

As wooden gears wear quickly and aren't reliably strong, there was obvious advantage in metal, at first just copying wooden methods, but later casting them whole.

'Fairly good' isn't ideal, and clock-makers were first to develop gears on scientific principles, looking for the optimal curves needed for meshing gear wheels to roll over each other. Clock gear tooth shapes favour low friction rather than power transfer, so industry stuck to traditional methods for many more years. Cast gears made with teeth of nearly the right shape were common. Far from perfect in that they were noisy, inefficient and wore out relatively quickly, but they did the job provided rpm was low. However, as industry demanded more power and speed, cast gears became less popular. By this time, the maths needed for power transfer rolling curves was well understood, so industry moved to gear cutting. Understanding the maths also made it possible to develop special purpose precision gears, opening the door to all sorts of mechanisms. Cut teeth are all correctly curved, the gear is uniformly strong, and the metal is tougher and harder than cast-iron. And accurately shaped teeth wear slowly and are quieter.

Quieter, not quiet! When motor cars appeared, the appalling racket made by their gearboxes was a serious problem. No one cared if working people were deafened in factories, but rich people wanted better. This led to a second burst of research that slowly got rid of most of the whine and clatter made by plain gears. Again the answer is precision shapes, no simple cast gears in this gearbox:

I don't know if rough toothed gear blanks are ever cast in steel and then finished. It would reduce the amount of cutting, but it might be quicker and more structurally consistent to work with a round blank. Quicker because blanks don't need to be aligned in machines, and consistent because cast teeth aren't quite the same temper as the body. A Production Engineer would understand the trade-offs.

Excellent work by the way! Impressive mastery of several techniques. Thanks for sharing.

Dave

After encountering frustrations trying to get Fusion360 to draw a parametric involute, I've found this add-in by Ross Korsky which looks very promising:

Link

It also seems to include provision for adding clearance for 3D printed gears, etc.

Andy

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Relevant notes for interest:

General Usage Instructions

Once the add-in is running its button can be found under the CREATE menu.

Description of inputs

Gear Standards:

The true involute pitch and involute geometry of a helical gear is in the plane of rotation (Radial System). However, because of the nature of tooth generation with a rack-type hob, a single tool can generate helical gears at all helix angles as well as standard spur gears. However, this means the normal pitch is the common denominator, and usually is taken as a standard value (e.g. 14.5 deg or most commonly 20 deg). In other words if you plan to have your gear manufactured with a standard hob you will likely want to use the "Normal System" and a pressure Angle of 20 degrees.

Normal System: Pressure angle and module are defined relative to the normal of the tooth (i.e. defined as if the tooth was rotated by the helix angle). When defining a gear in the normal system changes to the Helix Angle will cause the gears diameter to change as well as the working thickness (and therefore the strength) of the tooth.

Radial System: Pressure angle and module are defined relative to the plane of rotation. When defining a gear in the radial system changes to the Helix Angle does NOT affect the gear diameter but it does change the "normal pressure angle" which may require custom tooling to have the gear manufactured (obviously this is not an issue if 3D printing the part).

Sunderland: The Sunderland machine is commonly used to make a double helical gear, or herringbone, gear. The radial pressure angle and helix angle are fixed at 20° and 22.5°, respectively. The tooth profile of Sunderland gears is also slightly shorter (and therefore stronger) than equivalent gears defined in the radial system.

Handedness: Direction the tooth appears to lean when placed flat on a table.

Helical gears of opposite hand operate on parallel shafts.

Helical gears of the same hand operate at right angles.

Helix Angle: Angle of tooth twist. 0 degrees produces a standard spur gear. The higher the helix angle the more twist the gear has.

Pressure Angle: The pressure angle defines the angle of the line of action which is a common tangent between the two base circles of a pair of gears. The short of it is this: leave this value at 20 degrees until you have reason to do otherwise – but know that any pair of gears MUST have the same pressure angle.

Module: The module is the length of pitch diameter per tooth. Therefore m = d / z; where m is module, d is the pitch diameter of the gear, and z is the number of teeth.

Teeth: Number of teeth the gear has. The higher the helix angle, and to some extent pressure angle, are the fewer teeth the gear needs to have to avoid undercutting. It is possible to create a Helical gear with a single tooth given a high enough Helix Angle. CAUTION: due to performance reasons, do not make gears with several hundred teeth.

Backlash: [experimental] a positive value here causes each tooth to be slightly narrower than the ideal tooth. In the real world having a perfect tooth is not often desired, it is better to build in a little backlash to reduce friction, allowing room for lubricant between teeth, and to prevent jamming. Backlash is allowed to also be negative which has no real world application I'm aware of but may be useful for compensating for undersized teeth which were 3D printed, etc.]

I got them to mesh and polished them up a bit while I was at it. The silver 15T gear on the crankshaft will drive the 30T gold cam gear giving the correct ratio.

off topic: If you explore the Clickspring channel, he makes the metal, drill bits, files, etc. using contemporary technology. It really is remarkable.

Pat, regarding the angles, as I hinted to in a previous post when working out the helix height for one revolution when you work back from the angles Rod gave it all becomes clear.

Take another look at the second image on this site where the triangle is wrapped around the cylinder. If the 26.6 and 63.4 are used then using TRIG to work out the two sides of the triangle the base is 2 and the vertical 1 which ties in very well with the 2:1 ratio of the gears.

If we did not already know the helix angle but knew the ratio then the angles for a triangle of Xbase x Yheight can be worked out.

Gears look good, keep us posted on the casting progress.

1. No At least not for 2:1 ratio

2. Yes