Planetary Gear Systems

Ever since I was introduced to Lego Technic, I've been fascinated by gears. My favorite part of any Lego model were the parts that moved, even if by a simple joint, because you could manifest your imagination, making the play more real. Gears enabled the connection of movements: a turning tire moved the engine piston, the steering wheel actually turned the wheels.

I want to understand planetary gear systems. Planetary gear systems make up automatic transmissions in cars, and a differential planetary gear system can make very high ratios in little space. These systems are much more difficult than the Lego models I built, where gear ratios were simply ratios of teeth, and had only 1 gear ratio.

I started by designing the sun and planet gears. This design wasn't trivial, because most gear teeth are shaped by an involute curve, creating the involute gear profile. AutoCAD doesn't have a command to take formulas for curves, so I seached online, finding an AutoLISP script that would generate a gear. Unfortunately, this script takes many inputs that seem to require a spreadsheet of calculations to properly make a gear. I was quite frustrated until I found this gear template generator that reduced the inputs to something that made intuitive sense - Tooth pitch, number of teeth, and pressure angle. This generator used the Machinists Handbook formulas referenced in this youtube video (more succinctly here). I modified the AutoLISP script to take my inputs and to fully create a gear, learning LISP in the process. You can copy it here. My appreciation goes to the gear template generator author, whose webpage helped me understand the subtle differences between internal and external gears. Also much appreciation to the original author of the AutoLISP script, without which I could not learn LISP or AutoLISP.

Once I made the gears, I started designing the system, which consists of:

• Sun gear
• Planet gears
• Ring gear
• Planet carrier
• Ring gear lid
• Sun gear crank (I cheated and used another planet carrier)

Planet gears around the sun gear (with hex middle)

Minus the bottom side bleed-through, these gears came out pretty good. I'll sand down the over-exposed bottom. I ended up drilling the center holes because some gears had a tight fit on the planet carrier.

The ring gear printed at a 20 degree slant to prevent shrink warping

The slant did not prevent the bottom side bleed-through

The planet carriers were printed at a 20 degree slant, causing a uniform ripple texture

I printed 2 planet carriers: 1 to hold the planet gears, 1 to act as a lever to the sun gear. On both, the lowest axle is slightly deformed and not at a right angle to the disc plane. The unpictured side has a hex key to fit into the sun gear or another gear set, though I didn't make the shaft long enough to insert into another planetary gear system.

I printed the lid at 20 degrees with more than enough support

The system mostly assembled

Everything fits in and does rotate, even without lubricant

The lid, in addition to being stubbly due to all the supports, is slightly bent. I'm not sure if this is warp (the planet carriers and outer ring both slightly curved) or from my pulling of the object off the lift after the print.

The lid mounting holes are 3 mm for a screw and nut, though they seem just a little too tight.

In spite of all the warping, the gears do turn! Having the actual object in hand has solidified my understanding of the gear ratios in a way reading and watching illustrations just couldn't do.