What is it?

A type of gear system whose main advantage (for our purpose) is that it has no backlash

Also allows for high gear reduction ratios, torque, and accuracy

Another common name is Strain Wave Gearing

(Harmonic Drive is a brand name for a company’s strain wave gear)

Backlash

Regular types of toothed gears have small gaps between the teeth of mating gears

This allows them to mesh and rotate smoothly and without damage

A downside of this is it lets the gears “wiggle” a little bit - the small gap means that the gears can move back and forth a small amount without moving the motor

How does it work?

Main parts

Wave generator (green)

Elliptical shaped

Centre“hub” where the input shaft attaches, and a special bearing on the outside

Flex spline (red)

Cup made of flexible metal material
External teeth on the open end of the cup
End of the cup can change shape but the base is rigid
Output attached to the bottom of the cup

Circular spline (blue)

Rigid ring with inner teeth

Two more teeth than the flex spline

This is what allows the flex spline to rotate

Output ring

Can have a fourth part depending on the harmonic drive (as explained in this video)
located directly below the blue circular spline/stator ring. It has two teeth less than the circular spline (but the same circumference)
The flex spline acts to “line up” the two teeth on either end of the wave generator (using the wedge force of the flex spline teeth on both the output ring and circular spline) causing the output ring to slowly turn

Functionality

Wave generator inserted in the flex spline, causes the flex spline to assume the elliptical shape
As the wave generator rotates, the flex spline is deformed around it
Only the teeth at the ends of the elliptical flex spline mesh with the teeth in the circular spline
Because of the tooth count difference, the flex spline rotates in the opposite direction by two teeth per wave generator rotation
How does it have no backlash: the fixed shape of the elliptical generator means that there is always pressure along the major axis between the flex spline and the circular spline. This results in the flex spline being unable to wiggle, the flex spline connects to the output gear leading to no backlash

Examples of the flex spline’s rotation

Harmonic Gear

More Technicalities

Calculating gear ratio

The gear ratio is calculated differently depending on the driving arrangement. The standard

arrangement has the circular spline fixed, the wave generator as the input, and the flexspline as the output. In this case, the gear ratio is -input speedoutput speed. Other examples are shown on page 17 here. Products from Harmonic Drive®️, are displayed using this gear ratio.

Styles

Cup

Flexspline is a cup that fits through the circular spline
Circular spline is the largest diameter
Wires exterior

Hat

Flexspline is shaped like a top hat (like cup style, but with a “brim” on the output)
Brim of the flexspline is the outermost diameter
Hole for wires through the middle

Where we need it

Current motors:

Location

Voltage

(V)

Max Current Draw [A]

Stall Torque (N-m)

Max Speed

(RPM)

Reduction Ratio To Encoder

Max Speed at Encoder

(RPM)

Datasheet

Elbow

12

25

0.669

4150

252

16.46825397

here

Wrist

24

5.5

4.8

67

1

67

here

Elbow

Biggest issue

Wrist

Second priority
Would require significant design change

Advantages and disadvantages

Advantages

Advantage	Details	Significance
Lightweight
Precise	The robot’s claw has to perform careful tasks so high precision is very important
They require little maintenance -they are either working or broken and need replacing -apparently very reliable	-would not require maintenance (as much) -lasts a long time (fewer long term costs and time associated)
Preloaded	Def: applying pressure to fix a component in place/applying extra pressure to ensure the component can handle future strain -helps to ensure zero backlash for life of gear -top of flex spline is circular (output side) while the bottom is elliptical therefore flex spline teeth flare out slightly -this results in a conical angle that helps to preload the flex spline and circular spline -preloading removes free internal clearances (no shifting)
repeatability	-maintains positional accuracy when repeating a task over and over and over again

Disadvantages

Disadvantage

Details

Significance

EXPENSIVE

- None of the principle suppliers have prices listed (that I could find) but other sources show the price to be several hundred dollars for one unit

- Would likely need to get sponsored in order to actually acquire these

Low speed output

- The high gear ratio means that the output speed is significantly lower than the input speed

- This could be more or less important depending on the joint it’s used on

Suppliers

Harmonic Drive ®️

One of the original companies to commercialize strain wave gearing
This is probably the most reliable source, they also have the most variety and documentation
Doesn’t sponsor (according to Lance) :( not surprising

Cone Drive

Details:

Production centres in the US
Large variety of options

Product options:

Offers component sets (just the plain module, would require custom housing) and gearheads (component set with housing, easier to attach to things)
Cup, hat, or ring style

Ring: axially compact and hollow center but has backlash
Only offers gearheads for cup or hat

GAM

Details:

American company
Very positive values - maybe open to sponsorship?

Product options:

Offers component sets and gearheads (I think)
Cup or hat style with different options for input shafts
Includes an “ultra thin” option

Kofon

Details:

Chinese company
Not too many options but probably enough to suit our needs

Product options:

Component set (closed center)
A few different gearhead styles (hollow or closed center)

[still to research]

Make our own

Probably not the best accuracy which completely defeats the purpose
Cheap though!

Usage examples

From Cone Drive website

From Harmonic Drive®️ website

From this video (technically a cycloid gearbox, not harmonic drive, but similar enough concept)

From here

NASA Exploration Rover

General design observations

Styles: I’ve been working off of the examples in this section but there are others if you look at the suppliers section. The cup and hat seem like the most common and useful options which is why I was focusing on them. Don’t forget there are options with hollow centres (although less)
Elbow: The majority of real world examples have each segment offset from the previous one, with (I assume) the gearbox in one segment and the motor sitting inside the other. However I don’t think that will work for us because the bicep is much less heavy duty than those examples and is not designed to hold the entire weight of the forearm on one side. It probably wouldn’t hold and if it did it would unbalance the arm a lot.
Elbow: Keep the width of the forearm in mind, because that can’t change unless we decide to replace the wrist gearbox (or unless you really want to get into redesigning the wrist)

Wrist: This is lower priority but if we decide to go this route it could give us more freedom with the elbow. However it would require a significant design change