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Harmonic drives – the new kid on the block

Bill Stent

Old types of astro mounts

Until recently, most go-to mounts for astronomy have used worm drives. Worm drives are made up of a pair of gears, one at right-angles to the other. The worm looks like a screw, and it is driven by a stepper motor. As it turns, the worm works its way along gear that rotates the axis of the mount.

Tracking equatorial mounts include two of these, one for the right ascension axis, and one for the declination axis. On an equatorial mount, the right ascension turns continuously to keep up with the earth’s rotation. For viewing mounts, the declination motor doesn’t move unless you’re slewing the scope. But if you have an autoguider, the declination axis moves backwards and forwards, constantly reversing direction to compensate for tracking errors. And as you’ll see, this changing direction is a problem.

A worm gear. This one is out of an NEQ6 mount.

Backlash and how it can ruin your astrophotography

These drives have a range of problems. The most significant one is backlash. Whenever teeth mesh, there has to be a tiny gap between them or they’ll bind and wear. The effect of backlash is that there can be a delay between when the driving gear starts and when the driven gear starts. This delay happens every time the gear changes direction, as the gears have to cross the gap caused by the backlash.

The situation is only made worse if there is more than one gear in the train. Driving the worm gear with a belt eliminates some, but not all of your backlash.

When your autoguider is instructing the declination drive to go backwards and forwards to track the stars, it’ll seem as though the mount is hesitating for a while before carrying out the autoguider’s instructions. For extremely precise applications like autoguided astrophotography, this can mean the difference between a good result and ugly egg-shaped stars.

The solution? The harmonic drive!

Enter the harmonic drive. This has been around for a while, mainly being used in industrial robotics. In fact, Rainbow Robotics in Korea was a pioneer of the harmonic drive for astronomy.

How does it work?

There are three elements to the harmonic drive: the wave generator, a flexible spline with teeth on the outside and a circular spline with its teeth on the inside.

The wave generator is an elliptical plate surrounded by bearings. This is the driven element, normally connected to a stepper motor.

The wave generator sits inside the flexible spline. As the wave generator rotates, it physically deforms the flexible spline. Consequently, the spline assumes the shape of the rotating ellipse, even though it is not rotating much itself.

The flexible spline sits inside the circular spline so that the teeth on the flexible spline mesh with the teeth inside the circular spline only at the long axis of the ellipse shape. Along the short axis, the teeth don’t make contact at all.

The secret behind the magic is that the circular spline has two more teeth than the flexible spline. This means that as the wave generator rotates, and the shape of the flexible spline changes, the tooth on the flexible spline disengages from the tooth on the circular spline, then works its way to the next tooth along the circular spline rather than coming back to the same one. Genius!

Harmonic drive animation courtesy of Wikipedia user Jahobr.

Bye-bye backlash!

The advantage of this design for astrophotography is that there is always a part of the flexible spline in contact with the circular spline. Because of this, backlash is effectively eliminated.

Other advantages

Apart from no backlash, mounts powered by harmonic drives have other advantages.

The shape of the gears means that the motor effectively uses a series of wedges to drive the load. This means the motor has a very high level of torque. This means that the mounts can have a high carrying capacity for their weight. Typically, conventional wormgear mounts can accurately carry between about 1.5 to 2.5 times their own weight. Harmonic drives can carry a lot more: around 3 to 4 times their own weight. So, for a set amount of gear, the mount can be significantly lighter and more portable.

The high torque also means that if your gear is under a certain amount of weight, you won’t need a counterweight. The harmonic drive can hold it up and move it around with ease. Of course, working without a counterweight can mean your telescope can be worrying distance from the top of the tripod, so make sure the tripod is stable.

Any disadvantages?

The harmonic drive does not eliminate periodic error. Because every tooth in the splines might be a slightly different shape, the periodic errors seen in the drive’s behaviour can be very complex with short periods. For this reason, harmonic mounts work best with autoguiding.

Most autoguiding software products, including PHD, have guiding algorithms that can assess, then compensate for, periodic error displayed by the mount. This is the best way of handling the complex periodic error that harmonic drives produce. With adequate management, periodic error fades into the background, and your mount guides beautifully.

So where are we?

Harmonic drives are set to become widespread in astronomy. Whether or not it’s the “next big thing” isn’t certain, but manufacturers are scrambling to get their brands out there.

There are now several brands of astro mounts using harmonic drives. Sidereal Trading has the largest range of harmonic mounts in Australia, with mounts from Rainbow, iOptron, ZWO and Pegasus.

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