Selecting Gearing for Your Motion Control Rig

After you've selected the motor type appropriate for your project, it's time to move to the next stage of building your first motion control rig: gear selection.  Unless you've bought a motor with an attached gearbox (and even if you have, in some cases), it's time to figure out exactly how you intend transfer power from the motor into your final motion.  Just like the process of selecting a motor, you'll need to first examine your requirements, and how they might change over time.  In this article, we'll walk through the basic process of selecting the proper gear train, and the different factors that should affect your decision.

The basic factors to consider are: building vs. buying, complexity, gear ratio, precision, and braking requirements.

The Gear Train

Any transition of motion between two components requires at least two gear components: the drive gear and the driven gear.  These gears, and any shafting, bearings, or other mechanical components will be referred to as the gear train throughout this article.  This article is not intended to go deeply into the theory or operation of the different types of gear chains discussed, as there are both numerous and excellent articles on each elsewhere (and links will be provided where available), but instead to introduce the different types and provide information tailored towards DIY photography motion control.

For more Information on gear trains and operation, see the excellent article from Society of Robots.  Of course, there's also a Wikipedia article on the subject of gears.

Build vs. Buy

The first question you'll need to ask yourself is "Do I intend to buy a pre-built gearbox, or build one myself?" - if your intention is to build one yourself, you will obviously limit complexity of the gear chain based on your skills and available tooling.  While an old-hand at machining will happily design and build their gear train from the gears up, most of us will be at least purchasing the gears and mechanical components. If any tooling is an issue then you'll want to seriously consider buying pre-made gearboxes and/or limit yourself to gear trains that can be readily attached to them.  Worm, planetary, and spur gearboxes are readily available in standard and unique sizes for all types of motors.  Ready-made gear boxes can run several times the cost of one designed and assembled yourself from loose gears and mechanical components.  For highly precise, high torque, or high speed applications, it may be necessary to buy a pre-made gear box to your specifications. 

Consider your budget when deciding on the type of gear train you want to use, as the more complex your gear train is the more costly it will become.

Complexity

Without a doubt, complexity will be the largest driving factor in your decision.  The more complex a gear train is the less likely you are to succeed in producing it yourself if this is a first project.  As you add transitions between gears, the amount of effort required to line up the gears, and the number of design factors to consider increases.  While certain types of gear trains are simple to design and build in single transitions, they can quickly turn highly complex once multiple transitions are required.  Some gear types, like spur gears or timing belts, are much more simple and inexpensive to implement than a worm gear train until you make several transitions.  When considering the remaining factors, also take into account how your decisions on them will impact the complexity of the design that you will be left with.

Gear Ratio

The gear ratio determines whether the motor's output speed and torque are either increased or decreased.  When you decrease the speed, you increase torque by an equivalent ratio, and vice-versa. A gear ratio is considered reduced if the rotation of the drive gear results in fewer complete rotations of the driven gear, and increased when it results in more complete rotations of the driven gear.  We use a ratio to indicate this relationship, with the drive gear on the left-hand side and the driven gear on the right.  For example: 20:1 for a low gear would mean 20 rotations of the motor shaft (to which the drive gear is attached) result in 1 rotation of the driven gear.

Generally speaking, for motion control, we're almost always reducing the gear ratio.  This is done for two reasons: to slow the output motion down, and to increase the available torque.  Slowing down the motor allows us to more easily create timelapse shots where speeds tend to be much slower than in real-time work, and increasing the torque allows us to increase the payload we can move around while still staying within a power consumption or size budget.

Keep in mind, however, that while we can shift the speed band for a motor up or down with a gear train, we cannot change the range of speeds available.  A 100 RPM motor that has a 50% speed range with its controller can be used effectively from 50-100 RPM.  Reducing its speed with a 10:1 gear ratio allows the output speed to be 5-10 RPM.  We've only moved the band for the speeds, if you will, without increasing the overall range of speed available.

Some gear types lend themselves more easily to high reduction ratios than others, getting very high ratios (100:1 or greater) can often require too many transitions for spur gears, while worm gears can achieve this easily in a single transition.

We can increase or reduce even more by using a series of transitions.  You can put two gears on the same shaft, usually one much large or smaller than the other, and then use this second gear to transition to yet another.  Each transition is multiplied by the next so that you can reduce the gear ratio even further than the difference between just two gears can allow.  The following image shows a very simple form of reducing the gear ratio twice:

Precision

We want to design for as much precision as we need, and not as much as we think we want.  Like with any other part of our project, as we increase precision, we increase cost at a rate higher than the precision its self.  It's easy enough to think "I want extreme precision," without actually needing it.  Even for shooting sequences to be overlaid in post-production one usually doesn't require absolute precision -- available margins of error are defined by many factors, including lens focal length, focal depth, sensor size, output video resolution (1080, 2k, 4k, 8k..) frame rate, compression factors, etc.  Tiny variations will rarely, if ever, be noticed in most applications and even larger precision errors can often be compensated for - at a much lower cost than eliminating the error.

The primary precision issue we're going to be dealing with is backlash. When the teeth of two gears are pressed into each other in the direction of rotation, the distance between them in the opposite, or transverse, direction is called backlash.  This presents its self in a failure of the driven gear to move for a brief moment when first moving in a transverse direction.  In motion control applications this causes problems by "losing" part of the movement, or basically going a shorter and shorter total distance each time you change directions.  If your encoder is on the motor shaft, and not on the driven gear, this variation will not be accountable from the encoder - even with feedback, accuracy is reduced.  Few gear trains have no backlash, and the amount of backlash is usually inversely related to the expense of the components you are buying and the quality of the engineering.  That is to say, the less backlash your requirements can tolerate, the more you will be spending.  An exception to the general rule are timing belt gear trains - these usually have little to no backlash due to the fact that the teeth of timing belts are usually made of fairly flexible materials and can press deep into the teeth of a pulley and thus fill any gaps. 

(image from wikimedia commons)

Fortunately, backlash can usually be compensated for with motors that have a sense of discrete movements: steppers or DC motors with encoders.  To tune for backlash, simply measure the backlash by counting how many discrete movements it takes before the driven gear starts moving again after a direction change.  Then, to compensate, adjust your software to add that many movements after any direction change.

Complexity can reduce precision as well.  Backlash multiplies through gear trains with several transitions, as the backlash must be consumed at each transition before the next transition can begin its movement.  Consider the impact of backlash throughout entire gear trains.  Backlash in commercially-available gear boxes often ranges from a few arc-seconds to arc-minutes, in all but the most highly precise motors (having many thousands of discrete movements) even backlash in arc-minutes can be compensated for in software. 

To increase precision without reducing backlash, install an encoder on both your drive (motor) shaft and your driven (output) shaft, then measure movement from both encoder.  In this way, you will observe actual output motion and motion of the motor - with the measurements at the drive shaft offering the highest level of precision, and the measurements at the driven shaft used to correct for errors.

Braking Requirements

I've included this in the list of core factors to consider because it's an often over-looked factor, and yet plays such an important role in power consumption.  If power was one of the limiting factors in your motor selection, you'll want to consider how you handle axes that are moving your payload against gravity, namely the tilt, roll, or yaw axes.  A worm gear train has an interesting property wherein the driven gear (the worm gear) cannot move the drive gear (worm wheel) when a large amount of reduction is employed, due to the fact that the friction in this direction increases greatly the lower the ratio gets.  This means that it is nearly impossible to spin the gear chain by moving the camera or other object being rotated without exerting so much force as to damage the gear train - resulting in an ability to completely cut power when desired without much movement, if any.  While many DC motors can be put in a brake mode at a much lower power consumption than when moving, for systems that are very sensitive to power consumption, consider self-braking gear trains as one technique to aid in power consumption. 

Self-braking gear trains like a very low worm reduction (100:1 or lower) do have a drawback: they greatly reduce your maximum speed, and carry inefficiencies with them.  Again, when your budget is utmost concern, pick the choice that most closely matches you need, and not what you think you might need in the future.  You'll almost always end up making changes, and it's best to get something that just works today, than something that might work a long time from now.

Gear Types

There are a very wide range of ways to transmit power from one thing to another. Rather than create a large volume discussing every single type of gear train, we'll focus on the three most most commonly used in DIY motion control projects. 

• Spur


• Timing Belt and Pulleys


• Worm

Each of these types can be implemented, depending on the complexity you design for, by the average hobbyist.  We're not going to go deeply into the theory of gear operation and engineering models for implementing, but instead focus on the high-level information that will be most useful for selecting the type of gear train for your project, so that you may focus your research on the type that most meets your needs.

Spur

Spur gears are one of the most common types in use, and can be one of the more simple gear trains to implement for moderate to low reduction ratios. A spur gear is effectively a circle with teeth.  In essence, the reduction ratio is determined by comparing the pitch diameter of two gears* - that is, if you have two gears, one with a 1" PD, and one with a 2" PD, then the effective ratio of using the two together will be either 2:1 or 1:2, depending on which is the drive and which is the driven gear.  As discussed in the Gear Ratio section above, multiple transitions can be used to further reduce the gear ratio.

While simple spur gear trains are easy to implement, there are certain limitations, namely in the amount of reduction available in a single transition.  As we noted above, the ratio is determined by the relationship of the pitch diameters of the two gears, and the minimum pitch diameter is impacted by your motor shaft size.  You can't put a .25" pitch diameter gear on a .50" shaft!  This means that you will be limited in a single transition by sizing constraints -- if your drive gear is 1" in diameter, to get a 10:1 reduction ratio from a single transition, you will need a 10" pitch diameter gear!  To get around this limitation, you can do multiple transitions, each doubling or tripling the one before.  So, if you have three transitions between the drive and driven gears: 3:1, 2:1, 2:1, you simply multiply the ratios -- 3x2x2 = 12:1.

Backlash in spur gear trains is a function of both gear quality, gear design, and overall system design.  Since you are most likely not building the gears yourself, the backlash factor you can control is system design.  That is, the less perfect your gear placements are, the more backlash you will introduce into your gear train.  The more transitions you add, the more this factor will multiply.  It is for this reason, and the increased design requirements that we find that spur gears are less complex for low reduction ratios, but become increasily complex as the reduction ratio increases.

Spur gears are available in a wide variety of materials.  General experience tells you that metal is stronger than plastic, but this can be very misleading.  While it is true that more torque can be executed through metal gearing before reaching the fatigue point of the material, modern plastics such as Delrin wear less in daily usage, and have self-lubricating properties when blended with PTFE (Teflon).  Metal gears require lubrication, and the introduction of lubrication increases the backlash as there must be space between the teeth for this lubrication to inhabit.  For high-torque applications, choose metal gears (and deal with the ramifications), but for lower torque applications where easier precision is required and longer life is desired, choose Delrin or similar engineered plastics.  Generally speaking, avoid nylon as a material as it lacks both the high torque capabilities and long-life of materials like Delrin.

* - note: pitch diameter is determined using gear module

Timing Belt and Pulleys

A timing belt is a toothed belt used to transmit power from one pulley to another.  While we often hear of them in relationship to our vehicles, they are widely used in motion control applications for the simple fact that they are highly efficient, easy to implement, and have little to no backlash.  A timing belt pulley is a specially-designed pulley that have grooves for the teeth to mate into. While there are many other types of belts that can be used to transmit power, timing belts are usualy the best combination for function, precision, and low cost.

A timing belt and pulley combination is by far one of the easiest to implement for a first-time motion control project.  There are no backlash issues as long as the belt has a proper tension, and the parts required are generally of a very low cost.  Of course, nothing comes for free, and what you're giving up here is the ability to get very high reduction ratios.  The pulleys act as the gears in a system like this, and as such the pulleys pitch diameter determines the reduction ratio (a 1" PD pulley has the same relationship to a 2" PD pulley as in Spur gears).  Rarely are pulleys commercially available that offer greater than a 4:1 ratio.  This means that for systems requiring very high reduction ratios, numerous belts and pulleys must be used. 

It is possible, of course, to mix pulleys with spur gears, worm gears, etc, and pulleys are an excellent way to transmit power from a motor to a remote output shaft without modifying the gear ratio.

For linear motion, it is possible to make a simple drive train out of a single drive pulley, two idler pulleys, and two fixed anchor points.  This configuration is often referred to as "omega drive" as the design looks similar to to the Greek Omega symbol.  In such a design, the timing belt is fixed at both ends of the range of motion (at each end of a track, for example), and the belt is wrapped around an idler pulley (one that spins freely) and then back around the drive pulley (attached directly to the motor shaft), and then back around the second idler pulley.  This makes a very simple, low cost linear drive that is limited only by the maximum length of belt you can secure, with no backlash.  For linear motion, note that the distance traveled per revolution of the motor is the pitch circumference of the drive pulley.  The benefit of this configuration over others is that the idler pulleys provide tension on the drive pulley without requiring complex engineering.  It is considered superior to a closed-loop style belt drive (see above image) for a lower cost and greater system flexibility in linear axes.

Worm

Worm gears are a special type of gear configuration consisting of a worm wheel (the drive gear), and a worm gear (the driven gear).  The worm wheel is very similar to a screw in design, in that the gear teeth are fashioned as a ridge or thread that spirals around the wheel.  The worm wheel is a special kind of gear, that looks very similar to a spur gear, but has a special tooth configuration that is designed to mate properly with its companion worm wheel.  A worm gear train is especially useful for creating very high reduction ratios, as the ratio is not determined by the pitch diameter of the gears, but in a fixed formula: the number of teeth on the worm gear to one.  That is, a 100 tooth worm gear mated with a proper worm wheel will produce a 100:1 reduction ratio.

The complexity in a worm gear train comes from the fact that the rotation of the worm wheel is perpendicular to the rotation of the worm gear.  This means that for an output shaft at one angle, the input shaft (motor shaft) must be at a 90' angle in 3D space (see image below).  Additional complexity comes from the fact that worm wheels must be accurately mated to the worm wheel, otherwise backlash is greatly increased.  While very low backlash can be achieved, it often requires regular adjustment of the mating between the gears, and for this reason the motors are often mounted on adjustable plates to allow one to tune the drive as the gears wear.

Worms wheels are often made of un-hardened steel while worm gears are often made of bronze.  While both can be made out of plastic, plastic should not be used where very high torque in combination with a very high reduction ratio due to stress and fatigue on the material.  For many photographic motion control systems, engineered plastics such as Delrin can be well-utilized.  As with spur gears, avoid nylon gears due to poor fatigue and wear properties.

Once a very high reduction ratio is achieved (100:1 or greater), the braking effect of a worm gear train is nearly infinite.  This is due to friction between the worm wheel and the worm gear.  At high reduction ratios, it is nearly impossible to spin the gear train by moving the payload.  This means that worm gear trains can be used in applications such as tilting where cutting power to the motors between moves is desired (for reduced power consumption).

For very low reduction ratios (10:1 or less), worm gear trains should be avoided as they add unnecessary complexity over pulley or spur gear trains, but for very high reduction ratios they are impossible to beat.

Summary Table

The following table compares each gear train type based on the core factors needed to be considered for a motion control application:

I hope this article helps you choose the right gear train for your application.  Obviously, there is much more that can be said about the operation of each of these kinds of gears, but this article is designed to help you focus on which type will suit your needs best, so further research can be done on one type most relevant for your needs. 

In future articles, we'll cover electronics selection and overall system design.

- c. a. church