The Big Thread O' Linear Motion

I've been doing a whole bunch of research on methods of linear locomotion thanks to @Tweakie's pointers, and figured I should put some of those findings in one place where it can be discussed and added to over time, an accumulation of the combined experience of the forum.

I'm sure most of it is already known to most members- it's as much for my own understanding and reference as anything- but some will be further advanced than others (a fair amount of this would have been news to me last year), or travelling along different paths, so I like the idea of a collection of relatively specialised information. Obviously one thread can't contain the entirety of the world's knowledge on any given subject, but if we have all the basics down and provide links to good sources for further research, I think we can provide a solid starting point. Whether to members looking at options for upcoming builds, or to passers-by who might find this forum over, say, CNC Zone and look into the FOSSH(?) thing we got goin'!

So like a Wiki, but with less separation. A more linear read. But this way, questions, additions, etc. can be commented over time.

DRIVERS:

Stepper Motor

Theory

A stepper motor is like a multi-phase AC motor, in that it attracts a specifically shaped iron rotor in sequential order, though rather than relying on induced currents to generate magnetic field, it uses a gear-shaped rotor and applies the inverse cube law of magnetism to selectively attract only the tips of the teeth (which, furthest from the hub, applies the most torque on the shaft). The number and spacing of the teeth are selected so that they're spaced from the next phase winding appropriately to produce the desired number of steps per revolution (typically 200).

Now steppers tend to also contain use permanent magnets as a hybrid system, where there are two "gears" fore and aft with the teeth directly out of phase with each other. The gears are connected as a single magnet, with each one being a pole. This allows significantly increased power out of smaller packages since the magnetic pull is from both coil and rotor instead of just rotor.

The coils are energised in a sort of "digitised sine wave" by the stepper, pulling the rotor around a specific angle (typically 1.8 degrees +/-3-5%) on each step.

Practice

Steppers are the cheapest and easiest method of precision control. They give good repeatability and are pretty hard to damage.

Unforunately, the faster you drive them, the lower the torque gets; because coils of any kind take time to fully energise due to inductive reverse-voltage (Back-EMF; the coil induces a current in itself from the magnetic field caused by the increasing electric field through it), if the next step is initialised before the current step has had time to come up to full coil current, then maximum torque (from magnetic force between rotor and stator) is obviously never quite reached.

They require a driver, a circuit that converts two-channel step and direction logic commands into 4, 6, or 8-channel high-current coil power. These aren't really cheap- they start at around $10-12 and rise rapidly from there.

Typical steppers that you'll come into contact with (other than dismantling hard drives and printers!) are:

• NEMA 17 - good all-round low-power motor, can do most things you need them to do at 9-12V, 1.8A. Around $15-25. Drivers about $10.
  
• NEMA 23 - "high power" by typical hobbyist standards, can force spindles through Alu at 24V, 2.8A, though not especially quickly. Around $20-60. 3A drivers are more in the region of $12-20.
  
• NEMA 34- double or more the torque of NEMA 23s, but typically several times the cost. Necessary when you would be driving NEMA 23s at too high a speed to maintain a required torque (to push into metal, for example). Around $60-170. Tend to take somewhere in the region of 3.8-4.5A, so you probably shouldn't expect to pay less than $50 per motor for drivers.

Continuous Rotation Servo

Servomotors are servomechanisms (that is, a closed-loop system with corrective negative feedback). This is typically implemented in continuous form as a geared motor with some kind of rotary encoder which provides basic positional or speed feedback.

Industrial Servos

Industrial servos generally just look like high torque stepper motors, since they're typically a motor and a planetary gearbox. Unlike hobby servos, industrial servos use rotary encoders and tend to take AC power- the more powerful ones use 3-phase high voltage.

There are two types of rotary encoders available in these servos; incremental and absolute. Incremental encoders contain sufficient information on the rotating code for the servo driver to know how far the servo has turned since an arbitrary position and how fast it's currently turning (like a mousewheel). Absolute encoders contain significantly more information- and require equivalently complex driver controllers- so that the servo's position is known from startup, as well as the above information. These setups are more expensive, but useful for critical systems where positional immunity to power cuts or other hard resets, or instantaneous operability, are requirements. Incremental encoders can contain a zeroing code, which has to be found before the driver knows exactly where the servo's position is, as part of a startup sequence.

Industrial servos are better found used, but even then, you're probably still looking at NEMA 34 prices. They're significantly more powerful (up to tens of kW) and flexible than steppers (no loss of torque at high speed, higher resolution, option of absolute positional feedback) but are accordingly far higher priced. Good for more industrial type machines intended for small-scale commercial use, but typically not justifiable for hobbyist budgets.

Hobby Servos

Hobby servos tend not to be continuous motion, but turn at full speed between +/-60-90 degrees, as measured by a basic rotary potentiometer. Ones converted for continuous motion ignore the pot, remove the hard end stops from the output shaft gear and change the PWM control from position to speed; 1.5ms between pulses is stationary, 1ms is full reverse, 2ms is full forward.

The problem with hobby grade continuous rotation servos is that they're no longer true servos- there is no feedback mechanism unless the pot gets replaced with a continuous rotary encoder, and it typically doesn't- they simply get speed-controlled via PWM control of an H-bridge. Some other form of positional feedback is required for CNC applications.

They tend to be relatively low speed and torque, too, suitable only really for laser or 3D printing applications rather than milling. Only a few retailers sell continuous motion hobby servos, they seem to mostly be custom Futaba S148s by Parallax and a few OEM Hitecs, but they're not too difficult to find online.

Geared Motor

Adding gearing to a stepper, or even rolling your own servomotor solution, requires some form of gear mechanism customised to individual requirements. The most popular two I've seen are some variation on the spur gear and worm gear.

Spur Gear

Spur gear is the usual form of gearing on motors, proving both high and low ratios and gearing both up and down. They're simple and cheap, but can be susceptible to back-drive from a mill spindle without a sufficiently high power motor driving them.

Spur gears are subject to backlash- cheaper, non-rounded-tooth ones especially so, but they're available in more expensive helical tooth forms to maintain constant tooth contact to reduce lash. By design, it's impossible to entirely remove lash from a spur gear system without unduly wearing the teeth and overloading the motor.

Worm Gear

Worm gears are spiral gears that engage a rack or rack gear (a large spur gear, essentially) at very high gearing ratios. They're very good at resisting back-drive and dynamic loading, due to the angle of the meeting force vectors, but the downside is that they are, rather by definition, very slow linear drivers unless you're using the worm gear as a direct drive on a straight track- and even then it's not the fastest option.

Since it's a right angle gearing, worm-based gearboxes rotate the driveshaft direction 90 degrees.

Advantages: High forward force, low back-drive

Disadvantages: still not backlash-free, slow-moving.

DRIVENS:

Belt

Toothed, or timing, belts are the most simple solution and typically, in our use, used directly from a stepper motor with a toothed pulley. Belts are typically some form of skinned neoprene or rubber composite with internal fibreglass or Kevlar cords for strength.

The distance travelled per step is dictated by number of steps per revolution, number of teeth on the pulley, and the pitch of the teeth on the belt and pulley. Eg: a 2mm pitch belt on a pulley with 20 teeth will move 40mm per motor revolution. If the motor has 200 steps, then it'll take 200 steps to move the belt 40mm. Ergo, each step moves the belt 40/200 = 0.2mm.

Clearly, if you need positional resolution significantly lower than this, you'll have to use microstepping- and lose accuracy- or a high-toothed wheel- and lose torque. Since it's hard to make finer-toothed belt without sacrificing durability, it's probably generally best left to rapid prototyping uses- 3D printers and foam carvers- though it did work pretty well on my timelapse slider build.

Screw Drive (lead screw)

Screw drive is the next best thing in the cheap-linear-motion stable. ACME (29 degree thread angle) and trapezoidal (30 degree thread angle) threads are extremely accurate and, since they're available in various diameters and thread pitches, can be used for a variety of applications.

Since thread pitches tend to be under about 10mm, and often under 5mm, the resolution can be much greater than belt. A 200-step motor turning the 8x8mm screw in the OBPS will move 8mm per turn, or 0.04mm per step. A fifth the resolution of the OBPS GT2 belt.

For some applications like timelapse photography, cutting power to the motor driver won't result in the camera taking a tumble, and this could be used to save battery power in off-grid applications.

There is, however, an issue with screw drive. The nuts, typically either Delrin or brass, are designed to be softer than the screw material because they're easier to replace. Their longevity, however, depending on application, can be limited. Light, low-power uses like 3D printers are probably safe, and a good alternative to belts for thinner filaments. Lasers are low-load but tend to be high speed, and would probably be good with brass. Milling and other loaded applications don't seem to fare so well- I've seen multiple reports of lead nuts lasting a few days to a few weeks before backlash became overpowering, though this could be the result of poor lubrication.

Anti-backlash lead nuts with two sections under spring tension are available, though the anti-backlash mechanism only holds so long as the force applied by back-drive is lower than that applied by the spring.

Ball Screw

The solution to high-load precision applications? Ball screws. Here, the threads are curved to accept tiny ball bearings as a helical race, and instead of face-to-face contact, the nut threads are made up of spirals of ball bearing tracks, looped over to begin again from the beginning of the nut.

Ball screws naturally have very low friction and thus require relatively little lubrication, whilst operating at around twice the mechanical efficiency than lead screws, and therefore reduce motor power requirements. However, because the friction is so low, higher-torque motors down-gearing, or some kind of active braking mechanism is required to eliminate the natural tendency to back-drive.

Ball screws can be made in one of two ways: ground or rolled. Rolling is cheaper, and the better ones are accurate to around a thou per foot of linear motion, or 0.025mm per 300mm. If you need tolerances tighter than this, it's better to go with ground (often called "precision" or "high precision") screws, which are steel rods, hardened and ground to shape. Grades vary, but typically an order of magnitude more precise than rolled- measured in thousandths of mm rather than hundredths.

Backlash typically isn't a concern, as ball screw nuts tend to have anti-backlash mechanisms, built to push the bearings into the screw threads at an angle, to quite high loading tolerances, and are sometimes user adjustable via screws.

Rack and Pinion

Rack and pinion is a popular control mechanism for CNC machines. It takes up little space and is easy to implement, it can be made quite powerful, it's cheap, it's harder to back-drive than ball screws, and can be made to high precision. In helical rather than spur tooth format, it's quiet and low-backlash too, though here you encounter the higher prices of more precise and complex machined geometry.

Rack and pinion, essentially, is a metal belt, so it's probably the cheapest and easiest method of driving high power machines, providing you don't have a problem with the belt problems I mentioned earlier. Of course, metal teeth can take more power at smaller dimensions without damage or distortion than rubber ones can.

Rack and pinion tends to be more dimensionally stable over longer runs than ball screws, and can be moved faster if feed rates are a concern.

CONTROL

Feedback

Servos and motors must have feedback loops of some kind in order to provide positional information, as the only inputs that can be provided are power (not necessarily directly equatable to speed) and duration. The easiest way to do this would be to provide stepping information via a rotary encoder on the turning shaft.

Alternatively, some form of linear resistive track can frequently be used- indeed, are sold as stand-alone kits in various lengths for digitising traditional handwheel mills as well as hobbyist linear pots like these from SparkFun.

Alternate methods that I'm looking at are/will be in this thread (primarily narrow-beam LED intensity calibration and magnetic linear Hall effect).

THE END

I hope this is/was helpful to somebody, it's not complete by any stretch of the imagination, I don't think it's actually even all the information contained in my head since I have memory access issues sometimes! But it should be most of it.

I'm planning on coming back through and adding relevant photos and illustrations at some point too.

The conclusion for my own (500x500x200) machine was NEMA 23s (price!) driving 12x2mm rolled ball screws (Chinese ones are reasonably priced, hopefully they're not lying about the accuracy), for those interested. Haven't decided on linear positional feedback yet.

Additions, corrections, questions, relevant links, whatever; just fire away!