# The USMSG part 3 – Determine the accuracy

Once we know our motor’s torque specification we’re almost ready to start looking at catalogs. We just need to define the level of accuracy or resolution that our motor and gear train need to have. This all comes, obviously, from our initial high-level specification. Let’s make it specific now.

## Step 3: Determine (remember) the accuracy

Your mechanism’s accuracy and precision will be only as good as your motor’s and gears’ are. If you need to have really fine motion (say, for an antenna or laser pointing mechanism) you will be looking at different motors and components than if you just want to spin at a constant speed in only one direction and don’t really care where you stop.

So let’s start by looking at the motor’s accuracy:

Your stepper motor has a spec called “Step Angle” that determines how many degrees the shaft rotates when jumping from one step to the next one (detent to detent). The smaller the number the finer the step.

The most common steppers come with 1.8 deg/step (200 steps/rev), but other common finer motors have 0.9 deg/step, and coarser motors can go as high as 7 deg/step or more (I recently heard about a 15deg/step motor). The step angle will affect both the torque and the ultimate max speed of your motor. Higher step angles will usually be able to spin at higher max speeds for the same voltage than finer motors, and will also be able to output more torque.

Stepper motors also have a spec called “Step Accuracy” that is usually given in % (the most common being +/-5%), which is how accurately the rotor jumps from one step to the other.

For example, in a 1.8 deg/step motor an accuracy of +/-5% means that the rotor will have a positional error of 0.09 deg on each step. Not bad!

This error is not cumulative (which is good), but is an intrinsic characteristic of the motor due to how the metal bits respond to the electro-mechanical impulses. So, if you’re really concerned about this error, you could microstep since each microstep will carry the same error.

“Microstepping” means splitting each step into a discrete amount of virtual steps. This is accomplished by energizing the different phases of the motor with variable voltage instead of with pulses. The higher the number of microsteps (uSteps) per step, the smaller the uStep.

For example, if you microstep (uStep) that same 1.8 deg/step motor at 10 uSteps, the shaft will rotate 0.18 deg +/-5% with each uStep. The motion starts to become really fine without the need of high gear reductions, and the error will be of 0.009 deg/uStep. Pretty darn good!

Another option would be to find a motor with finer Step Angle, but you need to look at the whole picture (Thy Spec) and make sure that it doesn’t affect your other specs (speed and torque). Yet one more option is to get a coarse motor and attach it to a high-reduction gear train. Remember that what matters is the output, and there’s many ways of getting to the same result. It all depends on your application, your budget, your space envelope, or as I’ve been calling it: Thy Spec.

Motors with smaller % error can be found but will most likely be more expensive. But you can get around this with a gear train. Depending on your design, your drive train (gear trains, gearboxes, or pulleys) may have a multiplying or dividing ratio. A multiplier (more common) will minimize your motor error, while a divider will amplify it. Gears have their own issues and challenges, so at the end it is your application (Thy Spec) will tell you what’s more critical, the motor or the drive train.

So, moving on to the gear train:

Gearboxes, as well as belts and pulleys, have a “Backlash” spec, which means how much “play” there is between gears so that they can engage and rotate freely when connected to each other in a gear train. This spec varies with the gear type and gear train type, so you have to ask your supplier.

A typical spur gear has a backlash of +/-2deg. But some gear types, like the helical ones, can have significantly less backlash than a typical spur gear mainly due to how many teeth are engaged at the same time. There’s also Zero backlash gears, that have spring loaded teeth, so there’s ways to avoid it.

Also, look at your spec, if you are always rotating in the same direction you might not be too concerned about the backlash since you’ll always be on the same side of it. But if you are expecting your mechanism to frequently change direction (as in most CNC machines), you should take this spec into account as it could potentially have a great impact on your accuracy and repeatability. A good thing is that, since it depends on the type of gear and gear train, it can be considered a constant and you may be able to compensate for it with encoders and software (or not).

So, kind of throwing out a rule of thumb here, you can think of the different type of geartrains the following way:

• If you don’t really care too much about the effect of the backlash on your accuracy you can go with a simple spur gear gearbox.
• The next level is a gearbox made with Honed-gears, which are slightly better than spurs since these gears were carefully machined, polished and finished in pairs.
• If your mechanism requires high positional accuracy you’ll probably want to choose a planetary gearbox, that can have a typical backlash of 30 arc-min (0.5deg) or less.
• But if you want absolute zero backlash, and you got the money, go for a harmonic drive. These babies have zero backlash and are super cool. Your mechanism will automatically become a superstar if it has a harmonic drive. People will buy it drinks and invite it to parties and be the center of attention.

Keep in mind that if a gearbox has a backlash spec of +/-1 deg (or more), it doesn’t mean it’s a bad or low quality gearbox. It may actually be a really nice, high quality, durable, strong gearbox, but just not suitable for your application. So, once again, KNOW THY SPEC.

So our motor spec is complete! We know the torque, speed, resolution and accuracy of our motor. Lets look at catalogs and torque curves!

Oscar