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Showing posts from 2018

One table to run them all

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In previous entries, I have delved into the idea of using different shapes for the speed pattern for a motion using steppers and have presented how the timing can be based on a look-up table. Such a table would be pre-calculated and flashed with the firmware. But a single table provides a pattern for a given max speed, acceleration, number of steps and speed shape.


You can use that for timing the steps of the motor and it will accelerate properly as many steps as entries on your table. But it won't be practical if we want to change any of these parameters for other movements.
The idea I am not yet sure this works as expected, but first tests look ok, finally, as it took me a while to figure this out.
I have created a lookup table as the graph above, where each entry contains the delay needed for each step, for a movement of 1000 steps total, where speed will increase to 2Π while time goes till 2Π too. Maximum speed for each different motion pattern will be different though, but th…

More experiments with motion curves for steppers

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Though I have been experimenting with Arduino, I realize that as soon as the computing requirements grow a bit the results quickly show the processor is actually slowing down my results. So now I am using a DOIT Espduino featuring an ESP32 processor that makes that sensitivity go away.

It was a bit of a challenge to get this board to work with CNCshield v3. The culprit was resistor R1 (enable pin) that would affect the booting capability of the ESP32. Once R1 was removed (brutally destroyed with a wire cutter in my case) the problem was gone and I could upload and run code with the Arduino IDE.

I created a simple program that uses some pre-calculated delays to perform the motion using different expressions for the acceleration. Four have been used and shown in the video below:

Uniform acceleration a=kSinusoidal acceleration a=1-cos(t)Exponential a=(e^(cos(t/2)-1)*sin(t/2))/2Exponential2 a=(e^(-(t-sin(t))/pi)*(1-cos(t)))/pi The expectation from a former entry was that adding the exponen…

Stepper motor step signal timing calculation

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While we use stepper motors in many devices, the timing of the step signals is not always well understood. Most of us can see how a fixed speed is a bad idea unless the speed of motion is really slow, but it is fixed speed what is really to generate with simple code. You just can use the Arduino Blink example to send a fixed frequency of pulses to a stepper motor driver. If too slow, just reduce the delay value.

But for most real-life applications variable speed controls will perform better. These systems will speed up the motor to a given maximum speed and it will slow it down to stop at the desired step count. But understanding the math behind this process is sometimes not obvious.

Let us start with the simple case of the so-called trapezoidal speed motion profile. Here motion takes place in three phases: acceleration, constant speed (cruising) and deceleration. But the point is how can our code create such a behavior.

Stepper motor drivers usually accept two signals to control moto…

A better stepper drive s-curve?

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One of the not so desirable features of stepper motors is the fact that output torque falls quickly with shaft speed. This is one of the reasons these motors cannot reach high speeds.

So I was thinking that when we use a s-curve to drive them, instead of choosing a symmetric one, where acceleration is is max in the middle of the acceleration section (as speed raises), I could try one where higher accelerations happen to lower speeds. However, in order to still keep the s-curve shape instead of a sawtooth, I would use the following expression: 1-e^(cos(t/2)-1)and it is shown in blue in the graph.

This will produce a s-curve shape, but modulated with the exponential behavior. Resulting signal will grow faster as the beginning (where more torque is available) and more slowly at the end (where faster speeds are reached and less torque is available).

A first test shows me that, for a bare motor, a faster move can be achieved, more reliably (no missed steps), using this pattern instead of …

How to get sinusoidal s-curve for a stepper motor

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After some experimentation, and delving a bit into the math of motion, I realized there can be a significant difference on the motion of a machine by just making small changes.

A common and popular approach to smooth one axis of motion is to use a trapezoidal speed pattern, where acceleration and deceleration are uniformly accelerated movements (aka constant acceleration motion) separated by a portion happening at cruising speed.

The problem comes with the fact that, while that approach is simple to understand and to code, it does contain sudden changes in the acceleration, that show as spikes on the acceleration derivative, called jerk. These sudden changes in the acceleration translate into undesired vibration in our machines.

Most of that can be eliminated by selecting a motion pattern that does not contain sudden changes of acceleration. If we chose a mathematical function for our speed whose second derivative is continuous, then we reduce system vibration quite a lot. One may thi…

Moving code from ESP8266 to ESP32

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A while ago I made a mashup of Dan Royer's code CNC 2 Axis Demo with my own code for trapezoidal motion stepper and servo control for ESP8266.

I assumed porting the code to the ESP32 would be trivial, and that was true for the most part: changes like library name being Wifi.h instead of Wifi8266.h were not a problem. UDP now does not like multicharacter writes but you can use print instead. So far so good.

However, when it came to the interrupt code I was stuck with the stepper interrupt causing an exception sometimes. And to make things weirder, the servo interrupt worked flawlessly (both of them had the IRAM_ATTR directive if you ask me).

Going little by little, I could narrow down the culprit to a floating point operation during the interrupt, that would cause problems sometimes but not always. Browsing around I found this post. Where the solution was simple: do not use floats within the interrupt routines but doubles. The reason was the float calculation would be performed by…

Servo control on ESP32

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One of the things that do not work the Arduino way in the ESP32 so far is the PWM generation using analogWrite() command. There is, however, a library to handle PWM signals using timers, so up to 16 PWM signals can be handled.  You can find fine examples like this one.

However, I wanted to use timers in my project and I wanted to have a clearer view of what was going on, so I decided to handle the PWM timing myself. Here you have an example of how to handle a single servo using a timer. Same timer and routine could be extended to handle more output pins in a similar fashion, but I just needed one here.


It is just a simple sketch that moves the servo back and forth using a sin function to get this motion easily, ranging the signal pulse width from 600 to 2200 microseconds.
This is the end result:


All in all, I am impressed with the simplicity and power of the ESP32 and the great Arduino-esp32 code. Kudos to Espressif.

ESP-32 in UNO format

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A few years ago, the IC manufacturer Expressif surprised many of us with their ESP8266 SoC.  A 32- bit processor, running at 80 or 160 MHz with built-in wifi support. It proved to be a very interesting proposal and, eventually, a versión with the same form-factor as the Arduino UNO was made available (which opened compatibility with many available shields).

The same manufacturer developed the next versión, a new and improved SoC this time with Bluetooth and Wifi support, more I/O pins and low-power modes.

I almost forgot, the main reason these chips got successful in the DIY world was that the price was right and a powerful SDK was made available, that eventually led to a group of enthusiasts to create an Arduino-compatible library that made possible to use Arduino code and Arduino IDE to develop with these chips.

A few weeks ago I was contacted to see if a wifi-enabled stepper motor controller board could be done with an ESP. As that is something I had already done the obvious answer…

Testing sinusoidal S-curves

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My main goal here was to keep a simple mechanism to be easy to calculate and able to be included into 8-bit firmware like Marlin. Which by the way already has support for s-curves for quite a while (at least on this mod for Ultimaker).

So the goal is to have a function f(t) that will map the speed at each given moment but in a way that the maximum speed will be reached at the same time as it would using a uniform acceleration, so the rest of the math and motion planning is not affected. In doing so, the peak acceleration is going to be higher than that when using uniform acceleration. However, if that is a problem it is ok to reduce the maximum acceleration so the system can work flawlessly.

I have tested a couple of functions, both based on sinusoidal functions, the former is:
f(t)=V*(1-cos(PI*(t/t1))/2 (where V is max speed and t1 marks the end of the S-curve ramping up). It is the dotted-green curve below. The shape of the acceleration for this speed pattern is the dotted-pink curv…

Sinusoidal functions for s-curve motion

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While trapezoidal speed motion pattern is good and well. It is well known that the sudden changes in acceleration it requires, also known as jerk (jerk being the time derivative of the acceleration) is the cause of trouble in many machines.


That first model can be improved with another acceleration shape that will remove the sudden changes, thus improving the system performance.

However, will there are no sharp edges on the acceleration values, there is still a couple of points where there is a not so smooth change. So the next idea, while still within the use of a sinusoidal acceleration profiles is to change to this other acceleration profile:
This new curve has smoother transitions from zero to any other value, thus no more problems with the jerk. However, we still can think of a combination of this latter case and the initial one, where corners are smoothed out using a sinusoidal: That is what they suggest in this paper
While I was not eager to use any complex math in my dcservo

Speeding up my CAM

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A while ago, I created from scratch a CAM software. It has been consistently working ok with a minor problem of occasional wounds in some parts, which I narrowed down to a bad condition.

But solving the math was only part of the problem. A problem my students found too difficult to crack. So I have to provide them a solution (this was for a ball end mill).


The computing time of the algorithm depends on how many calculations are done. And the brute-force approach of checking every single point, edge and triangle for each sample point is just too slow (but works flawlessly).

I have used a dual approach to speed up the code. On one hand, I am selecting only a few elements to be checked for each vertical scan line, that reduces significantly the number of checks to those that are relevant for the current scan line. The second idea is to write multi-threaded code that can handle different scan lines using a different thread, that in turn will run in a different core of the processor if I d…

I bought a Prusa MK3 too

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first layer adjustment). I have been testing each new version of Josef Prusa printers and I am glad at how good and predictable the build process is turning, and documentation is getting better at each new release.

Prusa i3 MK3 is addressing quite a few shortcomings of these type of printers with a good dose of innovation and ingenuity.

I ordered my printers in October 2017 and got it here last Monday. I knew there was a significant waiting time but I was not in a hurry at the time. And it seems to wait has played in my favor as I have received some improvements over the original release (mine are definitely hardened rods). But I  will yet have to wait for a PEI laminated steel sheet.

This time I built the printer by myself: it is more entertained when you have a helper that can double-check the manual, but version 3.0 of the manual is already very good. My only complaint on that front is that although it is clear Prusa Research is doing an effort with a full-color manual in a large …

More SAMD21 M0 weirdness

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My assumption was that using Arduino IDE was the quickest and simplest way to venture into the world of 32 bit ARM processors, but I am starting to think otherwise. This post is the second about things not working as expected and time used to figure out what's wrong.

For a motor-controller project, I was testing Allegro's A4950 h-bridge when I realized that while varying motor speed using a PWM signal, sudden torque spikes were happening.

My first idea was that the power supply was to blame, so I replaced it, to obtain exactly the same result.

The code I was running was very simple and on close inspection, I could not find any reason for the observed glitch, that somehow had a periodic nature: one acceleration and deceleration period would work ok and the next one will show three or four torque spikes.

As I was using an Arduino-form M0 board (SAMD21-based) I decided to bring back my trusted Arduino UNO and to run exactly the same code. This time all worked nicely, no sudden ac…

Guess who is coming home?

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Have you ever wanted to know if someone is coming home even before they ring the bell? I do not have a dog (they have that kind of power too) so I have to look for a solution on another domain.

So last weekend I decided to see if I could use an ESP8266 for that purpose, given that my sample subjects, aka sons, are equipped with smartphones with a MAC address I am aware of.

But the point is that if I wait till I can detect their phones are joining the home wireless network, they are probably at the door already. I am looking for something else that can pick them up sooner, even if their phones cannot yet pick up the home network wifi signal.

Googling around I found this code. It is a basic sniffer of wifi control frames. In particular, it is looking for probe frames that wireless stations can emit from time to time to discover nearby wireless networks.

But be warned that while the trick seems to work fine for Android phones, it does not seem to work for iPhones as they use to use a ran…

Wemos M0 PWM weirdness

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One of the things I have received as Xmas gift is thus Arduino UNO form factor board with a Cortex-M0 processor running at 48 Mhz.

After getting some trouble with the Arduino IDE I managed to get it working as an Arduino M0 in 1.8.5 IDE. However, though I could upload code, analogWrite seem not so work for me.

I used Fade example code that should work with built-in LED on pin 13 but it did not.

I had to use my logic analyzer to check which pins work with PWM and which do not. I could see that Adafruit using a similar processor mentioned some trouble with some pins but my board was even worse than that. Only pins 12, 11, 10, 9, 8, 5, 4, 3, & 2 worked with PWM while others, like pin 13 should work but did not.


At least now I know which pins I can use for analogWrite. I am not sure what the root cause of the problem is though.