# Serial Accelerometer

During my naive days as a university student the only time I graphed data was when some professor required a graph in the lab report. Back in those days I always just.

Intro: 3 Axis Arduino Accelerometer / Inclinometer Tilt / Roll / Yaw From the minds at Years ago I saw a neat dash gadget for a.

Intro: Accelerometer Gyro Tutorial. Introduction This guide is intended to everyone interested in in using Accelerometers and Gyroscopes as well as combination IMU.

This guide is intended to everyone interested in in using Accelerometers and Gyroscopes as well as combination IMU devices Inertial Measurement Unit in their electronics projects

We ll cover:

What does an accelerometer measure.

What does a gyroscope aka gyro measure.

How to convert analog-to-digital ADC readings that you get from these sensor to physical units those would be g for accelerometer, deg/s for gyroscope

How to combine accelerometer and gyroscope readings in order to obtain accurate information about the inclination of your device relative to the ground plane

Throughout the article I will try to keep the math to the minimum. If you know what Sine/Cosine/Tangent are then you should be able to understand and use these ideas in your project no matter what platform you re using: Arduino, Propeller, Basic Stamp, Atmel chips, Microchip PIC, etc.

There are people out there who believe that you need complex math in order to make use of an IMU unit complex FIR or IIR filters such as Kalman filters, Parks-McClellan filters, etc. You can research all those and achieve wonderful but complex results. My way of explaining things require just basic math. I am a great believer in simplicity. I think a system that is simple is easier to control and monitor, besides many embedded devices do not have the power and resources to implement complex algorithms requiring matrix calculations.

I ll use as an example a new IMU unit, the Acc_Gyro Accelerometer Gyro IMU. We ll use parameters of this device in our examples below. This unit is a good device to start with because it consists of 2 devices:

- LIS331AL data sheet - a triaxial 2G accelerometer

- LPR550AL data sheet - a dual-axis pitch and roll, 500 deg/sec gyroscope

Together they represent a 5-Degrees of Freedom Inertial Measurement Unit. Now that s a fancy name. Nevertheless, behind the fancy name is a very useful combination device that we ll cover and explain in detail in this guide.

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Signing Up Step 1The AccelerometerTo understand this unit we ll start with the accelerometer. When thinking about accelerometers it is often useful to image a box in shape of a cube with a ball inside it. You may imagine something else like a cookie or a donut, but I ll imagine a ball:

If we take this box in a place with no gravitation fields or for that matter with no other fields that might affect the ball s position - the ball will simply float in the middle of the box. You can imagine the box is in outer-space far-far away from any cosmic bodies, or if such a place is hard to find imagine at least a space craft orbiting around the planet where everything is in weightless state. From the picture above you can see that we assign to each axis a pair of walls we removed the wall Y so we can look inside the box. Imagine that each wall is pressure sensitive. If we move suddenly the box to the left we accelerate it with acceleration 1g 9.8m/s 2, the ball will hit the wall X-. We then measure the pressure force that the ball applies to the wall and output a value of -1g on the X axis.

Please note that the accelerometer will actually detect a force that is directed in the opposite direction from the acceleration vector. This force is often called Inertial Force or Fictitious Force. One thing you should learn from this is that an accelerometer measures acceleration indirectly through a force that is applied to one of it s walls according to our model, it might be a spring or something else in real life accelerometers. This force can be caused by the acceleration, but as we ll see in the next example it is not always caused by acceleration.

If we take our model and put it on Earth the ball will fall on the Z- wall and will apply a force of 1g on the bottom wall, as shown in the picture below:

In this case the box isn t moving but we still get a reading of -1g on the Z axis. The pressure that the ball has applied on the wall was caused by a gravitation force. In theory it could be a different type of force - for example, if you imagine that our ball is metallic, placing a magnet next to the box could move the ball so it hits another wall. This was said just to prove that in essence accelerometer measures force not acceleration. It just happens that acceleration causes an inertial force that is captured by the force detection mechanism of the accelerometer.

While this model is not exactly how a MEMS sensor is constructed it is often useful in solving accelerometer related problems. There are actually similar sensors that have metallic balls inside, they are called tilt switches, however they are more primitive and usually they can only tell if the device is inclined within some range or not, not the extent of inclination.

So far we have analyzed the accelerometer output on a single axis and this is all you ll get with a single axis accelerometers. The real value of triaxial accelerometers comes from the fact that they can detect inertial forces on all three axes. Let s go back to our box model, and let s rotate the box 45 degrees to the right. The ball will touch 2 walls now: Z- and X- as shown in the picture below:

The values of 0.71 are not arbitrary, they are actually an approximation for SQRT 1/2. This will become more clear as we introduce our next model for the accelerometer.

In the previous model we have fixed the gravitation force and rotated our imaginary box. In last 2 examples we have analyzed the output in 2 different box positions, while the force vector remained constant. While this was useful in understanding how the accelerometer interacts with outside forces, it is more practical to perform calculations if we fix the coordinate system to the axes of the accelerometer and imagine that the force vector rotates around us.

Please have a look at the model above, I preserved the colors of the axes so you can make a mental transition from the previous model to the new one. Just imagine that each axis in the new model is perpendicular to the respective faces of the box in the previous model. The vector R is the force vector that the accelerometer is measuring it could be either the gravitation force or the inertial force from the examples above or a combination of both. Rx, Ry, Rz are projection of the R vector on the X,Y,Z axes. Please notice the following relation:

R 2 Rx 2 Ry 2 Rz 2 Eq. 1

which is basically the equivalent of the Pythagorean theorem in 3D.

Remember that a little bit earlier I told you that the values of SQRT 1/2 0.71 are not random. If you plug them in the formula above, after recalling that our gravitation force was 1 g we can verify that:

1 2 -SQRT 1/2 2 0 2 -SQRT 1/2 2

simply by substituting R 1, Rx -SQRT 1/2, Ry 0, Rz -SQRT 1/2 in Eq.1

After a long preamble of theory we re getting closer to real life accelerometers. The values Rx, Ry, Rz are actually linearly related to the values that your real-life accelerometer will output and that you can use for performing various calculations.

Before we get there let s talk a little about the way accelerometers will deliver this information to us. Most accelerometers will fall in two categories: digital and analog. Digital accelerometers will give you information using a serial protocol like I2C, SPI or USART, while analog accelerometers will output a voltage level within a predefined range that you have to convert to a digital value using an ADC analog to digital converter module. I will not go into much detail about how ADC works, partly because it is such an extensive topic and partly because it is different from one platform to another. Some microcontroller will have a built-in ADC modules some of them will need external components in order to perform the ADC conversions. No matter what type of ADC module you use you ll end up with a value in a certain range. For example a 10-bit ADC module will output a value in the range of 0..1023, note that 1023 2 10 -1. A 12-bit ADC module will output a value in the range of 0..4095, note that 4095 2 12-1.

Let s move on by considering a simple example, suppose our 10bit ADC module gave us the following values for the three accelerometer channels axes :

AdcRx 586

AdcRy 630

AdcRz 561

Each ADC module will have a reference voltage, let s assume in our example it is 3.3V. To convert a 10bit adc value to voltage we use the following formula:

VoltsRx AdcRx Vref / 1023

A quick note here: that for 8bit ADC the last divider would be 255 2 8 -1, and for 12bit ADC last divider would be 4095 2 12 -1.

Applying this formula to all 3 channels we get:

VoltsRx 586 3.3V / 1023 1.89V we round all results to 2 decimal points

VoltsRy 630 3.3V / 1023 2.03V

VoltsRz 561 3.3V / 1023 1.81V

Each accelerometer has a zero-g voltage level, you can find it in specs, this is the voltage that corresponds to 0g. To get a signed voltage value we need to calculate the shift from this level. Let s say our 0g voltage level is VzeroG 1.65V. We calculate the voltage shifts from zero-g voltage as follows::

DeltaVoltsRx 1.89V - 1.65V 0.24V

DeltaVoltsRy 2.03V - 1.65V 0.38V

DeltaVoltsRz 1.81V - 1.65V 0.16V

We now have our accelerometer readings in Volts, it s still not in g 9.8 m/s 2, to do the final conversion we apply the accelerometer sensitivity, usually expressed in mV/g. Lets say our Sensitivity 478.5mV/g 0.4785V/g. Sensitivity values can be found in accelerometer specifications. To get the final force values expressed in g we use the following formula:

Rx DeltaVoltsRx / Sensitivity

Rx 0.24V / 0.4785V/g 0.5g

Ry 0.38V / 0.4785V/g 0.79g

Rz 0.16V / 0.4785V/g 0.33g

We could of course combine all steps in one formula, but I went through all the steps to make it clear how you go from ADC readings to a force vector component expressed in g.

Rx AdcRx Vref / 1023 - VzeroG / Sensitivity Eq.2

Ry AdcRy Vref / 1023 - VzeroG / Sensitivity

Rz AdcRz Vref / 1023 - VzeroG / Sensitivity

We now have all 3 components that define our inertial force vector, if the device is not subject to other forces other than gravitation, we can assume this is the direction of our gravitation force vector. If you want to calculate inclination of device relative to the ground you can calculate the angle between this vector and Z axis. If you are also interested in per-axis direction of inclination you can split this result into 2 components: inclination on the X and Y axis that can be calculated as the angle between gravitation vector and X / Y axes. Calculating these angles is more simple than you might think, now that we have calculated the values for Rx,Ry and Rz. Let s go back to our last accelerometer model and do some additional notations:

The angles that we are interested in are the angles between X,Y,Z axes and the force vector R. We ll define these angles as Axr, Ayr, Azr. You can notice from the right-angle triangle formed by R and Rx that:

cos Axr Rx / R, and similarly :

cos Ayr Ry / R

cos Azr Rz / R

We can deduct from Eq.1 that R SQRT Rx 2 Ry 2 Rz 2.

We can find now our angles by using arccos function the inverse cos function :

Axr arccos Rx/R

Ayr arccos Ry/R

Azr arccos Rz/R

We ve gone a long way to explain the accelerometer model, just to come up to these formulas. Depending on your applications you might want to use any intermediate formulas that we have derived. We ll also introduce the gyroscope model soon, and we ll see how accelerometer and gyroscope data can be combined to provide even more accurate inclination estimations.

But before we do that let s do some more useful notations:

cosX cos Axr Rx / R

cosY cos Ayr Ry / R

cosZ cos Azr Rz / R

This triplet is often called Direction Cosine, and it basically represents the unit vector vector with length 1 that has same direction as our R vector. You can easily verify that:

SQRT cosX 2 cosY 2 cosZ 2 1

This is a nice property since it absolve us from monitoring the modulus length of R vector. Often times if we re just interested in direction of our inertial vector, it makes sense to normalize it s modulus in order to simplify other calculations.

To understand this unit we ll start with the accelerometer. When thinking about accelerometers it is often useful to image a box in shape of a cube with a ball inside it. You may imagine something else like a cookie or a donut, but I ll imagine a ball:

Triple Axis Accelerometer and Gyro Breakout

Is the operation of this thing still locked up tight, away from hobbyist access.

I recall something about the whole capable of processing complex 9-axis MotionFusion algorithms meaning capable if you re a big company and we decide to share the documentation with you.

And hobbyists were just able to get the raw sensor data still neat but not access the nice algorithms. Has that been remedied. Is this a magic IMU in a chip now. minus compass

Because if those algorithms are still not something we can use, I think Sparkfun needs to mention that in the description.

Wow, the I2Cdevlib repository made it into the Documents list. I m honored, really. However, instead of the main class library parent source folder, you might want to point to the main MPU-6050 device page here:

I guess they are both good links, but the device page has much more information including an interactive register map, highly detailed I2C capture analysis of InvenSense eval/ARM board DMP traffic, and some very, very rudimentary reverse-engineered info on DMP registers and usage. More documentation may come as some encouraging and ongoing talks with InvenSense continue they appear to be legitimately trying to satisfy the OSHW community. I m hopeful anyway.

EDIT: adding link to the new I2Cdevlib support forum:

According to the I2Cdevlib link you provide it says: Due to the lack of good publicly available documentation about the inner workings of this device, all DMP-related information has been reverse-engineered from I2C signal analysis correlated against the company-provided Embedded MotionApps software

It goes on to say: Currently, the source code available will only provide basic device configuration and raw accel/gryo readings which is certainly useful, but missing the main selling point of the MPU-6000 series, which is the device-powered motion processing ability.

What the heck

I am trying to set the sampling rate for the accelerometer and the gyroscope.

From the register map page 11 of 60 :

Register 25 â Sample Rate Divider

SMPRT_DIV

The Sample Rate is generated by dividing the gyroscope output rate by SMPLRT_DIV: Sample Rate Gyroscope Output Rate / 1 SMPLRT_DIV where Gyroscope Output Rate 8kHz when the DLPF is disabled DLPF_CFG 0 or 7, and 1kHz when the DLPF is enabled see Register 26.

The accelerometer output rate is 1kHz. This means that for a Sample Rate greater than 1kHz, the same accelerometer sample may be output to the FIFO, DMP, and sensor registers more than once.

In my understanding, if the DLPF Digital Low Pass Filter is enabled then both the gyroscope and the accelerometer sample at 1kHz and setting a value of say 4 in register 25 will make the sample rate: 1kHz / 1 4 200Hz for BOTH the accelerometer and the gyroscope. Is that correct. Does enabling the DLPF not affect the sampling rate of the accelerometer as it does for the gyroscope

I want to eventually design a digital filter by converting a continuous time filter using conventional Bode plot techniques and need to know the sampling rate for the conversion.

For anyone that is struggling to get this sensor to work with an Arduino Leonardo using the libraries provided the example code link, I was able to get it to work by doing the following:

First, the Leonardo I2C interface is detailed here:

SDA - Digital Pin 2

SCL - Digital Pin 3

Second, the Leonardo interrupt setup is detailed here:

The DMP6_test is setup to use interrupt 0 which is Digital Pin 2 on the Leonardo. I changed the line:

attachInterrupt 0, dmpDataReady, RISING ;

to:

attachInterrupt 4, dmpDataReady, RISING ;

And connected the interrupt to Digital pin 7.

The DMP6_test and Processing sketch now works like a charm. I hope this helps anyone else that was struggling with the Leonardo setup.

I ve just started with Arduino and sensors and I am not experienced with any of this things.

For a university project we bough an Arduino UNO and an MPU-6050 sensor. I started connecting the two as follows:

MPU UNO

- VCC 3.3V

- GND GND

- INT Digital Pin 2

- SCL Analog Pin 5 without resistor.

- SDA Analog Pin 4 without resistor.

- VIO 3.3V

FSYNC, CLK, ASCL and ASDA unconnected.

We used the I2cdevlib libraries and examples given on the sparkfun site https://github.com/jrowberg/i2cdevlib. We tried a test and the sensor worked fine and gave signals for a while. We shook it a bit to see if the values changed and it suddenly stopped responding and gave only 0 s as output. Since then, we ve been unable to get any response form the sensor. We did an i2c connection test and it responded correctly connection found on 0x68, yet the sensor test says the device is not connected.

We later discovered that for the UNO R3 there are dedicated pins for SCL and SDA. Furthermore, the two analog pins are used as input for the sensor instead of output. Being the Arduino UNO a 5V system, did we fry the sensor by sending an excessivly high input voltage. How is it possible that it worked fine for 5sec before crashing. Could we have broken the sensor by shaking it.

Thanks for taking the time to read this, we could really use some help

Hi everybody.

I ve bought two MPU-6050 evaluation boards and started using them with the code provided by Jeff Rowberg btw really great work, namely the example to get raw data. what happens is that keeping the board still i get x,y,z acceleration values around 260, -92, 24216, respectively when i turn the board so that gravity vector appears on x and y axes i see the value 16300 on each axis, which was what i expected since it corresponds to 1g. What i dont get is the 24216 on z axis. When i try the same code on the other board this doesnt happen and the values are just like expected.

Does anyone have any idea why this happens. Is one of my boards broken.

Thanks.

Nov 30, 2009 Some time ago I ve purchased an ADXL345 accelerometer breakout board from SparkFun.com. After some searching and.

Some time ago, we wrote up a tutorial about using an ADXL330 accelerometer with an AVR microcontroller. A couple of years have passed, and so we ve returned to.

High Sensitivity 2g USB Accelerometer X2-2. General. The X2-2 uses a high sensitivity, low noise, 3-axis, /-2g accelerometer sensor ideal for low amplitude.

SEN-11028: The MPU-6050 is a serious little piece of motion processing tech. By combining a MEMS 3-axis gyroscope and a 3-axis accelerometer on the same.