Accelerometer

[1] An accelerometer is a device measuring an object's proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of the object relative to an observer who is in free fall (that is, relative to an inertial frame of reference). Proper acceleration is different from coordinate acceleration, which is acceleration with respect to a given coordinate system, which may or may not be accelerating. E.g., an accelerometer at rest on the surface of the Earth will measure an acceleration due to Earth's gravity straight upwards of about g ≈ 9.81 m/s2. By contrast, an accelerometer that is in free fall will measure zero acceleration.

proper acceleration: true accelerometer an object experiences relative to an observer in free fall (or relative to a local inertial frame of reference).

An accelerometer is often packaged alongside a gyroscope to a small component called an IMU (inertial measurement unit). Both can use MEMS (micro electrical mechanical system) that combine electric and mechanic systems as structure in microscopic sizes.

[2.4] Unlike a gyroscope, which measures angular velocity in units of degree per second (°/s), an accelerometer measures linear motion in G-force unit.

Note: Accelerometers don't measure the speed, only the acceleration (change in speed), and neither do gyroscopes record the current angle, only the angular speed.

[2.4] An accelerometer's structure of measuring 1 axis.

Operation

[2.3] For a MEMS accelerometer, an individual axis is measured using a microstructure can be represented as shown on the right and specifically measures capacitance change in its microscopic system comprised of a mass (proof/seismic mass), an H-shaped structure, attached to a spring or substrate at its ends to confine it to only move along a line back and forth (on a specific axis).

[2.4]

The proof mass has sense fingers extended along its main body.

When an acceleration in a certain direction is applied, the mass moves toward it where the capacitance between the fixed plates or electrodes and its sense fingers change as it moves. Note that the sense fingers and electrodes never touch each other and are only close to each other, to create capacitance, which depends on the distance between the 2 objects (C=εA/d)

[2.4]

[2.3]

[2.4] In this case, the accelerometer uses a differential capacitor, a capacitor combined of 2 stationnary plates and one free-moving plate. Using this, the accelerometer measures the capacitance between the middle and top plate, and the capacitance between the middle and lower plate. If the middle statinonary plate is at the center, the capacitance between the 2 other plates are balanced.

Moving the middle plate down decreases the top capacitance and the increases the lower capacitance, since the distance is reduced so mathematically numerator is greater than the denominator.

E.g., if 2 plates of both 1.5 cm2 are 3 cm apart (ignoring permittivity), the capacitance is 1.5/3 = 0.5 F (Farad) and will increase to 1.5/0.9 = 1.67 F if they're 0.9 cm apart.

[2.4]

[2.4] The changes recorded by the differential capacitor goes through charge amplification, signal conditioning, and low-pass filtering, and finally to an ADC to be converted into a digital signal.

Programming functions

An accelerometer can be controlled and powered through Arduino.

Its specific functions used to control it are:

Measurements recordings

[2.1] Acceleration can be defined by the an object's force over its mass, i.e., how much force to move each unit of mass.

Gravity is often used to measure acceleration and many force units are used to express acceleration:

m/s2
Gal (Galileo) = (1 cm/s2)
Standard gravity (G-force or g): The nominal gravity we feel an object's nominal gravitational acceleration in a vacuum near the Earth's surface, often denoted as g0 or gn, meaning without any other forces, like air resistance, standard gravity is the rate an object would fall onto Earth. 1 g = 9.81 m/s2 = 32.2 ft/s2

[D1]

Measurement values By operating an LSM60S3 accelerometer in Arduino IDE, moving it along certain axises will either increase/decrease the acceleration values, by having them printed on the IDE serial monitor.

Note: The direction of axis of the sensor is indicated on the sensor itself with a 3 axis label.

By moving the sensor forward along the x-axis, the x-axis value will increase.
By moving the sensor backward along the x-axis, the x-axis value will decrease.
Same principles for the y-axis.

When accelerometer is lying on flat on a surface, the measured z-value is 1 g (9.81 m/s2), since gravity pulls down the sensor's internal mass along the vertical (z) axis while flat horizontal (y and x) axis will read roughly 0 g, as shown below.

In freefall, i.e., if the sensor is dropped onto the floor, it accelerates downward with gravity, making the internal mass float weightless, causing all axes to read 0 g.

[D1]

Axis movement readings

X-axis measures side-to-side horizontal movement (left and right tilt).
Y-axis measures front-to-back horizontal movement (forward and backward tilt).
Z-axis measures vertical movement (straight up and down i.e. against the ground)

[4]

Thought accelerometers don't directly measure angular rotation speed, like gyroscopes do, they can measure static tilt angle θ via Earth's gravity vector (1 g). By tilting the sensor, a component of the constant gravitational force projects onto its sensing axes, allowing the angle to be calculated mathematically.

But as this relies on gravity, accelerometers can only measure static tilt angles relative to the Earth. If the sensor moves/vibrates wildly, the sensor can't easily tell from raw movement acceleration and gravity, as to why devices like smartphones combine them to gyroscopes.

With gravity acting perpendicular to the x-axis (of the sensor), the axis output reads 0 g.

Bt tilting the sensor by an angle θ, a vector gravity component aligns to the x-axis. The internal sensor reads this fractional acceleration as: ax = 1g*sin(θ).

The sine function is used as it involves using the x-component and y-component (gravity).

Note: 'x-axis' doesn't refers to the ground itself, but to the sensor's axis, such as being depicted in the right diagram.

Why the right triangle isn't drawn around the angle θ The right triangle isn't draw around the around the angle θ as shown is due to θ not being where gravity is acting. In physics vector problems, the real-world total force is always the hypotenuse.

So the angle θ that's actually being considered is between the gravity component relative to the sensor's x-axis or gravity's portion perpendicular to it (purple-dotted line) and the graviational downward force (blue vector).

The value sin(θ) on its own represents the fraction/percentage of the hypotenuse that's acting along the opposite side at the sensor's tilt angle. Thus, by mutliplying the g force to the ratio (sin(θ)) gives the x-axis' acceleration.

And sin(θ) is also the ratio of the acceleration (red arrow) over the gravitational force (blue arrow).

How gravity "aligns" to the x-axis Gravity is always a purely vertical force, perpendicular to the floor. It aligns to the x-axis because the axis is rotated into gravity's gravity. When the sensor is titled at angle θ, the gravity doesn't change direction but because the x-axis now points at a downard slope, part of the straight-down gravitational pull now slides along the tilted x-axis' direction.

In physics any force vector (like gravity pulling down) can be split into 2 components:

A component through the board (along the z-axis).
A component along the board's length (along the x-axis).

In the diagram above, notice that a right triangle forms behind angle θ, where

The hypothenuse side is the 1 g gravity
The adjacent side is the sensor's x-axis (purple-dotted line).
The opposite side is the gravitational force aligned to the sensor's axis that lies opposite to it.

E.g., by tilting an (MEMS) accelerometer at 58° along the x-axis, the x-axis measurement would be 1g*sin(58) = 0.84804809615 g.

By lying it flat on the ground, it'd measure 1*gsin(0) = 0 g.

However, the inclination angle is only accurate if the device is oriented so that the x-axis is always on gravity's plane, i.e., all the action occur on a flat surface running straight up/down.

Rotation about any other axes reduces the x-axis' acceleration magnitude and causes an error in the inclination angle's calculation. This is due to the total 1 g gravity vector is split is being split across the 3 x, y, z axis instead of 2:

(1 g)2 = (ax)2 + (az)2 + (ay)2.

The values have exponents of 2 as it involves with vector magnitude in 3D spaces, where the Pythagorean theorem is used.

Sensitivity and measurement ranges

[2.1] A small g-force (< 1 g) is shown as a waveform of a smaller amplitude. Whereas a larger one would be at higher amplitudes.

[2.1]

[2.1] An accelerometer's datasheet should provide the component's dynamic g-force range it's capable of.

E.g., this MMA8451Q accelerometer is able to measure g-forces of ±2,±4 g, ±8 g settings.

[2.1]

[2.1] This accelerometer has a sensitivity of 4096 counts per g, meaning it changes by 4096 each and can only measure an amplitude of ±2 g.

The 8 g setting can measure higher amplitude signals for larger detection ranges and only has 1024 count per g.

This shows a more sensitive accelerometer can measure subtle acceleration changes but with limited ranges, any signal higher than its designated amplitude is clipped off/distorted.

[2.1] An acelerometer of larger range can measure higher range of g-forces but will be less sensitive.

Types

[2.1] Accelerometers often come in 2 types: MEMS and piezoelectric.

[2.1]

MEMS accelerometer

[2.1] A MEMS (microelectroic mechanical system) accelerometer use microscopic systems that convert mechanical motions into electric readings, being more often used than piezoelectric types.

It uses specifically microscopic component comprised of a proof mass attached to springs to allow it to move along an axis, so that compsensing fingers, whenever acceleration is applied onto the device, to produce capacitance changes between the mass and

[2.1]

3 of such MEMS components are installed together to be able to measure 3 axises.

[2.1]

Piezoelectric accelerometer

[2.1] A piezoelectric accelerometer uses a crystal under stress for high-frequency dynamic data, unlike

MEMS types using a microscopic silicon proof mass to measure static (DC/gravity) and dynamic motion.

The right diagram depicts a piezoelectric sensor that uses a crystal layer between 2 electrodes. The crystal comprises of a positive and negative ions. By applying force on to the device, the structure distorts, causing the ions' electrons to shift around, generating electric charges, which is proportional to charges being applied.

Applications

[2.1] Accelerometers can be used in video games, airpods, smart phones, crash sensors in cars.

References

My documents

[D1] Week 12 Theory Accelerometers IMU Part 1 (Canva)
- [D1.1] Week 12 Theory Accelerometers IMU Part 2

Page updated

Google Sites

Report abuse

Accelerometer

Operation

Programming functions

Measurements recordings

Sensitivity and measurement ranges

Types

MEMS accelerometer

Piezoelectric accelerometer

Applications

References

My documents

Site navigation

Main Site

Science Site

Math Site

Computer Science Site

Usual headlines

Definition structures

Headlines for references

Webcull - to store all links

Legend: