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Position Sensing

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A2:
General Principles
Damping
Position Sensing

Measurement of Rotation

These are devices used to count the revolutions of rotating shafts.

They can sense the speed but sensing direction is not so easy.
They can count revolutions but not determine the absolute position.

Here is a simple arrangement that gives one pulse for each shaft rotation. It can be used to measure vehicle speed or engine RPM (revolutions per minute). Infrared light is generally used because there is too much visible light in the environment for reliable operation.

Angular Resolution - Slotted Wheel - Relative Position

Here is another arrangement used in computer mice of the ball variety.

When the mouse is moved, the ball rotates.
This is coupled to a small shaft connected to a slotted wheel.
An optical arrangement similar to the one above detects the light as the slots in the wheel go past.
The one below generates 16 pulses per revolution.

The wheel above has 16 slots.

One complete rotation is 360 degrees.
One slot is 360 / 16 = 22.5 degrees.
This is the angular resolution.
The resolution can be improved by using a wheel with more slots.

Reflective Wheel - Relative Position

A wheel painted with black and white zones can be used too. This relies on the measurement of reflected light.

All the devices, above, measure rotation but not absolute position.

Measuring Position

RELATIVE position sensing - the robot knows how far it has moved but not exactly where it is (methods above).
ABSOLUTE position sensing - the robot knows its actual position (methods below).

Gray Code Scale Absolute Position (Better)

Four photo detectors measure the colour of the four stripes on the wheel. This pattern is a binary code that is designed such that only one stripe changes colour at any given position. This means that the Gray code does not suffer from incorrect wheel position problems.

With four tracks (stripes) 16 positions can be detected. This is a 2^N calculation so 2⁴ = 16. With 8 tracks 2⁸ positions can be measured = 256.

Gray code can be used for straight line movement measurement too.

Binary Coded Scale Absolute Position (Problems)

Four photo detectors sense the position of the wheel from the binary output. This arrangement has one serious disadvantage. As the wheel rotates, at certain positions, more than one bit changes state. If the sensors are slightly misaligned, this can lead to large errors in the apparent wheel position.

The numbers in the diagran show how many bits change at each transition.

Linear movement can be sensed with a binary coded scale but this suffers from the same limitation as the circular scale above.

Tachometer

This is a device that produces a voltage proportional to the speed of a rotating shaft. Common examples include the rev' counter found in many vehicles. This measures the rotation of the engine crank shaft. The speedometer in vehicles measures the wheel rotation speed. Wind speed gauges use a similar system.

Here is a convenient way to detect the rotation of a shaft.

Shaft rotation can also be measured with a mirror attached to the shaft. Another alternative is to attach a magnet to the shaft and place an induction coil near the magnet. As the magnet passes the coil, a voltage pulse will be induced.

As the notched wheel rotates, the light beam is interrupted. This appears as a small square(ish) wave output from the photodiode. When the shaft rotates faster, more pulses are produced but the pulses are also shorter. This means that the average output remains constant. To make a useful measuring device, the variable length pulses from the photodiode need to be converted into fixed length pulses. A monostable circuit achieves this. The monostable needs to be triggered by short pulses.

System Diagram

The photo-detector generates low voltage, variable length pulses.
The amplifier increases the amplitude (size) of the pulses to be compatible with the trigger input of the monostable (5 volt pulses for TTL chips).
The limiter ensures the pulses all have the same voltage.
The monostable converts the short variable length trigger pulses into longer fixed length output pulses.
The integrator smooths the pulses to an average DC level.
A passive low pass R C filter can be used for this.
The volt meter measures the DC level. This voltage is proportional to the shaft rotation speed.

This is a linear system. This means that the tachometer output voltage is directly proportional to the speed. A graph plot gives a straight line as shown below. This system has been neatly calibrated to give one volt representing ten km/h.

A Graph of Tachometer Voltage Output against Speed