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Rotary Encoder Based Linear Caliper

Developed for the MTE 201 design project, using a rotary encoder as well as data analysis techniques we developed a fairly accurate digital calliper that came within a few millimetres of the actual measurement. 

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Mechanical Design

The measurement system built for this project consists of a rotary encoder connected to an Arduino board, which processes the digital output signal and outputs a numerical value corresponding to the number of ticks passed on the encoder. A gear system was manufactured by 3D printing and assembled on a wooden board to construct the measurement device.

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1 / Groove Milling

A manual 3-axis milling machine is used to carve out a groove spanning the board's length. The intended purpose of this groove is to provide a channel for a rack and pinion system. By limiting the movement of the rack to this linear axis, the linear movement was effectively converted into rotational values.

3 / Optimizing Gear Ratios

A  combination of a compact gear and a larger gear is designed to establish a specific gear ratio. This design decision was selected for a deliberate reduction in linear displacement experienced by the rack with each complete revolution of the rotary encoder. This reduction in turn amplifies precision in measurement operations.

4 / Production of 3D printed Gears

Within the mechanism, three distinct gears are present: a rack, a larger pinion, and a smaller gear. The creation of all three gears was manufactured through the process of 3D printing. 

5 / Incorporation of Rotary Encoder and Wooden Foundation

The rotary encoder has the responsibility of gauging the position or rotation of the smaller gear. This assembly is affixed beneath a substantial block, thus ensuring a stable foundation for the rotary encoder's efficiency.

6 / Establishment of Zero Point

Wooden components are judiciously affixed to both ends of the rack and the wooden block. This addition serves the purpose of establishing a zero point of reference for a calliper. The calliper benefits from this calibration for precise measurements relative to a specific reference frame.

Data Analysis and Calibration

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General Overview

A digital calliper was the secondary standard used to measure true displacement values (mm) during calibration. The measured value from the system was an integer output (unitless) returned based on the digital output signal sent from the encoder to the Arduino board. The apparatus used for the calibration is shown to the left: 

Data Gathering and Analysis

  1. Measure an object’s true displacement (mm) using a digital calliper.

    1. Turn the knob clockwise to close the jaws of the calliper.

    2. Tare the Value.

    3. Turn the knob counter-clockwise and place the object to be measured within the jaws.

    4. Turn the knob clockwise so that the jaws snugly fit against the object to be measured.

    5. Record the true value from the digital calliper display in the measurement table's Displacement (mm) column.

  2. Using the encoder measurement system, measure the same object.

    1. Set the system to zero position by closing the wooden claws and pressing the reset button on the Arduino.

    2. Slowly open the claws so that the object fits between them.

    3. Record the Arduino output value in the Output Value column of the measurement table.

  3. Repeat steps 1-2 on four more objects for a total of five measured objects.

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This process was repeated numerous times for additional objects to generate an array of raw calibration data. The data was then plotted onto a calibration curve, using Linear Regression, that compared true dimension metrics to the summed encoder value observed through the Arduino Serial Monitor. The graph developed from this data is to the right:

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Uncertainty Analysis

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After the device was fully developed and created, the outputted measurement was then compared to the true measurement. From this new data, we developed a Deviation plot to estimate uncertainty values. The estimated maximum positive uncertainty was 1.1mm, and the maximum negative uncertainty was -0.68mm.

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Systematic and Random Errors

Based on the deviation plot, it is evident that there was some random error in the entire range of displacement measurements, with the most significant deviations occurring in the upper range. Regarding the systematic error, the deviation values tend to skew in the positive direction, but overall, there seems to be little deviation.

Logic Design

1 / Read Encoder State

The Rotary encoder does not increment its own values like a potentiometer, it changes its states of power and this is reflected on the two pins. The DT and CLK pins.

2 / Pin Differences

Due to the encoder's architecture, the DT pin will always connect before the CLK pin. This allows us the to determine the direction of rotation as the DT pin will not equal to the the CLK pin on clockwise rotation and vice versa.

3 / Apply Data Variation Equation

As the encoder turns, we have a counter that increments per tick. This value is then applied to our calculated estimation equation. 

y = 1.8756546x + 0.7709043

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