# Vibratory Clock

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## Team Members

Left to right: Brian Lesperance, Jennifer Breger, Daniel Pinkawa
• Jennifer Breger - Mechanical Engineering Class of 2009
• Brian Lesperance - Electrical Engineering Class of 2008
• Daniel Pinkawa - Mechanical Engineering Class of 2008

## Overview

The vibratory clock is a horizontal circular platform actuated from below by three speakers placed at the corners of an equilateral triangle. The vibration of the platform causes a small object (e.g., an IC socket or a coin) to act as an hour "hand" on top of the platform. The object slides around the circular platform, impelled by friction forces due to the vibration which we can adjust by varying the phase and amplitude of each speaker. Due to the nodes created by the speaker vibrations, the object will move back to the correct hour if it is moved away. Our project was provided by Professor Colgate and based upon the research of Professor Lynch.

### Theory

Through his research, Professor Lynch discovered that when a platform is rotated about a line placed beneath it, sinks and nodes can be created by placing speaker vibrations at different amplitudes and phases. Applying his research to our project, it was determined that if we placed two speakers at equal amplitudes and opposite phases, a sink would be created in between the speakers. This result can be thought of as the center being the center of a teeter-totter, in which two people of equal mass but at completely opposite phases would cause the teeter-totter to rotate perfectly around the center pivot point. However, if the two speakers were at equal amplitudes and perfectly in phase with each other, that side of the plate would move up and down in one motion, causing the sink to be at the other side of the plate.

We found that if we alternated between two different phases that created two orthogonal sinks, we could create a node at the intersection. For example, if we wanted to create a node at 12 o'clock, we would alternate between the radial and orthogonal phases. In the radial phase, we created a sink along the diameter of the plate between the two speakers that were not at 12 o'clock, namely speakers B and C. Using the theory of creating sinks, we placed speakers B and C at equal amplitude and 180 degrees out of phase with each other. If several small objects were placed on the plate at this point, all the objects would converge to the central line of the plate. Next, in order to create the orthogonal sink that would create a node at 12 o'clock, we placed speakers B and C in phase and at equal amplitude. However, in order to counteract the forces from speakers B and C, we put speaker A (the speaker at 12 o'clock) at a weak amplitude and 180 degrees out of phase with speakers B and C in the orthogonal phase.

This same notion was the used to create all of the even number nodes on the clock face. In order to create the nodes at the odd numbers, we slightly changed the amplitudes of the speakers at the previous time until the correct placement was found.

Although theoretically our design should have allowed us to program the clock using symmetry, due to slight imperfections in the design and in the electrical components, we had to use some trial and error methods to place the nodes correctly. Nonetheless, the theory allowed us to create nodes almost exactly where we wanted them to be.

## Mechanical Design

The Vibratory clock consists of a wooden base, held up by adjustable legs, three speakers, and a circular platform. The following material were used to create the design:

Base:

• wood: 16" diameter, 0.75" thick
• holes: 6" diameter (3 total)
• adjustable legs: 3 rods: 3/8"-16; 4" long; 6 nuts total

Speakers:

• 3 Pyramid Power PW677X: 300W, 4 Ohms, 6.5" Chrome Subwoofer
• previously adapted speakers replaced center of speaker with attachments 3" in height and 1/2" hole on top
• 1/2" diameter PVC used to attach previous attachment to platform with a screw
• held in place by 2 set screws each
• centers placed 7.125" apart

Circular Platform

• PVC/Acrylic: 11.75" diameter, 0.25" thick
• machined on the LaserJet
• screw holes counter-sunk at 7.125" apart
• 2.875" above wooden base
• Silver Sharpie used for numbers

Reasoning for Geometry of Design

Equilateral Triangle: By having the speakers equidistant from each other, we were able to create symmetry in our design, which made programming the various nodes much easier. For example, we were able to use the same theory to find the node at 12 o'clock, 4 o'clock, and 8 o'clock. If the speakers were not placed equidistant from each other, two speakers placed at equal amplitudes and opposite phases would not have created a sink in the exact middle of the two speakers.

We needed to make the legs adjustable since it is essential that the platform be perfectly level in order for the objects placed on the platform to move in expected patterns. For example, if one leg is slightly shorter than the other two, the objects placed on the platform would tend to move towards that leg and we could no longer rely on symmetry to program the various nodes due to the effects of gravity.

Height of Platform:

Through our own experimentation and from Professor Lynch's research, we found that we needed to have the pivot point (i.e. the speaker diaphragm) significantly below the platform in order to create sinks. At one point in the design process, we attempted to create a different pivot point by replacing the PVC with 1/2" outer diameter, 1/4" inner diameter Tygon 2001 tubing that only was able to bend in one point since it had stand-offs and screws inside the tube. However, this replacement in a sense created two pivot points (the speaker diaphragm and the Tygon), causing the platform to only create sources and not sinks. In addition, the different height of the pivot point may have also led to the plate acting differently.

## Electrical Design

Circuit Board

### Component List

PartPart No.QtyVendorPrice (Total)
Microchip 8-bit PIC Microcontroller (U1)PIC18F45201N/AN/A
Maxim Quad, 2-Wire Serial 8-Bit Digital-to-Analog Converter (U2)MAX5201Digi-Key\$9.28
Emtel 150W, 12V Power SupplyEMV15012V1N/AN/A
Emtel EMV15012V Wiring Kit61-EMV15012VWK1N/AN/A
Legacy Series II 4-channel, 300W Power AmplifierLA1601N/AN/A
Keystone Electronics Snap-Fit 90 PC Phono Jack901K-ND3Digi-Key\$3.81
20-ft Monster Cable 16-Gauge Speaker WireS16-2XLN1Radioshack\$9.97

### Design Description

The PIC sends a digitized version of three sine waves to the DAC for conversion. The signal then passes through a LPF filter before going to a power amplifier and finally the speakers themselves, which vibrate the surface plate.

Digital-to-Analog Converter

The PIC would step through the sampled sine wave, stored in program memory, and send the values to the DAC. Since we need 3 individual sine waves, we selected the Maxim MAX520, a quad DAC IC. It uses I2C with which our PIC easily interfaces and a simple message protocol.

Design Evolution

Originally, our hopes were to use the PIC's built-in PWM functionality to control the speakers and pass the signal through a low-pass filter to create our sine wave. Quickly, we realized that method did not give us the control over the amplitude and phase that we needed to create a line sink. Another idea was to use digital potentiometers in a configurable all-pass filter as a second filter, after low-pass filtering a PWM/square wave signal. This would allow us to control the amplitude and phase response of the filter by controlling the digital potentiometer. Despite, it's usefulness, this method was very complex since it would require fine control of the filter and be very susceptible to noise or error. Our final method, as mentioned previously, involved a Look-Up Table with a full period of a sine wave and a DAC.

### Circuit Diagram

Vibratory Clock Circuit Diagram

## Software Design

### Code Description

The PIC has a sine wave stored in program memory in the form of a look-up table (LUT) (really not necessary but larger projects might need this). The main code simply steps through the LUT and outputs that value to the DAC. This will create a "stepping" sine wave, which get smoothed out by the passive LPF before the signal is sent to the power amplifier. There is a interrupt service routine that occurs every .825 seconds to alternate between two orthogonal line sinks, to create a node to which a time piece will go. Additionally, every 10 seconds within the interrupt, the time is changed in that the position of the node moves to the next hour. Our code has the hour positions hard coded and simply steps through all of them. More positions can easily be added for better resolution, which would be useful in an hour hand.

## Results

We were able to get our project working so that the plate moves an object placed anywhere on the plate to the correct time and then moves the objects around the clock face, acting as the hour "hand" of a clock. However, we increased the speed so that it takes about 2 minutes for objects placed on the clock to move around so that it is easy to demonstrate. Check out the working Vibratory Clock here.