Lissajous Clock
Introduction: Lissajous Clock
Having previously made a couple of clock projects with different themes I wanted to retain the differentiation on the next clock themed project. Therefore, there would be no Neopixels or mechanical indicators and in this case elected to use an LCD display.
Yet another departure was with regard to the microcontroller which previously had been a Microbit and this was to use a Raspberry Pi Pico.
However, not wanting to go for a classic numeric display the plan was to display the time using Lissajous figures in the style of a carriage clock, using wood, Acrylic and Brass.
The attached video shows 29 minutes compressed in to 27 seconds (Showing time from 21:09 to 21:38), to illustrate the changing figures.
Supplies
Raspberry Pi Pico Lipo
Pico Display Pack 2.0 (320 x 240) IPC LCD
Pico Omnibus (Dual Expander)
RGB Encoder Breakout
RV3028 Real Time Clock (RTC) Breakout
Switch - Momentary SPST
Switch - Rotary SPDT
Brass sheet - 0.5mm
Acrylic sheet Clear - 3mm
Acrylic sheet Black - 5mm
Vent Grille Covers - 45mm
Straight Pin Header 1 row x 36 way - Qty 5
Right Angle Header 1 row x 36 way
Straight PCB Socket 1 row x 10 way - Qty 16
LiPo Battery 3.7V/500mAh
Stripboard
Jumper wires (socket to socket) - Qty 24
Jumper wires (socket to pin) - Qty 4
Handle Bow type 110mm(L),x 22mm(H)
Decking Plank 120mm(W) x 180mm(L) x 24mm(D) - Qty 2
Screws - M2 x 16mm - Qty 6
Screws - M2 x 8mm - Qty 10
M4 Allen bolts 25mm - Qty 4
M4 Allen bolts 50mm - Qty 4
M4 Allen bolts 10mm - Qty 2
M4 threaded insert nuts - 10mm(L) - Qty 10
M4 screws contersunk 25mm - QTY 4
Stick on feet - Qty 4
No affiliation to any of the suppliers used in this project, feel free to use your preferred suppliers and substitute the elements were appropriate to your own preference or subject to supply.
Tools
Step cone drill bit 4 to 12mm
2mm drill bit
5mm drill bit
7mm drill bit
9mm drill bit
Counter sink bit 8mm
Counter sink bit 10mm
Counter sink bit 12mm
2mm Allen Key
4mm Allen Key
Saw
Drill
Oscillating Multitool
Combination Square
Scribe
Marker
Soldering Iron
Solder
Clamps
Sander
Know your tools and follow the recommended operational procedures and be sure to wear the appropriate PPE.
Step 1: Lissajous Figures
Lissajous figures named after <PERSON> (Also known as Bowditch Curves after the initial work of <PERSON>), who devised a method to study compound vibrations. Originally employing pendulums, tuning forks and optical methods. Reflecting light from mirrors on two tuning forks vibrating at right angles will display <PERSON> figures as will other devices such as Harmonographs and Pantographs.
Different patterns will be produced by the variation in frequency and phase between the two input stimuli.
Lisaajous figures are used in many areas Acoustics, Electronics and Communication to name a few areas.
We can forego the mechanical methods and produce them using mathmatical calculation.
Assuming sinusoidal waveforms as they are applicable to both mechanical and electrical systems and simplify the mathematical and visual process.
If we use Excel as our display for our compound waveform.
Assume two sinusoudal waveforms of the same amplitude, phase and frequency one assigned to the x axis and one to the y axis these representing our two tuning forks.
X = sin(t) and Y = sin(t) as we can consider the period of a sinewave in relation to the circumference of a circle.
With one revolution equal to 2Pi radians or 360 degrees, sin(t) will range from -1 to +1.
Plotted on an X-Y chart will produce a straight line with an angle of 45 degrees.
If the phase difference is 180 degrees than the straight line displayed will be at 135 degrees.
If we change the phase of one of the waveforms by 90 degrees. 134