Cheatsheet & Glossary

This is the volume you print, laminate, and keep on the bench. It carries no new argument — everything here is derived and explained across Vols 1–9 — but it pulls the numbers that actually slow you down mid-build into a single dense reference: the gear and stepper formulas, the TMC2208 microstep table, the three builds’ bills of materials, the IC pinouts, the tuning-fork serial protocol, where every source file lives, and an A–Z glossary. Tables are the heart of it; where a formula appears it carries its units, and a worked example follows. Cross-references point back to the volume that derives the result.

10.1 Formulas at a glance

10.1.1 Gear and reduction math (derived in Vol 3)

Table 1 — 10.1.1 Gear and reduction math (derived in Vol 3)

Quantity	Formula	Units	Notes
Module	m = d / N	mm/tooth	d = pitch diameter, N = tooth count
Pitch diameter	d = m · N	mm	inverse of the above
Center distance	C = m (N₁ + N₂) / 2	mm	two meshing external gears, equal module
Simple ratio	i = N_driven / N_driver	—	>1 is a reduction (output slower)
Belt/pulley ratio	i = T_driven / T_driver	—	GT2 60T/20T → 60/20 = 3:1
Planetary, ring fixed	i = 1 + N_ring / N_sun	—	input = sun, output = carrier
Planetary, carrier fixed	i = −N_ring / N_sun	—	sun→ring, sign = reversal

Clock reductions every movement hides: the minute hand turns at 1 rev/hour and the hour hand at 1 rev/12 h, so the hour:minute reduction is 12:1; the second hand turns at 1 rev/minute, so the minute:second reduction is 60:1 (Vol 3 §3.2).

Worked — center distance, sun + planet, m = 1 mm: with a 30T sun and a 15T planet, C = 1 mm × (30 + 15) / 2 = 22.5 mm between shaft centers.

Worked — planetary ratio: ring fixed, N_ring = 60, N_sun = 20 → i = 1 + 60/20 = 4:1 (carrier turns once for every four sun turns).

10.1.2 Stepper resolution (derived in Vol 4)

Table 2 — 10.1.2 Stepper resolution (derived in Vol 4)

Quantity	Formula	Units	Notes
Steps per revolution	360° / step angle	steps/rev	1.8°/step → 200 steps/rev
Microstep angle	step angle / microsteps	degrees	finer commanded increment
Microsteps per rev	(360° / step angle) × microsteps	steps/rev	total addressable positions
Needle resolution	microstep angle / gear reduction	degrees	smallest hand move at the dial

Worked — microstep angle: 1.8° / 16 = 0.1125° per microstep → 200 × 16 = 3 200 microsteps/rev.

Worked — needle resolution through 3:1: 0.1125° / 3 = 0.0375° of needle travel per microstep — finer than the eye resolves on a typical dial (Vol 2).

10.1.3 Tuning fork (derived in Vol 5)

Table 3 — 10.1.3 Tuning fork (derived in Vol 5)

Quantity	Formula	Units	Notes
Pulses per minute	f × 60	pulses/min	440 Hz → 440 × 60 = 26 400 ppm
Pulses per second	f	pulses/s	the fork’s own frequency
Rate error from miscount	Δppm / 26 400	fractional	one extra pulse/min ≈ 38 ppm
Calibration target	set P register = measured ppm	pulses/min	the P serial command (§10.5)

The fork is the timebase: the ATtiny4313 counts pulses, not crystal cycles. If the fork truly runs at 440.0 Hz but the firmware’s P value is wrong by one pulse/minute, the clock gains or loses 1/26 400 ≈ 38 ppm ≈ 3.3 s/day. Tuning is therefore a matter of nudging P until the long-term drift vanishes (Vol 5 §5.4).

10.1.4 Accuracy — ppm to seconds (derived in Vol 5)

The conversion that anchors every accuracy claim: 1 ppm = 0.0864 s/day (because 10⁻⁶ × 86 400 s = 0.0864 s) and 1 ppm = 31.56 s/year (× 365.25 days).

Table 4 — 10.1.4 Accuracy — ppm to seconds (derived in Vol 5)

Timebase	Rate spec	s/day	s/year	Used by
AC mains, short term	wanders ±a few ppm	up to ~±5	—	(legacy synchronous movements)
AC mains, long term	grid-corrected	≈ 0 over weeks	≈ 0	utilities hold the cycle count
Tuning fork, untrimmed	~±300–700 ppm	~±25–60	~±15 000	TuningFork before P tuning
Tuning fork, trimmed	~±23 ppm	~±2	~±730	TuningFork after P tuning
DS3231 RTC	±2 ppm	±0.17	±63	PlanetaryGear, Aviation
NTP / Wi-Fi sync	bounded by sync	≈ 0	≈ 0	Aviation (ESP32) when online

The trimmed-fork figure is the designer’s own “within a couple of seconds per day” result (Vol 9). The DS3231’s ±2 ppm is why two of the three builds need no calibration at all; the fork is the build where calibration is the whole game.

10.2 Stepper microstep quick-ref

10.2.1 TMC2208 MS1/MS2 strapping (as wired on the Aviation board)

The Aviation build sets each TMC2208’s microstep mode with the MS1/MS2 pins tied to GND or VCC_IO. The values below are read directly off the project schematic’s configuration table (Vol 4 §4.5). Note these mappings are the board’s chosen set; two of them differ from the bare TMC2208 datasheet default, which is why the schematic annotates them.

Table 5 — 10.2.1 TMC2208 MS1/MS2 strapping (as wired on the Aviation board)

MS2	MS1	Microstep setting
GND	GND	8 microsteps
GND	VCC_IO	32 microsteps (differs from TMC2208 default)
VCC_IO	GND	64 microsteps (differs from TMC2208 default)
VCC_IO	VCC_IO	16 microsteps

10.2.2 Resolution table — 1.8°/step (200 steps/rev) NEMA-17

Table 6 — 10.2.2 Resolution table — 1.8°/step (200 steps/rev) NEMA-17

Microstepping	Microstep angle	Microsteps/rev
Full step (1/1)	1.8°	200
1/8	0.225°	1 600
1/16	0.1125°	3 200
1/32	0.05625°	6 400
1/64	0.028125°	12 800

Higher microstepping buys smoothness and quiet (StealthChop), not torque or absolute accuracy — the average position is unchanged, the increments are just finer (Vol 4 §4.4).

10.3 The three builds — BOM quick-ref

One compact table per build: the parts that define the design. Full schematics, complete BOMs, and assembly are in Vols 6 and 9.

10.3.1 PlanetaryGear (Arduino gear-train clock)

Table 7 — 10.3.1 PlanetaryGear (Arduino gear-train clock)

Block	Part / value
MCU	Arduino (AVR)
Stepper driver	L293D dual H-bridge
Motor	NEMA stepper, 1.8°/step (200 steps/rev)
Reduction	GT2 belt, 60T/20T pulleys (3:1) + ~400 mm belt
Timebase	DS3231 RTC (CR2032 backup)
Homing	A3144 hall sensor + neodymium magnet
Supply	5 V 2 A
Mechanism	3D-printed sun / planet / ring / carrier + hands + case

10.3.2 TuningFork (440 Hz resonator clock, per the README BOM)

Table 8 — 10.3.2 TuningFork (440 Hz resonator clock, per the README BOM)

Block	Part / value
MCU	ATtiny4313-PU (20 MHz max; F_CPU 1 MHz), 4k flash / 256 B RAM
Timebase	440 Hz tuning fork in 3D-printed mount
Pickup/drive	2 × 22 mH inductors (11 mm) + 15×5 mm neodymium rod magnet
Sustaining amp	BC547B ×7 (TO-92 NPN)
Squarer	NE555P (PDIP-8)
Shift register	74HC595 (8-bit)
Display	5 × SC39-11YWA 7-segment
Regulator	L7805 (TO-220, 5 V)
Input	Alps EC12E rotary encoder + switch
Status / IO	3 × 5 mm LED, panel-mount BNC (scope tap), 1N4148
Passives	1 k ×13, 10 k ×8, 100 k ×2, 1 M ×2, 4.7 k; 100 n ×10, 47 n ×2, 100 µF/16 V

10.3.3 Aviation (ESP32 aviator-gauge clock)

Table 9 — 10.3.3 Aviation (ESP32 aviator-gauge clock)

Block	Part / value
MCU	ESP32-WROOM-32D
Motors	3 × NEMA-17 (seconds / minutes / hours)
Drivers	3 × TMC2208 microstepping
Homing	3 × 3144E hall sensor (one per gauge)
Timebase	DS3231 RTC + NTP over Wi-Fi
Audio	JQ6500 voice module (DCF77-style chime)
Presence	PIR module (wake the display)
Supply	MP1584EN buck converter
Mechanism	3 printed aviation gauges + decals / faces

10.4 Pinouts & key ICs

Compact reference pinouts for the ICs that recur across the three builds. Verify against the datasheet before wiring a board — package orientation (pin-1 dot) matters.

10.4.1 NE555 (PDIP-8) — fork squarer

Table 10 — 10.4.1 NE555 (PDIP-8) — fork squarer

Pin	Name	Pin	Name
1	GND	8	VCC
2	TRIG	7	DISCH
3	OUT	6	THRES
4	RESET	5	CTRL

10.4.2 74HC595 (8-bit shift register) — display scan

Table 11 — 10.4.2 74HC595 (8-bit shift register) — display scan

Pin	Name	Function
1–7	QB–QH	parallel outputs (with QA)
8	GND	ground
9	QH’	serial-out (daisy-chain)
10	SRCLR̄	shift-register clear (active low)
11	SRCLK	shift clock
12	RCLK	storage/latch clock
13	OĒ	output enable (active low)
14	SER	serial data in
15	QA	parallel output
16	VCC	supply

Data is clocked in on SER at each SRCLK edge, then transferred to the outputs on RCLK; OE blanks all outputs (used for display dimming/multiplex).

10.4.3 L293D (dual H-bridge) — planetary stepper driver

Table 12 — 10.4.3 L293D (dual H-bridge) — planetary stepper driver

Pin	Name	Pin	Name
1	EN1,2	16	VCC1 (logic)
2	IN1	15	IN4
3	OUT1	14	OUT4
4	GND	13	GND
5	GND	12	GND
6	OUT2	11	OUT3
7	IN2	10	IN3
8	VCC2 (motor)	9	EN3,4

One bipolar stepper uses both bridges: coil A on OUT1/OUT2, coil B on OUT3/OUT4; EN1,2 and EN3,4 gate them; IN1–IN4 set winding polarity (Vol 4 §4.3).

10.4.4 ATtiny4313 — fork counter (relevant notes)

8-bit AVR, 4 kB flash, 256 B RAM, run at F_CPU = 1 MHz in this build. One timer counts fork pulses (overflows give the per-second and per-minute ticks); a second timer scans the display and runs housekeeping; the USART does serial at 9600 baud (§10.5). Inputs: the EC12E encoder + button. Note INPUT_PULLUP is not available on certain pins (the schematic flags pins needing external pull-ups) — relevant if you re-pin the encoder.

10.4.5 L7805 (TO-220 regulator)

Table 13 — 10.4.5 L7805 (TO-220 regulator)

Pin	Name
1	IN (Vin)
2	GND (tab)
3	OUT (+5 V)

10.4.6 DS3231 RTC (I²C module)

Table 14 — 10.4.6 DS3231 RTC (I²C module)

Pin	Function
SDA	I²C data
SCL	I²C clock
SQW	square-wave / 1 Hz interrupt out
32K	32.768 kHz output
VCC / GND	supply; CR2032 backs the clock

I²C address 0x68; temperature-compensated to ±2 ppm (§10.1.4).

10.4.7 TMC2208 (driver control lines)

Table 15 — 10.4.7 TMC2208 (driver control lines)

Line	Function
STEP	one edge = one microstep
DIR	direction
EN (ENN)	enable, active low
MS1 / MS2	microstep select (§10.2.1)
VREF	sets coil current (analog)

10.4.8 ESP32-WROOM-32D (Aviation roles)

3 × {STEP, DIR} pairs to the TMC2208s; shared EN; 3 × hall inputs (3144E); I²C (SDA/SCL) to the DS3231; UART/IO to the JQ6500; a PIR input; Wi-Fi for NTP. Avoid the strapping pins (0, 2, 12, 15) and input-only pins (34–39) for outputs. A pinout reference diagram is slotted below if a labeled map reads cleaner than this list.

FIGURE SLOT 10.1 — A labeled ESP32-WROOM-32D pinout reference highlighting the pins used by the Aviation build (3× STEP/DIR, EN, 3× hall, I²C, JQ6500 UART, PIR); to be fetched license-clean via the Photo Helper in the figure pass, or authored as a project-original SVG; credit verbatim.

10.5 Tuning Fork serial protocol quick-ref

The firmware exposes a 9600-baud serial console. Each command is a single uppercase letter followed by a value (to set) or ? (to query), terminated by newline. Every command is answered by a line beginning with = and OK or ERR (an error appends a code). Some options are read-only or write-only (Vol 9 §9.x).

Table 16 — 10.5 Tuning Fork serial protocol quick-ref

Cmd	Meaning	Access	Set example	Query
E	Echo characters	write-only	E0=off, E1=on	—
A	Auto-send time each second	write-only	A0=off, A1=on	—
C	Charset	write-only	C0=PAWScript (Elian), C1=plain numbers	—
T	Time	read/write	T12:34 (HH:MM only)	T? → HH:MM:SS
P	Pulses per minute (calibration)	read/write	P26400	P?
M	Mode	read-only	—	M? → one of D/H/M/T/E
R	Run state	read/write	R1 runs + clears errors¹	R? → 0 or 1

¹ The README’s R example reads P1\n — a documentation typo; the run command is R1 (you cannot stop the clock with R).

Modes returned by M?: D time display · H hour-setting · M minute-setting · T pulses-per-minute tuning · E error (lost fork signal or other fault).

Error codes (appended after =ERR): :UC unknown command · :INV invalid parameter.

Calibration loop: put the clock in tuning mode, read P?, let it run against a known reference for a day, compute the drift, and adjust P by Δppm × 26 400 (§10.1.3). 26 400 is the nominal value for a true 440 Hz fork.

10.6 Source URLs & where the files live

All three designs are held on disk under Clocks/Mechanical/02-inputs/, one folder per build. The canonical upstream sources:

Table 17 — build. The canonical upstream sources

Build	Folder	Upstream
PlanetaryGear	02-inputs/PlanetaryGear/	Looman_projects, “Planetary Gear Clock,” Instructables (build PDF + full STL/DXF set)
TuningFork	02-inputs/TuningFork/	NuclearLighthouseStudios, “Tuning Fork Clock” — KiCad project, BOM, fork-mount CAD, article
TuningFork firmware	02-inputs/TuningFork/code/	github.com/NuclearLighthouseStudios/Tuning-Fork-Clock-Firmware (C / avr-gcc, make flash)
TuningFork video	—	https://www.youtube.com/watch?v=TgB_1jr5b_c
Aviation	02-inputs/Aviation/	Nobby123, “ESP32 Aviator Clock Using Three Aviation-Style Gauges” (FreeCAD bodies, decals, schematic, firmware zips)

The deep-dive Markdown for this series lives in 02-inputs/volume_sources/vol1.md … vol10.md; figure sources in 02-inputs/volume_sources/figs/. Hub-shared docs: Clocks/_shared/comparison.md, Clocks/_shared/deep_dive_protocol.md, Clocks/_shared/safety.md.

10.7 Glossary A–Z

• Accutron — Bulova’s 1960 tuning-fork watch; a 360 Hz fork sustained by a one-transistor circuit advancing a 300-tooth index wheel. The conceptual ancestor of the TuningFork build (Vol 1).
• Backlash — lost motion (free play) between meshing gear teeth; the enemy of repeatable hand position. Minimized by center-distance and tooth-thickness control (Vol 3).
• Balance wheel — the rotary oscillator + hairspring in a mechanical watch; the resonator a tuning fork or quartz crystal later replaced.
• Barkhausen criterion — the condition for sustained oscillation: loop gain ≥ 1 and total phase shift = 0° (360°). The fork’s transistor amplifier must meet it to self-start (Vol 4).
• Carrier (planet carrier) — the arm/plate holding the planet gears in an epicyclic train; often the output member (Vol 3).
• DCF77 — the German 77.5 kHz longwave time signal; here the JQ6500 plays a DCF-style chime sample, not a real radio decode (Vol 9).
• Epicyclic / planetary gearing — a train with a central sun, orbiting planets on a carrier, and an outer ring; large compact reductions from a flat package (Vol 3).
• Escapement — the mechanism that feeds energy to a mechanical oscillator and counts its swings; the function the fork’s electronics replace (Vol 2).
• GT2 — a 2 mm-pitch timing-belt profile; the 60T/20T GT2 pulleys give the PlanetaryGear its 3:1 pre-reduction (Vol 3).
• Hall sensor — a magnetic-field switch (A3144 / 3144E here); detects a magnet to home a moving part to a known zero (Vol 4).
• Homing — driving a mechanism to a repeatable reference position (against a hall sensor) so commanded angles read true on power-up (Vol 4).
• Involute — the standard gear-tooth flank curve that gives constant velocity ratio through the mesh (Vol 3).
• Lavet stepper — the single-coil stepping motor in cheap quartz movements; one electrical pulse advances the seconds hand one step (Vol 4).
• Microstepping — driving a stepper’s coils with graded currents to subdivide each full step (1.8°) into finer increments for smoothness (Vol 4, §10.2).
• Module (m) — the gear sizing unit, m = pitch diameter / tooth count, in mm/tooth; gears mesh only at equal module (Vol 3).
• NTP — Network Time Protocol; the ESP32’s Wi-Fi time source, accurate to well under a second when online (Vol 5).
• ppm (parts per million) — fractional rate error; 1 ppm = 0.0864 s/day = 31.56 s/year (§10.1.4).
• Pressure angle — the angle of tooth-flank force, commonly 20°; must match between meshing gears (Vol 3).
• Q factor — an oscillator’s sharpness/energy-storage; a high-Q steel fork rings long and holds frequency, easing the sustaining amp’s job (Vol 4).
• RTC (real-time clock) — a battery-backed timekeeping chip; the DS3231 here is temperature-compensated to ±2 ppm (Vol 5).
• Ring (annulus) — the internally-toothed outer gear of an epicyclic train; held fixed for the 1 + N_ring/N_sun ratio (Vol 3).
• StealthChop — the TMC2208’s near-silent voltage-mode chopping mode; why the Aviation needles move quietly (Vol 4).
• Sun gear — the central gear of an epicyclic train; typically the input (Vol 3).
• Sustaining amplifier — the positive-feedback transistor circuit (BC547 stages) that keeps the fork vibrating, sensing on one coil and driving the other (Vol 4).
• Synchronous motor — an AC motor locked to mains frequency; the timebase of legacy mains clocks (Vol 5).
• TCXO — temperature-compensated crystal oscillator; the technique inside the DS3231 that holds ±2 ppm over temperature (Vol 5).
• Tuning fork — a U-shaped steel resonator; the TuningFork build’s 440 Hz “concert A” fork is its timebase, counted at 26 400 pulses/min (Vol 5).

10.8 Source URLs

• PlanetaryGear — Looman_projects, “Planetary Gear Clock,” Instructables. Files in 02-inputs/PlanetaryGear/.
• TuningFork — NuclearLighthouseStudios, “Tuning Fork Clock” (KiCad + article). Firmware: https://github.com/NuclearLighthouseStudios/Tuning-Fork-Clock-Firmware. Video: https://www.youtube.com/watch?v=TgB_1jr5b_c. Files in 02-inputs/TuningFork/.
• Aviation — Nobby123, “ESP32 Aviator Clock Using Three Aviation-Style Gauges,” Instructables. Files in 02-inputs/Aviation/.
• Hub-shared: Clocks/_shared/comparison.md, Clocks/_shared/deep_dive_protocol.md, Clocks/_shared/safety.md.