Improved and adapted electronic

Pendulum Driver

My version of David Williams's Nuts and Volts circuit

Plus a circuit to interface the pendulum driver to a clock motor


A solar-powered hybrid mechanical/electric clock

With some application notes.

Max Carter

2.5-Meter Pendulum

Any jerkiness is an artifact of the video. The pendulum's swing is super-smooth.

  • The pendulum bob is the permanent magnet and central pole piece from a loudspeaker. The outer pole piece has been removed from the assembly. The outer pole piece normally surrounds the speaker voice coil; it looks like a large washer. (A light tap on a cold chisel will usually separate the magnet from the outer pole piece.) The absence of the outer pole piece forces the magnetic field outward.
Bottom View Side View
  • In this example, the pendulum is 100 inches (2.5m) long, consisting of a 3" (75mm) threaded spacer (a small turnbuckle would work here) glued with epoxy to the bob/magnet assembly, plus two 96" (240cm) strands of dental floss. Its period is just over 3 seconds.
  • The bob is suspended ~⅛" (3mm) directly above the stationary (blue) driver coil. The horizontal swing is about 12" (305mm).

    The Driver Coil

  • The coil is from a 6-volt (DC) relay. The resistance of the coil is about 29 ohms. The center pole piece has been removed.
  • Magnetizable objects (nails, etc) can disturb the pendulum's swing. These should be kept away from the coil and pendulum bob.

    The Driver Electronics

    Figure 1

  • The 29-ohm, 6-volt relay coil replaces the hand-wound coil described in the Williams article. I don't think this particular resistance value is critical to the functioning of the circuit. Likely any low-voltage relay coil would work, as would Williams's hand-wound coil. The central core (pole piece) must be removed from a relay coil for it to function as a pendulum driver.
  • The white LED absorbs the inductive kickback induced in the coil each time the circuit fires. With R properly adjusted, the LED will flash with each beat of the pendulum.
  • I suspect any color LED would work as well; I just happened to have a white one on hand.
  • Rather than the transistors specified by Williams, I used the ones shown above from stock I had on hand. I suspect any small-signal PNP and NPN units would work.
  • The transistor amplifier/trigger circuit has a very high gain (10,000+) and the original circuit was prone to breaking into oscillation at a very high rate (>100kHz), firing multiple times with each swing of the pendulum. To eliminate this, the 1000 µF capacitor shown in the original circuit (C2) was replaced with a .0022 µF unit. The circuit as shown delivers one and only one pulse per beat of the pendulum when properly adjusted.
  • A 600 mAh NiCd cell and 1N5817 Schottky diode were added as shown to enable the pendulum to operate when the sun is not shining. Average current draw for the circuit (including the motor driver below) is 0.5 mA which suggests the pendulum should operate for at least a month without sunshine. The NiCd cell also provides a degree of voltage regulation which helps regularize the pendulum's period (useful in the following clock application). It's likely any NiCd or NiMH cell would work just as well. The Schottky diode prevents reverse current flow in the solar cells.
  • The two series-connected 1N914 diodes form a shunt regulator, limiting the charge on the capacitor to about 1 volt. This also serves to regularize the pendulum's period and may provide some temperature compensation.
  • The 1000µF value of the storage capacitor (*) in Fig 1 is suggested for a 2.5m pendulum. Values for shorter pendulums are shown in the chart below.
  • A variable series resistor and 1kΩ fixed resistor were added between the NiCd cell and the storage capacitor. The variable resistor is adjusted to optimize the firing rate of the trigger circuit. The adjustment is not difficult: The circuit should fire at a rate twice the pendulum's natural period, in other words, its pulse (or "beat") rate:

    R ≈ T/2C

    where R is the resistance (fixed plus variable) in ohms,
    T is the period of the pendulum in seconds, and
    C is the storage capacitor value in farads.


    Observe the white LED flashes. Setting the resistance too high will cause the circuit to skip beats. Setting the resistance too low will cause the circuit to fire randomly. A setting midway between these two points is near optimal.

  • The variable resistor setting also has a slight influence on the pendulum's period. Setting the resistance higher will lower the pendulum's amplitude and shorten the period. It will run a few seconds per day faster. Setting the resistance lower will have the opposite effect.

Adapting the Circuit for Timekeeping
  • Pendulums keep better time with relatively low swing amplitudes (<6°). The value of the energy storage capacitor (*) in Figure 1 determines the amplitude. The chart below shows some suggested values for various pendulum lengths. Chart assumes ~1.5kΩ charging resistance R (fixed plus variable).

Suggested Fig 1 Storage Capacitor Values

Pendulum Length (m)  Nominal Period (s)  Pulse Frequency (Hz)  Capacitor Value (µF)

More Notes

  • The threaded spacer above the pendulum bob allows fine adjustment of the distance between the bob and the driver coil. The spacer is adjusted to the system's "sweet spot", the spacing that produces maximum swing amplitude.
  • The heavy pendulum bob makes the as-built pendulum a reluctant self-starter; it needs a push to start.
  • If you can't get the pendulum to run, flip the driver coil over or reverse the leads to the coil. The coil and permanent magnet on the bob must repel each other when the coil is energized.
  • The pendulum and driver circuit shown were made with parts on hand. Other than the two transistors, it was all junk. Your results may vary, depending on what junk you have. Expect to do some experimenting.

More Junk

  • This shows the solar array suspended in a south-facing window. The solar cells (and NiCd battery) are from trashed-out "garden lights". Under direct sunlight, each cell puts out 1 volt into an open circuit or 50 mA into a short circuit. With all four cells connected (in series-parallel) the NiCd would be over-charged, so only two of these cells are actually wired (as shown in Fig 1). The array, as presently connected (2 cells only), charges the battery at a 15-30 mA rate under direct sunlight (obviously not when this photo was taken). Another connection option would be to wire three or four of these in series and use the current regulator circuit shown in the box below.
  • It looks like a single Futurelec SZGD3131 (2.2V/50mA) would substitute for the two 1-volt solar cells shown in Fig 1.

Larger Solar Cells/Regulated Battery Charging
  • After 15 hours without direct sunlight, in full sunshine the two solar cells shown in Figure 1 will recharge the NiCd battery to its pre-discharge state in less than one hour. While the NiCd will never reach full capacity with the specified solar cells, using solar cells of greater current output capability (>60 mA) risks over-charging and, more importantly, can cause erratic operation of the pendulum driver. The current regulator shown below can be added to accommodate more and/or larger solar cells. The regulator limits charging current to 15 mA. [This can be changed by changing the value of R per the equation.] Note that at least three 1-volt solar cells are required. The circuit as shown will accommodate any panel or array up to 25 volts no-load output.
  • A line-powered DC source could substitute for the solar cells. A 5-volt USB charger, for example, would work OK with the above regulator circuit. The charger could remain permanently connected.

Clock Motor Driver

If you'd like to experiment with timekeeping and build a cool clock, the pendulum circuit can be used to drive an electric (battery) clock motor. The result would be a mechanical/electric hybrid. [Solar-powered grandfather clock, anyone?] The electronics to do this are shown below. The circuit delivers alternating-polarity pulses to the motor winding. It has lots of transistors and resistors, but they're cheap:

Figure 2

  • Note that the driver circuit calls for two types of transistor: PNP type 2N2907A (or any small-signal equivalent), and NPN type 2N2222 (or any small-signal equivalent).
  • The value of the resistor connected from pin 5 to pin 4 of the CD4027 J-K flip-flop sets the length of the motor pulses. The 270k value shown generates pulses of around 25 mS duration, which I think will work for the majority of single-cell (1.5-volt) clock motors; "high-torque" motors may require a longer pulse. If the motor fails to "tick" correctly, try varying the value of this resistor.
  • The two 1N5817 Schottky rectifiers shown in the circuit operate as a charge pump to charge the 100µF capacitor connected to pin 16 of the CD4027 - to about 2.4 volts when the Ni-Cd cell is at 1.4 volts, and 2 volts when the Ni-Cd is at 1.2 volts. This provides power for the chip. Yes, the CD4027 will operate on 2 volts in this not very demanding circuit.
  • It will require 3 or 4 pulses from the pendulum to fully charge the +2.4-volt power rail on start-up.

Pendulum Driver Mated to Motor Driver

Connecting to the Motor Winding
  • Disassemble the clock to gain access to the solder pads on the circuit board where the motor winding is connected. Be sure to note the order in which the wheels (gears) are removed.
  • Using a utility knife or small hand grinder, cut one of the traces on the circuit board so as to isolate the winding from the on-board circuitry.
  • Tack solder a length of AWG 28 (.08mm2) two-conductor wire to the pads.
  • Route the wire to the outside of the motor case.
  • Reassemble the clock. Dab a tiny amount of white lithium grease on the wheel and motor rotor pivots as they are reinstalled. (It's not necessary to reinstall the battery.)

  • The pendulum should be about a meter in length. This length produces a period of two seconds, or one pulse per second. As with any pendulum clock, the pendulum's length (and/or center of mass) should be adjusted until the clock runs at the right speed to always tell the correct time. It will likely end up being somewhat longer than 1 meter, depending on where the center of mass lies on its length.
  • The value of the storage capacitor in Fig 1 should be changed to 680µF or thereabouts.

Shorter Pendulums
  • The clock motor driver circuit can be modified to accommodate a 25cm (10"), 11.1cm (4.5") or 6.25cm (2.5") pendulum by interposing a second CD4027 flip-flop (U2) at the point marked with a red X on Figure 2. Depending on how it's wired, U2 divides the pendulum drive pulses by 2, 3 or 4. This will allow the pendulum to oscillate with a shorter period, while the clock motor still receives 1 pulse per second.
  • The micro-power CMOS IC adds little to the driver's current consumption.

Figure 3

  • Shorter pendulums require shorter driving pulses. Modify the value of the storage capacitor in Fig 1 per the chart.
  • As with the 1-meter pendulum, the shorter ones' real-world length will likely end up being slightly longer after adjustment.
  • See a circuit for 62.5cm and 2.5m pendulums here.


Solar-Powered Hybrid Mechanical-Electric Clock

  • The dental floss has been replaced with 1/4" rigid aluminum tubing [6061 alloy], with a 1/8" threaded brass rod screwed into the lower end. The total length is 40.5" (1028mm) including the original 3" threaded spacer at the bottom. The suspension spring at the top adds another 1" (25mm).

  • This tab allows the coil to be precisely centered under the pendulum bob. The adjustment is made with the pendulum at rest. The screw, washers and tab are non-magnetic. A plastic screwdriver was used to tighten the screw.

  • The support is made with bits and pieces of scrap hardware. The suspension spring hangs between two closely-spaced (~0.2mm) cylindrical posts which restrict the movement of the spring. The posts' height effectively sets the height of the pendulum's pivot point, and thus its length, independent of the bob/coil spacing. The spring is from a defunct tape measure.

  • This is the fine adjustment nut on the pendulum shaft. The adjustment raises or lowers a sliding weight (brass pipe fitting) above it, which raises or lowers the pendulum's center of mass. This adjustment is also independent of bob/coil spacing. One turn of the nut produces a rate change of roughly 10 seconds per day.

  • Three thin brass washers placed on the bob were needed to slow the pendulum just enough to bring its rate within range of the fine-adjust nut.

Disruptive Kitten

I had to provide a shield to protect the pendulum from a very curious and playful kitten, seen here chewing on the wire that connects the electronics to the clock motor..

How Well Does it Keep Time?

The clock was coarse-timed with an oscilloscope and function generator to within a few seconds per day (<5mS/min), then fine-adjusted weekly against Official US Time. The clock is now regulated to within two seconds (on average) per week. I'm thinking this could be improved to a second or two per month. Only time will tell.

Fused Quartz Rod Replaces Tubular Aluminum Shaft

Fused quartz might be the ideal pendulum shaft material. With a coefficient of thermal expansion much lower than aluminum (5.5 x 10-7 m/m°C), a fused quartz pendulum shaft should out-perform one made with aluminum. Here's a fused quartz variation of the pendulum described on this page: Fused Quartz Pendulum.


Top of page.


2N2222 (PN2222):Futurlec/PN2222
2N2907A (PN2907A):Futurlec/PN2907A
Resistors, capacitors, diodes:Futurlec/components

Futurlec is cheap, but they're slow. Allow 2-3 weeks for delivery.

Related Pages

Build the Mystery Solar-Powered Pendulum

Official US Time

Fused Quartz Rod Replaces Tubular Aluminum Shaft

Running 72-Hour Phase Record


Schematics produced with DCCAD.