Plus a circuit to interface the pendulum driver to a clock motor
A solar-powered hybrid mechanical/electric clock
With some application notes.
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 pole piece from the magnet.) The absence of the outer pole piece forces the magnetic field outward. A small neodymium magnet would no doubt work here also.
Magnet Assy - Bottom View
In this example, the pendulum is 100 inches (2.5m) long, consisting of a 4" (10cm) threaded spacer (a small turnbuckle would work here) glued to the bob/magnet assembly, plus two 96" (240cm) strands of dental floss. Its period is just over 3 seconds.
The bob is suspended 1/8-3/16" (3-5mm) directly above the stationary (blue) driver coil. The horizontal swing is about 12" (305mm).
The Driver Coil
The coil is from a 6-volt 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
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. The central core (pole piece) must be removed for it to function as a pendulum driver.
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 is prone to breaking into self-oscillation at a very high rate (>100kHz). To eliminate this, the 1000 µF capacitor shown in the original circuit (C2) was replaced with a .0022 µF unit.
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). The 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.
Capacitor (*) and resistor (**) were changed from their original values.
A variable series resistor and 1k fixed resistor were added between the NiCd cell and the 1000µF storage capacitor (*). The variable resistor is adjusted to optimize the firing rate of the trigger circuit. It should fire at a rate approximately one-half the pendulum's natural period, in other words, its pulse (or "beat") rate:
R ≅ T/1.1C
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.
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 on hand. Expect to do some experimenting.
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.
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:
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 in duration, which I think will work for the vast majority of single-cell (1.5-volt) clock motors. So-called "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
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 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.
The dental floss has been replaced with 1/4" rigid aluminum tubing with a 1/8" threaded brass rod screwed into the lower end. The total length is 40.5" (1028mm) including the original 4" threaded spacer at the bottom. The suspension spring at the top adds another 1" (25mm). (This version is more accurately described as a compound pendulum. See Wikipedia/Pendulum.)
A wooden dowel might have been a better choice for the pendulum shaft. Wood has a coefficient of thermal expansion much lower than aluminum.
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, made with bits and pieces of scrap hardware, allows rough adjustment of the pendulum's length, independent of bob/coil spacing. The suspension spring is from a defunct steel 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.
Why do you call the 1 meter clock pendulum a compound pendulum?
[Tue Jan 24 19:38:59 2017] pend.....
Because its center of mass is not at the end. The aluminum shaft on the as-built clock pendulum causes the center of mass to be located at some point above the end. Flip it end-for-end and it will still behave as a pendulum [with a much shorter period due to the center of mass being closer to the pivot point].
But... When you think about it, it's really all in where you want to draw the line between simple and compound. The 2.5-meter pendulum, suspended with virtually massless dental floss, comes close to being a true simple pendulum. But it would still behave as a pendulum if turned end-for-end. Simple pendulums really exist only in theory. So strictly speaking, both the 2.5m and the 1m are compound pendulums.
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