The Rolling Ball Web
An Online Compendium of Rolling Ball Sculptures, Clocks, Etc.
By David M. MacMillan et. al.

Rolling Ball Display Clocks

In addition to, or entirely instead of participating in the timekeeping functions of a clock, rolling balls can also be used to indicate the time. In this function, they serve essentially as calculating devices, transforming by mechanical mathematics the steady time signal of the clock into human-readable time.

Vitruvius' Odometer (Hodometer, Waywiser)

[Note: Vitruvius' odometer is not a clock, of course. But given the possible historical links between it and subsequent Islamic clocks I couldn't think of a better place to put it for the present.]

The Roman architect and engineer Marcus Vitruvius Pollio, known commonly as Vitruvius, described a ball mechanism in Book X, Chapter 9 of his work de Architectura (also known as The Ten Books on Architecture).

The complete text of Vitruvius is online on Bill Thayer's outstanding LacusCurtius site in Latin, English, and (partially) French. The site is at:
http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman/index.html
The texts of Vitruvius are at:
http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman/Texts/Vitruvius/home*.html
The section on the Odometer, in the English version, may be reached directly at:
http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman/Texts/Vitruvius/10.html#9.1

The ball mechanism is described by Vitruvius in this way:

Above, in another enclosure, is a third horizontal wheel toothed similarly, and so that the teeth correspond with that tooth which is fixed to the side of the second wheel. In the third wheel just described are as many holes as are equal to the number of miles in an usual day's journey. It does not, however, signify, if they be more or less. In all the holes let small balls be placed, and in the box or lining let a hole be made, having a channel, through which each ball may fall into the box of the chariot, and the brazen vessel placed under it. (X.9.3)

... Thus, by the dropping of the balls, and of the noise they make, we know every mile passed over; and each day one may ascertain, by the number of balls collected in the bottom, the number of miles in the day's journey. (X.9.4)

Shortly after, while describing a marine version of this device, Vitrivius again makes mention of a channel through which the balls run.

In this horizontal wheel holes are made, wherein the round balls are placed; and in the box of the wheel is a hole with a channel to it, through which the ball descending without obstruction, falls into the brazen vase, and makes it ring. (X.9.6)

(English texts from the Joseph Gwilt translation of 1826, as presented on the LacusCurtius site (see links above)).

Vitruvius' machine is better known in the study of the history of technology for a controversy involving its "one-tooth gear" ("having one small tooth projecting beyond the face of its circumference" Vitruvius X.9.2) The problem isn't with the single tooth per se, but rather with getting a single tooth to mesh effectively enough with a 400 tooth gear to transmit sufficient power. There's a popular treatment of this in:

Sleeswyk, Andre Wegener. "Vitruvius' Odometer: A Machine for Measuring Mileage that the Roman Engineer Described but may never have Seen Proved Puzzling to Leonardo 1,500 Years Later. It may have been Invented by Archimedes during the First Punic War." Scientific American 245.4 (October, 1981): 188-200.

The formal presentation of Sleeswyk's argument appears in a paper that I have not yet read:

Sleeswyk, Andre W. "Vitruvius' Waywiser." Archives internationales d'histoire des sciences. Vol. 29 (1989): 11-22.

Sleeswyk cites historical objections to the practicality of meshing a single-tooth gear with a 400-tooth gear (e.g., Claude Perrault, in an unspecified commentary of 1673) as well as proposed alternatives by Leonardo da Vinci which, while perhaps workable, don't seem to match Vitruvius' text. Sleeswyk then proposes a version which seems both to work (or at least which worked in a 1/4 scale model) and to comform to Vitruvius' text.

Sleeswyk goes on to point out the possiblity of a connection between the ball-release mechanism of this device and the ball-release mechanisms proposed in a treatise on water clock making traditionally attributed to Archimedes. This treatise has been translated by Donald R. Hill, and has been published as:

Hill, D. R. On the Construction of Water Clocks: Kitab Arshimidas fi`amal al-binkamat [Kita/_/b Archimi/-/das fi`amal al-binkama/_/t, with /_/ representing a long mark over the prceeding vowel, and /-/ representing a short mark over the prceeding vowel] London: Turner & Devereux, 1976. [Turner & Deverux Occasional Paper No. 4]

Hill discusses in detail the difficulties of the attribution of this text and the devices it describes to particular individuals; most of it clearly postdates Archimedes. However, Hill opts for an attribution of the basic "water-machinery and the release of balls" (Hill p. 9) to Archimedes.

Sleeswyk cites Hills attribution and goes on to argue that Archimedes may have actually invented the Vitruvian odometer for the measuring of the early, expanding system of Roman roads.

I would like, as a historian of rolling ball devices, to cite the Vitruvian/Archimedean odometer as an extremely early example of a rolling ball mechanism. I'll be the first to admit that doing this is stretching the point - it's really a "dropping ball" device. But if one credits possible links with it to Archimedes, and then possible links of Archimedes to early and medieval Islamic "dropping ball" clocks (which used dropped balls, channels, and bells, as in Vitruvius X.9.6), there is an interesting, if highly conjectural, thread in the history of technology.

Medieval Islamic Clocks

Modern Tilting-Arm Clocks

The most common modern type of mechanism employs tilting arms both to compute and to display the time. Typically, in this style of clock, a new ball is raised to the top of the clock every minute. This ball rolls down a track and into the first of several tilting arms. Each arm is designed to hold a certain number of balls before tilting. When an arm is full, the last incoming ball triggers its tilting action. The arm tilts; one ball proceeds to the next arm in the series, while the others return to the ball reservoir. Together, the balls on the several arms indicate the time according to one of several arrangements.

"1-5-60" Clocks

For example, the common plastic "Arrow Mfg. Co." clock employs three arms. The uppermost arm holds 4 balls and tilts on the entry of the fifth. Each ball in this arm therefore indicates one minute. The second arm of the arrow clock receives a single ball from the first arm each time the first arm tilts. This second arm therefore carries balls which signify five minutes each. This arm carries 11 balls (5 through 55 minutes) and tilts on the arrival of the 12th ball on the hour. The third and final arm on the Arrow clock holds balls which signify one hour each. It receives a new ball each time the second arm tilts (one ball an hour). The ball in the 1 o'clock position on this arm is fixed, because it is always, numerically, at least 1 o'clock. This arm holds 11 movable balls (2 through 12 o'clock) and tilts on the arrival of the 13th (1 o'clock) ball.

The earliest reference that I have been able to find to a clock of this tilting-arm type is the 1978 patent by Harley Mayenschein in the US. It describes a clock of which might be called a "1-5-60" clock because the balls on the three tilting arms represent, respectively, 1, 5, and 60 minutes each. (This terminology isn't well-established; I'm just making it up here.) Clocks of this type were distributed in the 1980s in the US under the "Arrow Mfg. Co." name; a very similar clock is now (1997, 1998) back in distribution under the name "Time Machine." One or more clocks of this design were also built by Mayenschein in the late 1970s under the name "Idle-Tyme."

Clocks of this type are discussed in greater detail on the "1-5-60" Rolling Ball Display Clocks Page.
(6 images, approx 60.2k)

"1-2-10-60-240" Clocks

Helge Rustad, of Trondheim, Norway, has constructed what might be termed a "1-2-10-60-240" clock which displays 24-hour time. This clock is displayed at "Vitensenteret," a Science Centre and Exploratorium in Trondheim. Rustad's clock is also notable for its design and construction. It employs ping-pong balls lifted by fans, and is constructed largely of Lego ^TM.

This clock is illustrated and described on Helge Rustad's website.

"1-10-60" Clocks

Tod Flak

Tod Flak has constructed a "1-10-60" clock. His clock is constructed from wood (cherry). A ball carrier riding on a vertical, threaded rod carries a ball up to the top of the clock every minute. This threaded rod is turned by a stepper motor. An infrared emitter/detector is used to ascertain the carrier's position. Timing is done through a custom-programmed 8031 microcontroller. At one time this clock was featured on its builder's web page at Washington University, St. Louis. However, Mr. Flak has since left W.U. and this page is no longer online.

Gravity Clock (Ft. Lauderdale, Florida)

There had been a reported sighting of an RBS in central Florida some time ago. Dale Emery of the Bixworks Company noted that this might be a large RB clock, much like a Rhoads piece but larger (!) installed "in the open-air atrium of the Museum of Discovery and Science & Blockbuster IMAX Theatre, in Fort Lauderdale."

I cannot seem to find a website for this museum, but there's an online article on "Showtime Interactive": http://www.sun-sentinel.com/showtime/destinations/favorite/science.htm. This article calls this the "Great Gravity Clock," and confirms that it is in the Atrium. Dale further notes that the Atrium is visitable without charge. Apparently it is a three-arm rolling ball display clock of monumental size (52 feet tall) with 1-minute, 10-minute, and 60-minute arms (or "rails" as the article says).

Museum of Discovery & Science
401 SW Second
St., Fort Lauderdale, Florida
(954) 467-6637

Other Tilting-Arm Clock

In correspondence in 1996, Steven Berger of Timesavers has indicated that a clock similar to the "Arrow," but constructed of wood, was available in Europe for DM175. I have not seen this clock, however, and therefore cannot verify that it is of "1-5-60" operation.

Legal Matters

With the exception of any material noted as being in the public domain, the text, images, and encoding of this document are copyright © 1998 by David M. MacMillan.

This document is licensed for private, noncommercial, nonprofit viewing by individuals on the World Wide Web. Any other use or copying, including but not limited to republication in printed or electronic media, modification or the creation of derivative works, and any use for profit, is prohibited.

Version 1.11, 1999/05/13. Feedback to web@lemur.com
http://www.database.com/~lemur/rbc-display.html

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