Monday, July 21, 2014

Omni Wheels in the Temple

SUMMARY Omni wheels might be what King Solomon had in mind when he built his laver stands with "a wheel within a wheel."

Basic design of a First Temple laver stand.
In the First Temple, King Solomon built ten moveable stands [מְּכֹנוֹת] which supported the ten lavers [כִּיֹּרֹת] that stood in the Courtyard. These stands are described in I Kings 7:27-37 in very cryptic language, although the basic idea which emerges is that the stand was a type of wagon with four wheels and the laver rested on top of it. One drawback of the standard wagon design is that it can only be rolled forward or backward but cannot be steered. If the stand did need to be turned one way or the other, it would have to be done by pushing or pulling on one end, a difficult task considering that the stand was made of copper and quite heavy — just the laver itself, when full of water, weighed over 5000 pounds! While it is possible that a method of steering the stand was built into the design, the verses do not seem to indicate that this was so.

A further complication with the design of the wheels is that verse 33 states as follows:

ומעשה האופנים כמעשה אופן המרכבה
The design of the wheels was like the design of the wheel of the Chariot

Rashi explains:

אופן בתוך האופן שתי וערב כמו שאמר (ביחזקאל א טז) במרכבה גבוה
These wheels consisted of "a wheel within a wheel" (Ezekiel 1:16) with one wheel aligned along the warp and one along the weft, i.e., perpendicular to each other (Rashi to Ezekiel ibid. writes this more explicitly) as stated (ibid.) with regard to the Heavenly Chariot.
[Hebrew text courtesy of wikisource].

The concept of a "wheel within a wheel" which can roll along two axes presents something of a design challenge, although I recently came across what appears to be a very practical solution to this problem which satisfies — at least in spirit — the language of the Ezekiel verse with Rashi's explanation. In the latest edition of Make magazine I was introduced to the concept of the holonomic robot platform (one which can move in any direction). As they write in a similar article, "A holonomic robot uses special wheels, called omni wheels. Like conventional wheels they have grip in forward direction. Unlike normal wheels they can slide sideways without much friction. This is possible due to the rollers that make up the tread." This is what an omni wheel looks like:

A molded plastic omni wheel (Wikipedia).
By combining three or more omni wheels, a stable platform can be built which can move in any direction without requiring any of the wheels to rotate about their y-axis (the most common method of steering a vehicle). Steering this platform is accomplished by powering some of the wheels while allowing the others to slide on their rollers (see this video demonstrating the range of motion of a platform using four omni wheels).

If the laver stands were equipped with omni wheels, mounted one on each of the four sides, the stand could be easily rolled along the Courtyard floor in any desired direction. In the animation below some of the rollers have been painted with a checkered pattern to make their movement more obvious. Also, the Kohanim who would have been pushing the stands are not shown (although if laver stands are required in the Third Temple they could always be automated...).

The overall design of the stands shown in this animation and in the photo at the top of this post is based on the laver stand illustrated in the Artscroll's Rubin edition of Kings.

Beaten to the punch
After all of the above, I came to discover that it is no mere coincidence (or my great insight) that omni wheels should represent such an elegant solution to the design of the laver stands. Reading further on wikipedia and other pages, it turns out that Josef Blumrich, the NASA engineer who patented the omni wheel in 1974, apparently came up with this idea in order to explain, in practical terms, the verse in Ezekiel! (Just FYI, the premise of Blumrich's book, The Spaceships of Ezekiel, is that the prophet was not seeing a Divine vision of spiritual beings but an alien spacecraft visiting Earth.)

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