The key that unlocks the Jacob's Wheel system is found in the ancient kabbalistic book The Sepher Yetzirah.
There are various levels of knowledge and mystery in the text of this classic book. On one level it describes the ten sephiroth and 22 pathways of the Tree of Life, but encoded at a deeper level is the basic structure of Jacob's Wheel.
Sepher Yetzirah, II:4
Twentytwo Foundation Letters:
He placed them in a circle [GLGL, גלגל]
like a wall with 231 [RL"A, רל"א] Gates.
The circle oscillates back and forth.
A sign for this is:
There is nothing in good higher than Delight [ONG, ענג]
There is nothing in evil lower than Plague [NGO, נגע].[Translated by Aryeh Kaplan.]
Sefer Yesirah, §18
The twentytwo letters are their foundation.
It is fixed on the Hook [ThLY, תלי],
on a wheel [GLGL, גלגל] with
two hundred and twentyone [231, RL"A, רל"א] gates.
The wheel rotates backwards and forwards.
And this is the sign: if for good, above pleasure [ONG, ענג],
and if for evil, below pain [NGO, נגע].
[Sefer Yesirah (Short Recension) : Parma 2784.14 (Bibliotheca Palatina 2784/14), De Rossi 1390, fols. 36b38b. Italian semicursive script. 1286. Translated by A. Peter Hayman.]
[Note: In the Short Recension (quoted above) the number '221' is a recognized scribal error. The text should read '231'.]
The idea of a cycle (circle, or wheel  Heb: GLGL, גלגל) is a central one in the Sepher Yetzirah. That is why it focuses so strongly on the astrological archetypes. The book is actually an instruction manual for building a map of the energy cycles and currents that are flowing through our World (and our personal lives).
The word GLGL is one of three wordkeys that help define the correct arrangement of the 22 Hebrew letters within the Jacob's Wheel mandala. The other two are ONG (ענג, 'delight') and RL"A (רל"א, the number 231). These three words all occur in chapter II, verse 4 (quoted above).
GLGL is the mathematical key. It instructs us on how to arrange the 22 Hebrew letters within the Jacob's Wheel mandala by giving us the 'magic number' 33. GLGL is valued 66, where GL = 33, so that GL + GL = 33 + 33. This is the key formula.
When I say that the number 33 is 'magical' I mean it in the mathematical sense. For example, the 'magic square' of the number 6 consists of the numbers from one to 36 arranged in a 6x6 grid and every row of numbers in that square adds up to 111. Thus, the number 111 is 'magical' in relation to the 6x6 magic square.
The Jacob's Wheel mandala's basic blueprint contains the numbers from one to 21, and consists of seven rows of three numbers where each row (or 'spoke' of the wheel) adds up to 33.
The JW mandala uses the ordinal values of the Hebrew letters (1 to 21) to determine the correct arrangement (as depicted below). The 22nd Hebrew letter is positioned at the centre of the mandala.
The ordinal values of the Hebrew letters are listed in the table belowleft.

Note: The second column of numbers in the table aboveleft lists the base10 values of the Hebrew letters. These values are used when the Hebrew letters are employed to represent numbers in the Hebrew language.
In the mandala diagram aboveright, each row of three numbers adds to 33 like so...
1 + 12 + 20 = 33
2 + 13 + 18 = 33
3 + 14 + 16 = 33
4 + 8 + 21 = 33
5 + 9 + 19 = 33
6 + 10 + 17 = 33
7 + 11 + 15 = 33
Thus the Hebrew word GLGL (33 + 33) is seen to be an important key to the arrangement of the Hebrew letters on the JW mandala. The entire series of 22 mandalas that constitute the JW master mandala are likewise arranged according to the pattern derived above.
Interesting Note: The Hebrew word 'GL' is valued 33 because G (3) + L (30) = 33. Now, if we expand the word GL by spelling its Hebrew letters G (Gimel) and L (Lamed) in full we derive: GML (73) + LMD (74) = 147. Thus, the word GL has two main values: 33 (basic) and 147 (expanded). Interestingly, the 147 year master cycle of Jacob's Wheel is fundamentally important in the Jacob's Wheel system because it reflects the lifetime of the patriarch Jacob, and because it's the shortest possible Jacob's Wheel master cycle containing minor cycles and phases of whole months and whole years. (Master cycle = 147 years. Minor cycle = 7 years. Phase = 4 months.) 147 = 3x7x7. And note also that the 21 minor mandalas of Jacob's Wheel contain a total of 147 spokes (i.e. 21x7 = 147).
When the letters are substituted in place of their corresponding ordinal numbers we derive the following...
This is the first mandala of Jacob's Wheel. It is situated on the first spoke of the inner ring of the master mandala  the same relative position in that greater mandala as the letter aleph (A, א) has in this smaller one.
On the first spoke of the mandala (above) you will find highlighted in yellow the number RL"A ('231', רל"א)  read from the outer to the inner ring. The first spoke of the first mandala thus contains one of our important wordkeys, which tells us that our mandala pattern is correctly formulated.
Note: The appearance of the number '231' in Hebrew on the first spoke of the first mandala of Jacob's Wheel is an extraordinary 'coincidence'—that is, because it coincides (obviously) with the '231 Gates' of the Sefer Yetzirah. Its presence here suggests that this particular arrangement of the 21 letters/numbers is somehow mathematically 'special'. The sum of the numbers from 1 to 21 is 231—a fact that is reflected in the numerical value (i.e. 33) of each of the seven spokes of the mandala. 7 x 33 = 231. The first Hebrew letter is Alef (א), the twelth Hebrew letter is Lamed (ל), and the twentieth Hebrew letter is (ר) Raysh. The standard 'base 10' values of these three Hebrew letters when added together is: 1 + 30 + 200 = 231. It is a mathemagical mystery how their 'ordinal' number values (i.e. 1 + 12 + 20) can produce this amazing synchronicity with their 'base 10' values—that is, when the ordinal values are configured in this specific 'magical' arrangement. (!?!) (See the Hebrew letter table aboveleft for the decimal values of the letters.)
Our other wordkey is ONG ('delight', ענג). You will find it highlighted in green on the third spoke  also read from the outer to the inner ring. The word NGO ('plague') merely reconfirms this combination of third spoke letters. So we see that again our pattern is confirmed by the clues contained in this special verse (II, 4) of the Sepher Yetzirah.
Thus it can be seen, that with these three wordkeys GLGL, RL"A, and ONG, we are given enough encoded information to derive the first mandala of Jacob's Wheel. And from the pattern of the first mandala we can then derive the remaining 21 mandalas of the Jacob's Wheel master mandala.
Of further esoteric interest is the fact that the final mandala positioned on the spokes of Jacob's Wheel (i.e. the 21st mandala  corresponding with the Hebrew letter Shin/ש in the diagram above) contains, in Hebrew, the word "Israel" (YShRAL, ישראל).
The 'Israel' Mandala (#21 in the 'magical' sequence) 
This is the only one of all the 22 mandalas of Jacob's Wheel that contains the word "Israel". As you can see, the word 'Israel' occupies the same spokes (i.e. the first and third) as our original wordkeys do in the very first mandala (see the diagrams above). The initiatory name/formula 'Israel' symbolises the perfection of human consciousness in this Earth psycho/biosphere.
Interesting Fact: The State of Israel was created on the 14th May, 1948. Amazingly, this occurred during the Israel phase of the Israel cycle of the grand World 3087 year master cycle of Jacob's Wheel. The odds of this event occuring within this particular seven year phase of the 3087 year master cycle are 1 in 441. The Israel phase of the Israel cycle is identified by the Hebrew letter Qof (ק) in the mandala above right. It means that the nation of Israel is governed by the archetypes RayshQof [3/4], or MercuryPisces [3/4]. More Information. 
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Now all that is left to do is to substitute the astrological correspondences (as detailed in the Sepher Yetzirah) in place of the Hebrew letters and we have fully deciphered the cycle of archetypal energies that pour through our reality matrix. The first mandala in the JW sequence appears as follows...
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There is an ambiguity surrounding the number of 'gates' referred to in the text of the Sefer Yetzirah. Usually, the number 231 is assumed to be correct, but in commenting on verse 2:4 Aryeh Kaplan mentions: "In some versions of the Sefer Yetzirah, the actual reading is '462 gates'." [The Sefer Yetzirah. Aryeh Kaplan. Pg. 118.]
Sepher Yetzirah, II:5
How? He permuted them, weighed them, and transformed them,
Alef with them all and all of them with Alef,
Bet with them all and all of them with Bet.
They repeat in a cycle and exist in 231 [or, 462] Gates.
It comes out that all that is formed and all that is spoken
emanates from one Name.[Translated by Aryeh Kaplan.]
The number 231 is important in terms of the geometry of the metaphysical system described in the Sefer Yetzirah because it represents the total possible number of Hebrew alphabet twoletter combinations, but it excludes the permutations of the letters. In other words, the 231 combinations include the AB letter pairing, but not the BA pairing (i.e. because BA is a permutation of AB).
The fact is, however, that in verse 2:4 it is written: "The circle oscillates back and forth", and then it proceeds to give an encoded example of the permutation of the letters ONG. The Sefer Yetzirah is telling us that the circle (or 'cycle', GLGL) moves in two directions—from A to B, and from B to A. This is like two people standing on opposite sides of a closed door. Person A experiences the door as the 'gate AB', whereas person B experiences the door as 'gate BA'. This is due to the fact that they are moving in opposite directions through the same door.
Verse 2:5 (quoted above) confirms this concept when it states: "Alef with them all and all of them with Alef, Bet with them all and all of them with Bet." In other words: Alef with Bet, and Bet with Alef; Alef with Gimel, and Gimel with Alef, etc.
So, the number of gates is actually 231*2, or 462, but as you can see, both numbers are significant. There are a total of 231 gateways, but they are counted as 462 gates when considering the dual cycle of energies that are flowing through them in opposite directions—A to B, and B to A. The Jacob's Wheel system is comprised of 462 gates.
The 462 gates of Jacob's Wheel consist of 441 'revealed' (or 'manifest') gates, and 21 'concealed' (or 'unmanifest') gates. The 441 manifest gates constitute the 441 phases of the Jacob's Wheel spiralcycle. The 21 unmanifest gates correspond with the 21 Hebrew letters that compose the central 'key mandala' of Jacob's Wheel. These 21 Hebrew letters are also found at the centre of the 21 minor mandalas that form the main body of Jacob's Wheel. They represent 'seedforms' that are coming into manifestation as a result of the action of the unfolding spiralcycle that surrounds them.
And therefore, it's interesting to see in §18 of the Short Recension of the Sefer Yesirah (quoted above) a reference to the 'Hook' [ThLY, תלי]—because its numerical value is 440. It appears that the Hebrew word ThLY was included in the verse as a coded reference to the 441 gates of the Jacob's Wheel spiralcycle.
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Important Note: After the Hebrew letters have been arranged upon their mandalas in the 'magical' sequence, the twentyone Jacob's Wheel cycles/phases follow a course that is different to the original magical order. When using the Jacob's Wheel system the cycles and phases are read in the natural spiral sequence illustrated in the following diagrams. In other words, the 'magical' sequence formula is used only to arrange the twentytwo Hebrew letter archetypes and fix them in their places. The creativeevolutionary process then proceeds to unfold through them in a natural triple spiral, as follows... 
The Jacob's Wheel master cycle forms an endlessly repeating spiral loop. 

In conclusion, it seems quite probable to me that the author of the Sefer Yetzirah (all those hundreds of years ago) was sitting with Jacob's Wheel in front of him and thinking 'how can I preserve this secret knowledge for the generations to come?'. Then, knowing that the first mandala contained the words RL"A and ONG he decided to use those words as keys, along with the word GLGL as a mathematical key. And so he composed verse II,4.
There are other wordkeys in the Sepher Yetzirah that provide confirmation of the JW model, but it is this verse (SY: II, 4) that gives us our main clues as to the geometric structure of Jacob's Wheel.
The ultimate confirmation of the Jacob's Wheel system comes from the fact that it works in practice as an astrological tool. (If you would like to test for yourself the Jacob's Wheel system of kabbalistic astrology please download the free Jacob's Wheel software available from this website.)