The image of a wheel is important in both Daoism and Ba Gua Zhang. This essay by Tom Bisio explores this image and its relationship to Ba Gua and the Dao.
The image of a wheel is sometimes used as an example of the Dao. Hans-Georg Moeller’s excellent book, Daoism Explained, provides a detailed description of the “Wheel-Dao Analogy” that may be useful for Ba Gua practitioners.
Moeller begins by saying:
That the Dao is depicted as a wheel, as the wheel of a cart, shows right away that the Dao is not static, that it is not something that eternally stands still, but rather something that moves – even though it does not change its shape. The wheel is not merely a thing, it is a kind of event, it is rotation and motion. The wheel is a running, it is a “pro-ceeding,” a “pro-cess” (i.e., literally a “going forwards”).
In Ba Gua Zhang, Jiang Rong-Jiao tells us:
Yao ru zhou li,
Shou si lun xing .
Yao  like an axle,
Hands like revolving wheels.
Jiang explains this statement as follows:
In practicing Ba Gua Zhang, the yao is the axis of the movements. When the hand moves, the body must move first. When the body moves, the waist must move first, so the waist can drive and lead everything. When changing the palms in Ba Gua Zhang, the movements of the arm must be circular in shape like the movement of a wheel, because circular movement is quick and agile and contains ring-linked, continuous motion without interruption .
The axle, and the hub into which it inserts, form the center of this on-going movement. It is the center from which the movement takes place, and such a center must necessarily be still in relation to what is moving around it. This center space is specifically referred to as a metaphor for the Dao in the Dao De Jing:
We put thirty spokes together and call it a wheel;
But it is on the space where there is nothing that the usefulness of the wheel depends. 
Moeller expands on the idea of the hub and spokes as follows:
At the center of the wheel there is the hub, just as at the center of any efficient scenario there has to be an empty middle. This element has four main characteristics: it is positioned at the center, it is empty, it does not move and thus it is still, and, fourth and finally, being a center it is single. 
The hub is not made of something. All the spokes are made of a material substance, whereas the hub is nothing but an empty space; it does not have any positive qualities. Because the material the spokes are made of is necessarily always a specific one, it is exchangeable. The wood of this tree or that can be used, one can even use something other than wood. No matter which material is used for making the spokes, the hub remains untouched. It is always made of the same non-material. Materials like wood grow and wither, metal is cast and rusts. An empty space neither withers or rusts. It is there or not; emptiness cannot increase or diminish in substance. There are no degrees of emptiness.
Whereas the spokes turn around within the wheel, the hub always stands still. Unchanged, it keeps its position and it does this simply by doing nothing. But this non-action allows for the “action” of the spokes: it allows then to turn around in a regular and harmonious way. The stillness of the hub is the “source” for the orderly movement of the spokes. The circular rotation requires a pivot. Without such an unmoving central point, the movement of the spokes will immediately lose its balance. The wheel will no longer run smoothly and soon it will bend or break. The perfect circular movement is anchored in the stillness of the hub. The continuous stability of the wheel is entirely dependent on the hub’s being incessantly still. 
Many spokes are united in one hub. No smatter how many spokes a wheel actually has, it will only have one hub. The spokes are necessarily a multitude, the hub is necessarily single. In the strict sense, a geometric middle within a circle is always one. The hub is not only numerically one – it is also the place uniting the spokes. All the spokes are “united in one hub.” In this way, the hub provides for unity of the wheel by being single. 
Rotation is the heart of Ba Gua. Some practitioners liken the whole body to the universe, in which every part is constantly rotating in relation to all the other parts, like wheels within wheels. The whole body relaxes and turns so that each part can store and release power by winding and unwinding. Cheng Ting Hua said that when the practitioner rotates his body like a small screw and hub, the body rotates, but there is no axis internally. It means that in walking the circle, “one rotates as if the body turns along a nine thousand-kilo globe.”  If the turning is smooth, it is like “calm flowing water; that one doesn’t actually seem flowing, one doesn’t seem to move.”
The hub represents the inner unity of the wheel. It unites the spokes and is the pivot for all “contradictory” movement. In addition to the inner unity of the wheel there is the greater unity of the moving wheel as a whole and as a process. Within the wheel , the hub is some sort of “leader”; it is the decisive and core element. 
In Ba Gua Zhang, the hidden gentle force and strong firm force interchange constantly, storing and releasing power like a endlessly turning wheel. The contradictory, oppositional movements of wrapping, twisting, drilling and overturning, which are continually present in every movement, all emanate from the pivot, from the hub. Therefore, the postures and the palms all originate from the constant turning of the body, much like the spokes emanate from the hub.
Moeller takes the analogy further by describing the spokes of the wheels:
The spokes are in a certain sense the opposite of the hub. While the hub is in the center, the spokes are in the periphery; while the hub is empty, the spokes are full; while the hub is still, the spokes are in motion; and while the hub is single, the spokes are many. The spokes represent the realm of the visible and the realm of activity. They are the image for everything that has a definite and “positive” place – although these positions are constantly changing. When the wheel is turning, the spokes occupy every position, top and bottom, left and right. They run through the whole “positive” space of the wheel. Through their constant turning, they mark the space and borders of activity. This space of activity or motion is itself a space of opposition: top and bottom, and left and right. The space created by the turning of the spokes is constructed by the exchanging of opposite positions. Within this process of rotation the spoke on top changes position with the spoke on the bottom and so forth. The whole periphery performs a constant, harmonious alternation, a perfectly regular course of changeovers.
The order of the spokes within a wheel is based on the relation of opposite positions: top and bottom, left and right, and so forth. This opposition in the realm of the spokes is, however, only “relative,” and not “absolute.” First, the relationship of the spokes to each other is not antagonistic, but complimentary, they match. Secondly, the opposition is momentary: the positions constantly change. The complimentary opposition of the spokes within a running wheel resembles the natural cycle of time. In the course of the changes from day to night, from month to month and from one season to the next, complimentary segments follow each other in a cyclic sequence.
In Ba Gua Zhang, we are told that circle walking relies on the continuous interchange Yin and Yang. While walking, the circle is divided into eight directions, and the body, intent and qi unify into one:
Circle walking relies upon Yin and Yang,
Five elements and six harmonies.
Seven stars and eight steps form nine palaces,
One distinguishes firmness and gentleness internally and
externally in the three levels of the body
All unites into one energy on a supporting foundation,
Four aspects and four angles stabilize eight directions.
The body follows the kou bu steps,
Release force in the four tips and magnify energy by turning and walking.
Walking the circle is separated in eight directions,
In body movement pay attention to intent and Qi.
Be supple in turning and changing, do not stop to hold postures,
Yield infinite power high, low, far and near.
The waist movement coordinates the four tips,
The eyes watch eight directions.
(from the Circle Walking Song of Ba Gua Zhang) 
Walking the circle is to walk through the eight directions, which emanate from the center like the spokes of a wheel. These each have a name and resonate with the Eight Gua: Qian, Kan, Gen, Zhen, Xun, Li, Kun and Dui. The body revolves while inside there is stillness, the stillness at the center of the rotation.
Sun Lu-Tang further elaborates on this:
On the circle, Qian is in the south and Kun is in the North. Li is in the east and Kan is in the west. Yang rises on the left and Yin descends on the right. When Yin comes in contact with Yang the One Yin is created in Heaven above. When Yang comes into contact Yin, One Yang is created in Earth below. Yang creates Yin and Yin creates Yang. Each is the Circle’s true center. The circle is the shape of Heaven. Heaven is unified above and below. Above it is Yang. Below it is Yin. The shape of the One Qi moving is Yin and Yang. The Tai Ji symbol is the symbol of Yin and Yang combined. Then Taiji is the One Qi.
Ba Gua Quan is the left turning and the right turning. Both hips are like a picture that has no corners inside. The eyes gaze at the index finger tip of the front hand which is opposite the center of the circle. This is the appearance. The turning is not fixed like the Taiji One Qi. Therefore Ba Gua Quan, in this picture, corresponds to Heaven. In Heaven is completed the form. Therefore the empty center of the Ba Gua Quan picture seeks the dark mystery. It is also compared to a mysterious gateway.
Sun’s choice of words is interesting. The term, “dark mystery”, or the phrase “darker than any mystery”, is often used to describe the Dao. These terms and the “mysterious gateway” are referred to in the first chapter of the Dao De Jing, where Lao Zi essentially tells us that the “Way” cannot be grasped by ordinary senses and cannot be described or understood by words. It is “darker than any mystery.” Similarly the hub or axis of the turning in Ba Gua can only be experienced, as it is a manifestation of the “dark mystery.” 
 Daoism Explained: From the Dream of the Butterfly to the Fishnet Allegory, by Hans-Georg Moeller, Chicago and La Salle Illinois: Open Court Publishing, 2006, p. 27.
 Ba Gua Zhang by Jiang Rong-jiao (Jiang Rong Qiao; Chang Rong Chiao). Translated by Huang Guo-Qi; Edited by Tom Bisio.
 部构 yao bu “waist part” or 腰带 yao dai “waist girdle” refers to the area that wraps from the small of the back around the waist like a girdle. The key focal point being the small of the back.
 Ba Gua Zhang by Jiang Rong-Jiao.
 The Way and Its Power, A Study of the Tao Te Ching and its Place in Chinese Thought, by Arthur Waley. New York: Grove Press Inc., 1958, p. 155.
 Daoism Explained, by Hans-Georg Moeller, p. 28.
 Ibid, p.29.
 Ibid, p.29.
 The Real Explanation of Boxing Meaning by Sun Fu-Quan (Sun Lu-Tang).
 Classical Baguazhang volume XIII: Sun Style Baguazhang (Ba Gua Quan Xie and Bagua Jian Xue) by Sun Lutang. Translated by Joseph Crandall, Smiling Tiger Martial Arts: Pinole, CA. 2002, p. 22.
 Daoism Explained, by Hans-Georg Moeller, p. 33.
 Ibid, pp.31-33.
 Ibid, p. 32.
 Liang Zhen Pu Eight Diagram Palm, Li Zi Ming, compiled and edited by Vincent Black. pp. High View Publications: Pacific Grove, CA, 1993, pp. 35-37.
 Classical Baguazhang, Volume XIII: Sun Style Baguazhang (Ba Gua Quan Xie and Bagua Jian Xue) by Sun Lutang. Translated by Joseph Crandall, Smiling Tiger Martial Arts: Pinole, CA. 2002, p. 16.