There is no single position of mechanical advantage or a single definition. (A ‘monkey’ is an example of a position of mechanical advantage, see Monkey.) Generally, it can be described as a position of balance, which will aid lengthening and widening and the giving of directions.
The term originates from technology where the mechanical advantage is the advantage gained by the use of a tool or similar in transmitting force; e.g. the use of lever.
The ﬁrst appearance of the term ‘mechanical advantage’ (though not preﬁxed by ‘position of’) appears in a 1907 article by Alexander. Here it is used to indicate the advantageous use of the thorax which makes for efﬁcient breathing:
At the outset, let me point out that respiratory education or respiratory re-education will not prove successful unless the mind of the pupil is thoroughly imbued with the true principles which apply to atmospheric pressure, the equilibrium of the body, the centre of gravity, and to positions of mechanical advantage where the alternate expansions and contractions of the thorax are concerned.
Alexander refers to positions of mechanical advantage in his early writings and in MSI. There is only one mention in CCC, and none in UoS and UCL. The following statements from MSI provide some of the essentials of a position of mechanical advantage:
a position of mechanical advantage will secure that the parts of the muscular system intended by nature to be constantly more or less tensed, together with a relaxation of those parts intended by nature to be more or less relaxed.
if the pupil apprehends the position of mechanical advantage, and uses the new correct guiding sensations or orders, he will be able to bring about the proper use of his muscular mechanism with perfect ease.
the true uses of the muscular mechanism, i.e., the means of placing the body in a position of mechanical advantage, must be studied, . . .
the position of mechanical advantage may or may not be a normal position, i.e. it may be an abnormal position for the pupil . . .
the position of mechanical advantage is the position which gives the teacher the opportunity to bring about quickly with his own hands a co-ordinated condition in the subject and the opportunity to establish the mental and physical guiding principles.
The only known positions of mechanical advantage used by Alexander are: standing, ‘monkey’, lunge, leaning back in a chair, leaning forward in a chair, squatting (for squatting see Barlow).
Leaning against the back of a chair
Alexander gives the following example of a position of mechanical advantage used in his teaching.
A simple, practical example of what is meant by obtaining the position of mechanical advantage may be given. Let the subject sit as far back in a chair as possible. The teacher, having decided upon the orders necessary for the elongation of the spine, the freedom of the neck (i.e. requisite natural laxness), and other conditions desirable for the particular case in hand, will then ask the pupil to rehearse those orders mentally, at the same time that he himself renders assistance by the skilful use of his hands. Then, holding with one hand one or two books against the inner back of the chair, he will rely upon the pupil mentally rehearsing the orders necessary to maintain and improve the conditions present, while he, with the other hand placed upon the pupil’s shoulder, causes the body gradually to incline backwards until its weight is taken by the back of the chair. The shoulder-blades will, of course, be resting against the books. The position thus secured is one of a number which I employ and which for want of a better name I refer to as a position of ‘mechanical advantage’.
Since the term lacks clarity and disappeared from Alexander’s writings early on, it is rarely used today. Instead teachers today refer to his teaching procedures (see Classical Procedures), especially to ‘monkey’. Hence there are almost no discussion of ‘positions of mechanical advantage’ in the literature since Alexander’s early writings. The few exceptions include Frank Pierce Jones and Walter Carrington. 
Alexander was not satisfied with the term either:
My reader may justly ask, then, why I use them. Readers of Man’s Supreme Inheritance will remember that when I used the phrase ‘position of mechanical advantage,’ I pointed out that I did so because a better one was not forthcoming, and I mentioned then that I had called to my aid a number of scientiﬁc and literary friends.
See also Monkey, Lunge.