The Bone as a Compression Member in a Cable Tensioning Device: The Example of the Hip
Martin Möser und Werner Hein
(Wolff's Law and Connective Tissue Regulation, Editor Günter Regling, Walter de Gruyter, Berlin New York 1992, p. 81-92)
Flexion or Compression?
There is general agreement that nature is a master of lightweight construction. This does not apply, however, to the bones of vertebrates, if we assume that they are subject to flexion, which is characteristic of heavyweight construction. If we look at a match, we can see that its loading capacity is much greater along the axis than at right angles to it. The fractures and sprains of daily life also show us that flexion is not beneficial to the human extremities.
The entire support apparatus is rather to be understood as a cable tensioning device (rope latticing); i. e., the bones form a system of rods that are stressed purely on their axes, and only under pressure (compressed). This skeleton is braced by ligaments and muscles which act as tensile elements. Compression rods fail by buckling. The moment of buckling is equally great in all directions, which is why tubes are preferred.
In general, the basic geometric form of lattice constructions is the triangle, as, in contrast to a quadrangle, it is "unshiftable". Technical examples of cable tensioning devices are high-tension masts, tents, spoked wheels, suspension and tension cable bridges, and many forms of cranes. In addition to lightness, this principle for the vertebrate support apparatus has the following advantages:
- A high degree of mobility
- A high degree of flexibility
- A good ability to cushion blows
- Uniform loading of articular surfaces
The alignment of a rod depends on how it is braced. Thus we may assume that the interplay of muscle forces is individually predisposed, and that the bone accommodates itself to this in its development. In this way the growing bone is able to compensate for a rachitic deformation or an axial defect caused by a fracture.
Even Pauwels [1,2], the best-known advocate of the flexion theory, recognized that the development symphysis must place itself perpendicular to the incident force, as it would otherwise glide off. The assumption that bones bend results from the belief that the pelvis is supported by the two smaller gluteal muscles, the m. gluteus medius and the m. gluteus minimus, when a person stands on one leg. This is contradicted, however, by the experience that they are not perceptible as aching muscles even after the longest march (see also ). Please also note the editor's comment at the end of the article on page 92 !
As the respective side of the pelvis indeed feels hard to the touch when one is standing on one leg, something else must be stretched. One possibility is the iliotibial tract (Maissiat's ligament), and it is easy to determine by touching that the tension is equal from the ilial crest down to the knee.
The Tower Crane Principle
If man has to lift a load very high he uses a tower crane. There are types with rigid jibs and types with movable jibs. The first type carries the counterweight on the counterjib, i. e., at the working level. With the second type (Fig. 1a), the counterweight is below, on the crane truck. A strong double cable stretches the weight jib via the counter jib ("power jib") back to the foot of the crane. Only the latter type is a true cable tensioning device, and thus the actual tower crane.
It is striking that the cables are much thinner than the compression rods (tower and jibs). The main reason is that the cables are not subject to buckling and are made of a much stronger steel. The tower and both jibs are constructed as normal latticing; the tension in this case runs via rods.
The counter jib is free of bending only when it lies in the bisector of the retaining cable. This is because the retaining cable is not attached to the counter jib, but runs over a sheave. The angle of the counter jib is set so that it forms the bisector of an angle when the weight jib is horizontal and its lever arm is at its longest. The flexion in the counter jib is transmitted to the tower because of the rigid coupling.
The tower crane would function without a counterweight if it were possible to position its base directly beneath the load. This would be difficult technically, because the load could not be lifted from the ground, and a tower crane is not able to balance. Man can do so, however, and "getting one's foot on the ground", i. e., beneath the body's center of gravity, is the first step in standing up. Using a tower crane as an example, the human system of standing can be developed as follows:
|Figure 1: The tower crane as a cable tensioning device
1a: Technical tower crane, cables stretched;
1b: balancing tower crane exemplifying the principle of the one-leg stance
Simple Tower Crane
The tibia and the femur are rigidly connected, lie in one line, and form the tower up to the femoral neck attachment (Fig. 1b). The neck, which in its extension reaches to the center of the sacrum, unites with the pelvis and represents the weight jib. The trochanter major serves as the counter jib. The weight jib is stretched back by a retaining cable that, in its entirety, we call the tractus.
The intersection of the axes of the sacrum and the iliosacral joints ought to be the exact point of load induction; in reality, the body's center of gravity lies higher, in the lumbar spine. But in this case, the spine is assumed to be erect, and it is known that a force can be shifted along a line in any direction. The lower ankle joint was selected as the point of support, because as a joint it serves for movement in the frontal plane. The induced force G' equals the reaction of the support A (G' = total weight minus standing leg = 0.8 G).
The trochanter major works as a stationary sheave ("roller mound") over which the tractus glides. On a rope pulley the resulting compressive force adjusts itself as the bisector of an angle. The amount of force is determined by the radius of the trochanter (lever arm) in proportion to the distance between the neck attachment and the center of the pelvis (weight arm). For the purpose of illustration, we have chosen a relatively large radius; this gives a ration of 1:4. Thus the tractus must carry four times, the leg bones five times the body weight G'. The system has been developed as "statically determined". The forces of individual elements can be calculated both graphically and numerically. The graphic method offers the advantage that the direction of force is clearly recognizable and errors in design can be easily found.
It should be mentioned that a static system is usually calculated on the basis of the support. Each force value is entered on the figure. To illustrate the two-leg stance it is necessary to show the pattern only around the line of external forces, to halve the numerical values, and to replace G' with G'' = 0.6 G.