Balance of forces at the hip shown by models made from wood
and wire – frontal plane

Martin Moeser und Lothar Meinel

1. Basis of consideration: cable truss

The lightweight design is based on the triangle because of its structural stability. The elements of the triangle are stressed axially. The compression elements are subjected to buckling. Therefore they must be executed stiff (rigid). They are called rafters ore rods. The tension force can be transmitted by slack elements (ropes, cables). Then, we speak of a cable truss (Figure 1).

Triangle as the basis of lightweight construction
Figure 1:
Triangle as the basis of lightweight construction; wood-wire-model under load.
The compression elements consist of rods, the tension element is formed by a rope.

2. The two-leg stance (internal bracing)

2.1 Rhombus as base model

In the two-leg stance, the rigid elements are formed by the bones of the legs (tibia and femur) and the pelvis (neck of femur, iliac bone, sacrum). The center of gravity is located in the center of the sacrum (base of sacrum). On the floor, the legs meet at one point. Therefore, a rhombus is formed. This rhombus is balancing. As already mentioned, the both femur necks are components of the pelvis. The base of such a neck forms a pivot point (node).
The body weight acts as force F on the base of sacrum. In its further course, the force is transmitted through the pelvis and the legs to the feet and then on the ground and vice versa.
By inserting a "rope", which connects the basis of the both femur necks, two triangles are created. The supporting structure is treated as weightless.
The feet were brought together in one point, because of the oblique arrangement of the legs. As a result, horizontal forces are created which must be compensated.
A schematic representation of forces is given in Figure 2a. When a straight line is drawn from the base of femur neck to the feet, then the length of the legs are correctly reproduced. One can also prolong the femoral bones until they meet the line of outer load (dashed line), then the angle ratio (CCD angle) is properly shown. In the latter case, the pelvis-rope, herein referred to as pelvic floor, is stressed a little higher. The amount of the respective forces is registered, they were calculated graphically.
The corresponding wood-wire model is shown in Figure 2b.
The lines of forces were sketched into a skeleton model (Figure 2c).

The two-leg stance as coupling of two triangles
Figure 2: Two-leg stance represented as the coupling of two triangles; a cable connects the basis of both necks
a) schematic force diagram, force values registered; the both femoral bones are dotted, load F as body weight (G)
b) wood-wire model under load (coarse scaled)
c) lines of forces drawn into an upright skeleton, S = center of gravity

2.2 Hip joint introduced

The nod of the hip joint is placed into the joint gap. The hip joint is supported by the ischium. Of major importance are the rotators, especially the quadratus femoris muscle. Attached at basis of the femur neck, they pull to the ischium, where they produce a bending moment. To compensate the bending moment, the ischium is hold by the sacrotuberous ligament, wich leads to the center of the sacrum.
In the horizontal plane, the pelvis is held together by the sacrospinous ligament. Divided into two branches, it leads horizontally from the hip joint to the lower part of the sacrum and then further to the opposite hip joint. The rotators provide a load-dependent modulation of the stresses in the femur neck. As a result bending is avoided there.
The calculated forces scheme is given in Figure 3a. The wood-wire model is shown in Figure 3b. The lines of forces are drawn into an X-ray image (Figure 3c).

Hip joint introduced
Figure 3: Hip joint introduced; ischium as a support
a) schematic diagram of the forces. Both femurs were prolonged to the line of outer load.
The rotators respectively connect the basis of the femur neck with the ischium.
b) Wood-wire model: muscles represented by red wire, ligaments by blue wirec)
c) The lines of forces are drawn into an X-ray image (female, about 50 years old)

2.3 Sacroiliac joint introduced

The sacrum is a broad bone. Its horizontal branches are referred to as "pars lateralis" or "ala of sacrum". The surfaces of the sacroiliac joint are relatively large.
As in the case of the hip joint, the nod of the sacroiliac joint is placed into the joint space.
From the hip joint the force rises steeply and follows strictly the body of ilium until it reaches the sacroiliac joint. Then the force runs horizontally through the ala of sacrum to the center of the sacrum (base of sacrum). From the sacroiliac joint, the sacrum is held in place by ligaments which pull to the lower part of the sacrum. The sacroiliac ligaments are strongly fanned. They hold the sacrum is in a loop
The force diagram is given in Figure 4a. The wood-wire model is shown in Figure 4b.
The lines of forces are again shown in a radiograph (Figure 4c).

Figure 4: Introduction of sacroiliac joint
a) schematic force diagram; ligaments form a loop, in which the sacrum is suspended.
b) Wood-wire model: red wire as muscles, blue wire as ligaments
c) representation of the forces on the radiograph

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