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Quadrupedal Mechanics - Anatomy & Physiology (view source)
Revision as of 10:02, 25 April 2013
, 10:02, 25 April 2013→2 Elasticity: external forces and stored energy
::The work done in deforming the material is Fd, the product of force and distance. This is the area under the curve made during the application of the force (blue). The work done by the elastic restoring force is the area under the curve made during the removal of the deforming force (red hatching). In this example, these two areas are not the same. The difference in area is the energy lost as heat. The resilience is the red hatched area as a percentage of the blue area.
::The work done in deforming the material is Fd, the product of force and distance. This is the area under the curve made during the application of the force (blue). The work done by the elastic restoring force is the area under the curve made during the removal of the deforming force (red hatching). In this example, these two areas are not the same. The difference in area is the energy lost as heat. The resilience is the red hatched area as a percentage of the blue area.
[[File:QMSection2.5.png|thumb|'''Fig. 2.5 Hopping kangaroo''']]
[[File:QMSection2.5.png|thumb|'''Fig. 2.5 A hopping kangaroo''']]
::Fig. 2.5 A hopping kangaroo
::Fig. 2.5 A hopping kangaroo
::Compare the angle of the hock joint when the limb bears weight, and when not weight-bearing. The passive tissues supporting this joint store energy in A and release it in B. At hopping speeds of between 10 and 35 km/h, kangaroo locomotion is remarkably efficient. This is due to the almost 100% resilience of the elastic support of the hock joint.
::Compare the angle of the hock joint when the limb bears weight, and when not weight-bearing. The passive tissues supporting this joint store energy in A and release it in B. At hopping speeds of between 10 and 35 km/h, kangaroo locomotion is remarkably efficient. This is due to the almost 100% resilience of the elastic support of the hock joint.
'''What makes materials elastic?'''
[[File:QMSection2.6.png|thumb|Fig. 2.6 Elastin in the nuchal ligament of a sheep]]
::'''Fig. 2.6 Elastin in the nuchal ligament of a sheep'''
::a. Loose connective tissues surrounding the ligament.
::b. Elastin fibres, stained with Verhoeff’s hematoxylin, in the ligament.
The elasticity of materials comes about in several different ways:
:''Molecular elasticity:'' Stress may produce a molecular change. The keratinous structures of mammals (hair, wool, hooves and horns) are elastic because the keratin molecule changes from a tight helix to an extended form when it is stretched.
:''Crystalline elasticity:'' Stress on a material such as steel results in changes in distances between atoms. A large stress produces only a small distortion. The elasticity is therefore low.
:''Rubbery elasticity:'' The elasticity of the most elastic materials results from the cross-linking of long, flexible, convoluted polymers. In rubber, these cross-links are formed by sulphur during the process of vulcanisation. Distortion of a block of rubber results in a distortion of each molecule, which is restored when the stress is removed. Cross-linking is necessary to prevent the molecules from slipping past each other. Elasticity of rubber is lost when there are too many cross-links or when the temperature is too low.
Several biological materials show rubbery elasticity. In vertebrates, elastin is present in thin strands in loose connective tissue, providing the extreme elasticity of such tissues as the dermis. It predominates in the middle coat of the wall of large arteries and in the nuchal ligament of herbivores (Figs. 2.6, 2.7). It is not fibrous, but consists of thin homogeneous strands. Its elasticity is similar to that of lightly vulcanised rubber.
[[File:QMSection2.7.png|thumb|Fig 2.7 A grazing cow]]
::'''Fig.2.7 A grazing cow.'''
::Herbivores have heavy heads held at the end of a long neck. As they flex their neck to graze, the nuchal ligament is strained by 50%. The elastic energy stored is released as the head is raised, so that little muscular effort is needed. A spring loaded garage door borrows this principle from the cow.
''Fibrous elasticity:'' Polymeric molecules derive their elasticity by being arranged partly in ordered patterns to form crystalline regions, and partly with a random arrangement in amorphous regions. Examples of elastic materials of this kind include synthetic textiles like nylon and polyester, and natural ones like silk. Collagen, the main component of the passive musculoskeletal system, also has polymeric molecules, with the crystalline part composed of aligned and cross-linked molecules, appearing as fibrils (Figs. 2.8, 2.9). The molecules are aligned in a specific direction to form fibrils.
[[File:QMSection2.8.png|thumb|Fig. 2.8 Molecular structure of collagen in a tendon, diagrammatic]]
'''The significance of collagen'''
:The fibrous elastomer collagen is by far the most predominant passive supporting substance in vertebrates. 20% of the protein of a mouse is collagen. Tendon, ligament and dermis are almost pure collagen, and it is a major constituent of bone and fibrocartilage. Few tissues lack it entirely. Collagen quality is of commercial interest because it determines the tenderness and appropriate cooking methods of different muscles, at different stages of growth.
::'''Fig. 2.8 Molecular structure of collagen in a tendon, diagrammatic'''
::Tendon structure as envisaged by:
::a., protein chemistry;
::b., c., and d., X-ray diffraction;
::d., electron microscopy;
::e., light microscopy and
::f., as seen grossly in a large animal.
[[File:QMSection2.9.png|thumb|Fig. 2.9 Molecular structure of collagen in a tendon, diagrammatic ]]
::Fig. 2.9 Molecular structure of collagen in a tendon, diagrammatic
::Magnification x25,000.
::Lateral accessoriometacarpal ligament of a horse.
::• collagen fibrils, sectioned longitudinally
::• collagen fibrils sectioned transversely
::(from Deane, Massey thesis, 1991).
'''Collagen molecules, fibrils and fibres'''
:Collagen fibrils are formed when three tropocollagen molecules, each consisting of three helically arranged polypeptide chains 280 nm long, coil helically together, and align with other such "super helices". These polymeric molecules each overlap about one quarter of their length, so that an axial periodicity of 60-70 nm is visible with the electron microscope (Fig. 2.9). A collagen fibre is formed from bundles of fibrils (Fig. 2.8). Single collagen fibres are visible with the light microscope in connective tissues. They accumulate in bundles or sheets to form the gross structures ligaments, tendons and fasciae.