Studies in the Mechanics of the Tetrapod Skeleton

I. GENERAL INTRODUCTION Although the individual form of the muscles and bones of a tetrapod body is often known with great accuracy, few, if any, comprehensive attempts have been made to regard the whole system as a complete functional unit. The present studies constitute an attempt to consider the whole vertebrate body as a single mechanical system in which the function of the individual muscles and bones is co-ordinated with those of all, or many of, the others. From a mechanical point of view, the statics of a tetrapod standing at rest present a complicated three-dimensional system, whilst the animal in motion presents even more difficult dynamical problems. Nevertheless, the animal must conform to mechanical principles common to all animate or inanimate systems. For example, although a horse at rest can, by muscular effort, control the degree of support given by an individual leg towards the support of the body, yet the resultant of the thrusts of all four legs must always represent a force equal in magnitude but opposite in direction to the weight of the animal. In the following pages an attempt is made to reduce the living system to its simplest terms and to consider how far the co-ordination of its various parts can be deduced by purely mechanical arguments. As the general type of analysis is probably unfamiliar to some biologists, it may be convenient, at the outset, to make a comparison between the highly complicated living system with a relatively simple inanimate analogue, and to emphasize the main points in which they resemble or differ from each other. For this purpose, a four-legged table with overhung ends forms a convenient startingpoint. Fig. 1 represents a table resting on four legs, each of which is attached to the top (ABCD) by a universal joint (E, F, G, H). Within each leg is an elastic spring (L, M, N, O), and the centre of gravity of the table is assumed to be equally distant from the centre of each leg. So long as the springs within all the legs are identical in respect of length and elastic properties, each leg will carry one-quarter of the weight of the table and there will be no tendency for the table to rotate about either of the diagonals AC or BD. If, however, the temper of one spring (L) be reduced, the latter will shorten and the table will tip towards that leg; in so doing, the spring (N) under the diagonally opposite leg will extend and the thrust exerted by it against the table will be reduced. Equilibrium will be re-establisned when the thrusts of the two springs L and N are again equal but less than before the change occurred in spring L. If, however, the thrusts of L and N are reduced, those of M and O must be increased. So long as the legs are vertical and equally distant from the centre of gravity of the table, the general conditions of equilibrium are that the thrust of any one leg must be equal to that of the diagonal leg, and the sum of the thrusts of two ipsilateral legs must be equal to half the weight of the table. Precisely the same arguments apply to the legs of a horse when they are acting as vertical struts (see p. 91), the extensor muscles of the limb being functionally equivalent to the springs within the legs of the table. Further, if in either a horse or table the legs are not vertical and the feet not equally distant from the centre of gravity of the system, it is still possible to define the thrust made by each leg towards the support of the body, by means of equations which are identical in the two cases (§ II).