The Dynamics of Quadrupedal Walking

Abstract

The cat was used as a representative quadruped for a study of the action of the locomotor apparatus in walking. In the analysis the body was considered as being made up of eleven parts behaving in such a fashion that they could be considered as rigid bodies. The weight of each part was determined, the position of its centre of gravity and also its moment of inertia. Moving pictures were taken of the cat walking over a specially constructed platform which recorded the pressure exerted by each foot during the stride. The photographs recorded the position of the various parts of the body at successive instants. These records were analysed in terms of displacement, velocity and acceleration of the centre of gravity of the body as a whole, and also of its parts. A comparison of vertical forces acting on single limbs of the cat during the walk shows that the reactions are greater on the forelimbs. This is not only due to the location of the centre of gravity nearer the forelimbs, but also is the result of a thrust produced at the forelimb which is largely responsible for an upward acceleration of the centre of mass of the body. Horizontal forces produced at the forefeet also tend to be greater than those at the hind. When horizontal impulse over the whole step is considered, it is shown that the forelimbs produce more retarding action, while the hindlimbs contribute more forwarding impulse to the body. The arrangement of steps is such that horizontal reactions on fore- and hindlimbs are antagonistic, thus damping fluctuations in horizontal acceleration and velocity of the centre of gravity with a probable saving in energy expenditure. The kinetic energy of the body, derived from the data of the mass and velocity of separate parts, maintains an average level but undergoes cyclical changes during the stride. A possible transfer into gravitational potential energy can account for only a part of these kinetic energy changes which are thought to involve muscle action. An analysis of the relationship between muscle forces about the joints and forces of reaction which co-operate to produce the recorded movement of an individual segment of the limbs allows the calculation of the resultant muscle torque acting on that segment. This provided actual measurements for the total muscle torque about each of the joints of the limbs at any instant. Correlation of these torques with the action of definite muscle groups indicates roughly the manner in which these muscles function in quadrupedal walking.