A comparative collision-based analysis of human gait

Abstract

This study compares human walking and running, and places them within the context of other mammalian gaits. We use a collision-based approach to analyse the fundamental dynamics of the centre of mass (CoM) according to three angles derived from the instantaneous force and velocity vectors. These dimensionless angles permit comparisons across gait, species and size. The collision angle Φ, which is equivalent to the dimensionless mechanical cost of transport CoTmech, is found to be three times greater during running than walking of humans. This threefold difference is consistent with previous studies of walking versus trotting of quadrupeds, albeit tends to be greater in the gaits of humans and hopping bipeds than in quadrupeds. Plotting the collision angle Φ together with the angles of the CoM force vector Θ and velocity vector Λ results in the functional grouping of bipedal and quadrupedal gaits according to their CoM dynamics-walking, galloping and ambling are distinguished as separate gaits that employ collision reduction, whereas trotting, running and hopping employ little collision reduction and represent more of a continuum that is influenced by dimensionless speed. Comparable with quadrupedal mammals, collision fraction (the ratio of actual to potential collision) is 0.51 during walking and 0.89 during running, indicating substantial collision reduction during walking, but not running, of humans.

Keywords: biomechanics; bipedal; locomotion; mammal; mechanical cost.

Figure 1.

Parameters of a collision-based analysis are determined by the force vector F and velocity vector V of the CoM in each instance of ground contact. Force angle θ is defined as the deviation of F from a vertical axis, velocity angle λ, as the deviation of V from an axis in the direction of travel and collision angle ϕ is defined as the deviation from an orthogonal relationship of F and V. A compliant SLIP results in a full collision wherein F and V deviate in an opposite sense from their respective axes. At the other extreme, F and V may be kept perpendicular throughout stance, representing an idealized zero-collision case. Equations for collision-based parameters are provided in table 1.

Figure 2.

A schematic of collision-based CoM dynamics with respect to higher-level models of locomotion. Collision-based parameters of biological or robotic legged systems can verify conceptual and explicit models of locomotion. A collision-based perspective can also inform simplified mechanistic or conceptual models.

Figure 3.

Results of human walking and running analyses comparing normal (1g) and hypergravity (1.35g) conditions. (a) Force angle Θ (black), velocity angle Λ (light grey) and collision angle Φ (dark grey). The scale from 0 to 0.28 radians represents 0–16°. (b) Collision fraction is the ratio of actual to potential collision and is represented by solid areas of the pie charts. (c) Dimensionless stride length (left axis; black bars) and duty factor (right axis; light grey bars). Error bars indicate 95% CIs in all panels. Significant differences (p < 0.05) are found between gaits in all parameters except force angle Θ. Significant differences between 1 and 1.35g (p < 0.05) are found in force angle Θ (a), as well as dimensionless stride length and duty factor (c).

Figure 4.

Collision-based analysis of human locomotion together with gaits of other mammals from the literature. (a) Θ, Λ and Φ as a fraction of their sum plotted on ternary axes. (b) Mechanical cost of transport CoT_mech or Φ as a function of dimensionless speed . Filled circles indicate bipedal gaits and filled squares indicate quadrupedal gaits. Colour of data symbols indicates collision fractions with red indicating a collision fraction of one and violet a collision fraction of zero (for spectrum of intermediate colours, see colour scale at right). Collision-based analyses of non-human mammals are for goats and dogs [19], lemurs [17], monkeys [18], kangaroo rats (K-rat) and wallabies [33].