Soft Condensed Matter Seminar

Soft Condensed Matter Seminar

d’Alembert’s ‘virtual work’ shapes the cost of legged locomotion


December 3, 2019 - 3:00pm to 4:00pm


EBB Krone Building


CHOA Seminar Room 1st Floor



University of Nevada, Las Vegas

Content Images


Terrestrial animals are faced with the challenge of moving their center of mass using finite leg contacts — and this constraint is most severe in bipedal gaits, where no more than two leg contacts are possible in each stride of locomotion. Conceptual models of locomotion, such as the inverted pendulum (IP) and the spring-loaded inverted pendulum (SLIP) represent a dichotomy between rigid-legged walking and compliant running. However, a more general framework is needed to understand the compliant bipedal walking gaits used by humans and birds. d’Alembert’s principle of ‘virtual work’ can be used to determine the dynamics of locomotion by analyzing the relationship between the velocity of the center of mass and the force acting upon it. We apply this approach to show how humans are able to walk faster and more economically than other bipeds, including birds, robots, and simple models. Humans achieve a nearly constant mechanical cost of transport by increasingly rotating force and velocity vectors toward orthogonal to reduce work as walking speed increases. In contrast, ostriches reach only moderate walking speeds before transitioning to a grounded running gait that rotates force and velocity vectors away from orthogonal, as seen in a SLIP. Understanding dynamic strategies used by bipedal humans and birds can guide inquiry into structure-function relationships of fossil hominids and non-avian theropods, as well as informing the design and control of legged robots or robotic prosthetic and assistive devices.