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A model of scale effects in mammalian quadrupedal running

Hugh M. Herr¹, Gregory T. Huang^1,* and Thomas A. McMahon^2,

¹ Harvard/MIT Division of Health Sciences and Technology, Physical Medicine and Rehabilitation, Harvard Medical School, Artificial Intelligence Laboratory, MIT, 200 Technology Square, Room 820, Cambridge, MA 02139, USA
² Division of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
Deceased

View larger version (50K): [in a new window]   Fig. 1. Model structure: (A) large horse, (B) small horse, (C) goat, (D) large dog, (E) small dog and (F) chipmunk. Joint locations, segment dimensions and mass distributions are from photographic, video and anatomical data (Muybridge, 1957; Taylor et al., 1974; Fedak et al., 1982; Alexander, 1985; Farley et al., 1993). All segments are represented as rigid bodies. Pin (rotary) joints are included on the back and neck. Each leg rotates about a pin joint at the shoulder or hip and changes length through a prismatic (telescoping) joint at the elbow or knee. Active hip and shoulder torques control the forward motion from stride to stride. Motions are restricted to the sagittal plane.

View larger version (19K): [in a new window]   Fig. 2. Mechanical and energetic properties of trotting animals at the preferred trotting speed plotted versus body mass on logarithmic scales. Open circles are mean experimental values, and filled circles are model predictions. Least-squares regression lines are fitted to the model results (see text for equations). (A) Vertical stiffness, kvert. (B) Limb angle from the vertical at touchdown. (C) Peak vertical ground-reaction force. (D) Metabolic cost of transport. Animal data are adapted with permission from Farley et al. (1993) (A-C) and from Taylor et al. (1970, 1982) (D). Data include measurements from horses, goats, dogs and rats.

View larger version (18K): [in a new window]   Fig. 3. Mechanical properties of galloping animals at the trot—gallop transition speed plotted versus body mass on logarithmic scales. Open circles are experimental values, and filled circles are model predictions. Least-squares regression lines are fitted to the model results (see text for equations). (A) Stride frequency. (B) Hindlimb excursion angle, the maximum angle swept by a line drawn from the head of the femur to the toe. (C) Forelimb duty factor, the percentage of a stride period in which a forelimb contacts the ground, and peak vertical force per body weight. Animal data are adapted with permission from (A) Heglund et al. (1974), (B) McMahon (1975) and (C) McMahon (1977). Data were taken from horses, dogs, squirrels, rats and mice.