Article Figures & Tables
Figures
- 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.
- Table 1.
Key parameters of the model
Trotting Galloping Mass (kg) Leg length (m) Forelimb stiffness (kN m-1) Hindlimb stiffness (kN m-1) Speed (m s-1) Forelimb target speed (rad m s-1) Hindlimb target speed (rad m s-1) Neck stiffness (kN m rad-1) Back stiffness (kN m rad-1) Speed (m s-1) Forelimb target speed (rad m s-1) Hindlimb target speed (rad m s-1) Neck stiffness (kN m rad-1) Back stiffness (kN m rad-1) Chipmunk 0.115 0.048 0.097 0.077 1.2 0.9 1.1 0.001 0.002 1.8 1.5 1.9 0.001 0.002 Dog 1 5.09 0.20 1.9 1.2 1.9 1.5 1.8 0.03 0.013 2.8 2.5 3.1 0.005 0.025 Dog 2 23.9 0.50 2.9 1.9 2.9 2.4 3.2 0.15 0.01 4.0 3.5 4.5 0.20 0.10 Goat 25.2 0.48 4.9 2.7 2.8 2.3 3.1 0.19 0.015 3.2 2.8 3.6 0.20 0.10 Horse 1 134 0.75 18 9.1 2.7 2.3 3.0 1.0 1.7 5.2 4.3 6.1 1.0 1.7 Horse 2 676 1.5 37 22 3.9 3.2 4.6 11.0 8.0 5.8 4.8 6.7 9.0 17 -
Masses and leg lengths are based on published data (Fedak et al., 1982; Farley et al., 1993).
-
Comparisons among species are made at physiologically similar running speeds (Alexander, 1988; Heglund and Taylor, 1988).
-
The basic control methods are invariant with size. Mechanical and control parameters are constrained to satisfy smooth, periodic running dynamics and biologically realistic leg stiffness. The parameters listed determine the dynamics of each ground-contact phase and are critical to the constraints.
-
The values of limb-joint stiffnesses are used for both trotting and galloping, whereas back and neck stiffnesses are gait-specific.
-
Limb target speeds are the desired tangential velocities of the feet (relative to the hip and shoulder) during stance.
-
- 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.
- 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.
Article navigation
Related articles
Cited by...
More in this TOC section
Similar articles
Other journals from The Company of Biologists
Meet the Editors at SICB Virtual 2021
Reserve your place to join some of the journal editors, including Editor-in-Chief Craig Franklin, at our Meet the Editor session on 17 February at 2pm (EST). Don’t forget to view our SICB Subject Collection, featuring relevant JEB papers relating to some of the symposia sessions.
2020 at The Company of Biologists
Despite 2020's challenges, we were able to bring a number of long-term projects and new ventures to fruition. As we enter a new year, join us as we reflect on the triumphs of the last 12 months.
Critical temperature window sends migratory black-headed buntings on their travels
The spring rise in temperature at black-headed bunting overwintering sites is essential for triggering the physical changes that they undergo before embarking on their spring migration – read more.
Developmental and reproductive physiology of small mammals at high altitude
Cayleih Robertson and Kathryn Wilsterman focus on high-altitude populations of the North American deer mouse in their review of the challenges and evolutionary innovations of pregnant and nursing small mammals at high altitude.
Read & Publish participation extends worldwide
“Being able to publish Open Access articles free of charge means that my article gets maximum exposure and has maximum impact, and that all my peers can read it regardless of the agreements that their universities have with publishers.”
Professor Roi Holzman (Tel Aviv University) shares his experience of publishing Open Access as part of our growing Read & Publish initiative. We now have over 60 institutions in 12 countries taking part – find out more and view our full list of participating institutions.