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Rapid Inversion: Running Animals and Robots Swing like a Pendulum under Ledges

Figure 4

Comparisons of animal and robot kinematics to a pendulum model.

Panel (a) compares a pendulum model without transfer of kinetic energy (KE = 0; grey bob) and with complete transfer of kinetic energy (KE>0; magenta bob) to the animal and robot trajectories as a function of time (ms) from representative position data from the COM of the cockroach (red), gecko (green), and robot (blue). The pendulum base joint represents the average position of the feet during the maneuver. The cockroach and gecko started swinging at an angle of approximately 30 degrees from the body long axis relative to the horizontal, whereas the robot initiated swinging near the horizontal relative to the body long axis (0 degree). Panel (b) shows the change in angle relative to the initial angle at the start of the swing for animals and robot compared to our two models. Panel (c) shows the speed of the animals and robot. The grey area represents the period of swinging defined as the point of slowest speed following foot engagement until all legs contacted the underside of the ledge. Panel (d) shows the position of the COM of the animals and robot during the complete rapid inversion maneuver for a representative trial. Arrows indicate the resultant velocity vectors (m s–1) at intervals of 20 ms. The black open circle indicates the region where the speed is slowest. Panel (e) shows the corresponding energy profiles. The grey area represents the same period as defined in (c) above. The dashed curve in magenta shows the total kinetic energy for the pendulum model if transfer were complete.

Figure 4