Scaling of rotational inertia of primate mandibles

The relative importance of pendulum mechanics and muscle mechanics in chewing dynamics has implications for understanding the optimality criteria driving the evolution of primate feeding systems. The Spring Model (Ross et al., 2009b), which modeled the primate chewing system as a forced mass-spring system, predicted that chew cycle time would increase faster than was actually observed. We hypothesized that if mandibular momentum plays an important role in chewing dynamics, more accurate estimates of the rotational inertia of the mandible would improve the accuracy with which the Spring Model predicts the scaling of primate chew cycle period. However, if mass-related momentum effects are of negligible importance in the scaling of primate chew cycle period, this hypothesis would be falsified. We also predicted that greater "robusticity" of anthropoid mandibles compared with prosimians would be associated with higher moments of inertia. From computed tomography scans, we estimated the scaling of the moment of inertia (I_j) of the mandibles of thirty-one species of primates, including 22 anthropoid and nine prosimian species, separating I_j into the moment about a transverse axis through the center of mass (I_xx) and the moment of the center of mass about plausible axes of rotation. We found that across primates I_j increases with positive allometry relative to jaw length, primarily due to positive allometry of jaw mass and I_xx, and that anthropoid mandibles have greater rotational inertia compared with prosimian mandibles of similar length. Positive allometry of I_j of primate mandibles actually lowers the predictive ability of the Spring Model, suggesting that scaling of primate chew cycle period, and chewing dynamics in general, are more strongly influenced by factors other than scaling of inertial properties of the mandible, such as the dynamic properties of the jaw muscles and neural control. Differences in cycle period scaling between chewing and locomotion systems reinforce the suggestion that displacement and force control are more important in the design of feeding systems than energetics and speed.