Inverse dynamics solution of redundantly actuated parallel robots (RAPRs) requires redundancy resolution methods. In this paper, the Lagrange’s equations of the second kind are used to derive governing equations of a chewing RAPR. Jacobian analysis of the RAPR is presented. As redundancy resolutions, two different optimization cost functions corresponding to specific neuromuscular objectives, which are minimization of effort of the muscles of mastication and temporomandibular joints (TMJs) loads, are used to find the RAPR’s optimized actuation torque distributions. The actuation torques under the influence of experimentally determined dynamic chewing forces on molar teeth reproduced from a separate chewing experiment are calculated for realistic in vitro simulation of typical human chewing. These actuation torques are applied to the RAPR with a distributed-computed-torque proportional-derivative control scheme, allowing the RAPR’s mandible to follow a human subject’s chewing trajectory. TMJs loads are measured by force sensors, which are comparable with the computed loads from theoretical formulation. The TMJs loads for the two optimization cost functions are measured while the RAPR is chewing 3 g of peanuts on its left molars. Maximum and mean of the recorded loads on the left TMJ were higher in both cases. Moreover, the maximum and mean of the recorded loads on both TMJs were smaller for the cost function minimizing the TMJs loads. These results demonstrate validity of the model, suggesting the RAPR as a potential TMJ loads measurement tool to study the chewing characteristics of patients suffering from pain in TMJs.