Quantifying Energy-Efficient Evolution in Cursorial Avian Archosaurs Through Comparative Torque-Based Hindlimb Modeling

Understanding the way evolution drives adaptations that “optimize” energy-efficiency in cursorial species provides instrumental insights into both biomechanical and bio-inspired engineering fields. This study quantitatively models the cursorial evolution of energy-efficient locomotion in bird-line archosaurs by comparing the hindlimb mechanics of Deinonychus antirrhopus (extinct theropod) and Struthio camelus (modern ostrich). A Python-based two-dimensional framework was constructed to evaluate static torque and dynamic stride simulations across joint angles and skeletal lengths. Joint torque and quadriceps force (Fquad) were computed using vector-based external moment equations, nonlinear passive stiffness (k1 and k3), and normalized body-weight scaling. Sensitivity analyses were conducted on center-of-mass position, patellar tendon moment arm, and knee rest angle to assess model robustness. Results demonstrated that S. camelus exhibited a broader region of minimized Fquad and smoother torque fluctuations (which are indicative of a more “optimized” energy-efficient, extended posture), whereas D. antirrhopus required a greater muscular effort due to its intrinsic crouched posture. Across both static and dynamic conditions, a greater vertical limb orientation consistently reduced the magnitude of Fquad, confirming that distal limb elongation and posture evolution—key characteristics of cursorial evolution—enhanced mechanical efficiency. This study provides quantitative evidence that avian cursorial evolution can be mapped as an optimization of locomotor efficiency, offering a quantitative framework for translating evolutionary principles into energy-efficient robotic and prosthetic innovation.