Biomechanical evaluation of posterior deltoid exercises and kinematic trajectory modeling

Purpose: This study aimed to quantitatively evaluate posterior deltoid activation during common strengthening exercises and establish a mathematical trajectory model to guide the control systems of upper-limb rehabilitation robots. Methods: Kinematic data were collected from ten healthy males performing the Bent-over Dumbbell Lateral Raise (BDLR), Standing Face Pull (SFP), and Bent-over Dumbbell Row (BDR). Inverse Kinematics and Static Optimization were performed using OpenSim musculoskeletal modeling to estimate muscle forces. The optimal exercise was identified through statistical comparison of Root Mean Square muscle forces. A continuous trajectory model using cubic polynomial fitting was derived from the biomechanically optimal movement to enable future robotic path planning. Results: The one-way ANOVA indicated a significant main effect of exercise type on muscle activation ( p < 0.001). Tukey's HSD post-hoc tests revealed that both BDLR (58.591 N) and SFP (58.183 N) elicited comparable high activation levels with no statistically significant difference ( p > 0.05). However, both exercises produced significantly higher muscle forces compared to BDR (47.911 N, p < 0.001). Although statistically equivalent to SFP, BDLR was selected as the target for trajectory modeling due to its kinematic suitability for end-effector based robotic rehabilitation. Conclusions: Bent-over dumbbell lateral raise demonstrates high efficacy for posterior deltoid recruitment. The kinematic trajectory model derived from optimal biomechanics provides a mathematically precise movement template for programming intelligent rehabilitation robots and training devices, enabling standardized execution of evidence-based strengthening protocols.