Decoding the Contribution of Shoulder and Elbow Mechanics to Barbell Kinematics and the Sticking Region in Bench and Overhead Press Exercises: A Link-Chain Model with Single- and Two-Joint Muscles

Objectives: This study investigates the biomechanics of the bench press and overhead press exercises by modeling the trunk and upper limbs as a kinematic chain of rigid links connected by revolute joints and actuated by single- and two-joint muscles, with motion constrained by the barbell. The aims were to (i) assess the different contributions of shoulder and elbow torques during lifting, (ii) identify the parameters influencing joint loads, (iii) explain the origin of the sticking region, and (iv) validate the model against experimental barbell kinematics. Methods: Equations of motion and joint reaction forces were derived analytically in closed form. Dynamic simulations produced vertical barbell velocity profiles under various conditions. A waveform similarity analysis was used to compare simulated profiles with experimental data from maximal bench press trials. Results: The sticking region occurred when shoulder torque dropped below a critical threshold, resulting in a local velocity minimum. Adding elbow torque reduced this dip and shifted the velocity minimum from 38 cm to 23 cm above the chest, although it prolonged the time needed to overcome it. Static analysis revealed that grip width and barbell constraint had a greater effect on shaping the sticking region than muscle architecture parameters. Elbow extensors contributed minimally during early lift phases but became dominant near full extension. Model predictions showed high similarity to experimental data in the pre-sticking (SI = 0.962, p = 0.028) and sticking (SI = 0.949, p = 0.014) phases, with reduced, non-significant similarity post-sticking (SI = 0.881, p > 0.05) due to the assumption of constant torques. Conclusions: The model offers biomechanical insight into how joint torques and barbell constraints shape movement. The findings support training strategies that target shoulder strength early in the lift and elbow strength near lockout to minimize sticking and improve performance.