Three-dimensional mechanical modeling of the barbell bench press exercise: Unveiling the biomechanical function of the triceps brachii

Abstract

A three-dimensional biomechanical model has been developed to understand and quantify the effect of the triceps brachii force during bench press exercises executed with different external loads, grip widths, and positions of the barbell relative to the shoulders at the beginning of the lift. The upper limbs, chest, and barbell were modeled as a closed three-dimensional articulated system. The elbow extension torque ${\tau }_{\mathrm{E}}^{\mathrm{ext}}$ developed by the triceps brachii is transferred through the links of the closed chain, yielding a shoulder transverse-flexion torque $f^{\mathrm{flex}}{\tau }_{\mathrm{E}}^{\mathrm{ext}}$ , shoulder adduction torque $f^{\mathrm{add}}{\tau }_{\mathrm{E}}^{\mathrm{ext}}$ , and shoulder internal-rotation torque $f^{\mathrm{ir}}{\tau }_{\mathrm{E}}^{\mathrm{ext}}$ proportional to ${\tau }_{\mathrm{E}}^{\mathrm{ext}}$ . The proportionality factors $f^{\mathrm{flex}}$ , $f^{\mathrm{add}}$ , and $f^{\mathrm{ir}}$ are independent of the load and displayed a considerable change during the lift: $f^{\mathrm{flex}}$ increased from 0.5 to 2, while $f^{\mathrm{add}}$ and $f^{\mathrm{ir}}$ decreased progressively to zero, with a value at the beginning of the lift between 0.5 and 1 depending on the starting barbell position and grip width. Overall, ${\tau }_{\mathrm{E}}^{\mathrm{ext}}$ considerably decreased the demand for shoulder transverse-flexion and adduction muscle-torque, slightly increased the demand for shoulder abduction muscle-torque in the final phase of the lift, and induced a shoulder internal-rotation torque that should be equilibrated by an opposite torque developed by the shoulder external rotators. With the results of this study, sport practitioners can manage the variants and kinematics of the bench press exercise to modulate the effect of the triceps brachii force on the mechanical output during different phases of the lift and planes of movement.