A Mechanical model for flexible exercise bars to study the influence of the initial position of the bar on lumbar discs and muscles forces

A single-degree-of-freedom model is considered for flexible exercise bars based on the lumped-element approach. By considering the side segment of a flexible bar as a cantilever beam with an equivalent mass at the free end, its free-vibration response, as well as the forced response under the excitation of the grip, are expressed parametrically. Experiments are performed on a particular flexible bar (FLEXI_BAR) in order to obtain numerical values for quantifying the model´s parameters. The model is also computationally simulated to study the response of the flexible bar to various excitations. The results are imported into a multi-segment musculoskeletal software (AnyBody), where the effect of different initial hand positions on the lumbar disc and back muscle forces is investigated (including Longissimus, Iliocostalis, and Transversus) during up-down exercises. The results show that all intervertebral discs and muscles forces are more sensitive to the horizontal position of the bar as compared to its vertical position.