Four degree-of-freedom lumped parameter model of the foot-ankle system exposed to vertical vibration from 10 to 60 Hz with varying centre of pressure conditions

Modelling the foot-ankle system (FAS) while exposed to foot-transmitted vibration (FTV) is essential for designing inhibition methods to prevent the effects of vibration-induced whitefoot. K-means analysis was conducted on a data set containing vibration transmissibility from the floor to 24 anatomical locations on the right foot of 21 participants. The K-means analysis found three locations to be sufficient for summarising the FTV response. A three segment, four degrees-of-freedom lumped parameter model of the FAS was designed to model the transmissibility response at three locations when exposed to vertical vibration from 10 to 60 Hz. Reasonable results were found at the ankle, midfoot, and toes in the natural standing position (mean-squared error (e) ¼ 0.471, 0.089, 0.047) and forward centre of pressure (COP) (e ¼ 0.539, 0.058, 0.057). However, when the COP is backward, the model does not sufficiently capture the transmissibility response at the ankle (e ¼ 1.09, 0.219, 0.039). Practitioner summary The vibration transmissibility response of the foot-ankle system (FAS) was modelled with varying centre of pressure (COP) locations. Modelling the FAS using three transmissibility locations and two foot segments (rearfoot and forefoot) demonstrated reasonable results in a natural standing and forward COP position to test future intervention strategies. Abbreviations: COP: centre of pressure; DOF: degrees-of-freedom; FAS: foot-ankle system; FTV: foot-transmitted vibration; HAVS: hand-arm vibration syndrome; LDV: laser Doppler vibrometer; LP: lumped-parameter; VWT: vibration-induced white-toes; WBV: whole-body vibration