Wobbling mass influence on impact ground reaction forces: A simulation model sensitivity analysis

To gain insight into joint loadings during impacts, wobbling mass models have been used. The aim of this study was to investigate the sensitivity of a wobbling mass model, of landing from a drop, to the model's parameters. A two-dimensional wobbling mass model was developed. Three rigid linked segments designed to represent the skeleton each had a second mass attached to them, via two translational non-linear spring dampers, representing the soft tissue. Model parameters were systematically varied one at a time and the effect this had on the peak vertical ground reaction force and segment kinematics was examined. Model output showed low sensitivity to most model parameters but was sensitive to the timing of joint torque initiation. Varying the heel pad stiffness in the range of stiffness values reported in the literature had the largest influence on the peak vertical ground reaction force. The analysis indicated that the more proximal body segments had a lower influence on peak vertical ground reaction force per unit mass than the segments nearer the contact point, 340 N/kg, 157 N/kg and 24 N/kg for the shank, thigh and trunk respectively. Model simulations were relatively insensitive to variations in the properties of the connection between the wobbling masses and the skeleton. Given the proviso that estimates for the other model parameters and joint torque activation timings lie in a realistic range, then if the goal is to examine the effects of the wobbling mass on the system this insensitivity is an advantage. If precise knowledge about the motion of the wobbling mass is of interest, however, more experimental work is required to determine precisely these model parameters.