## 2 Review of Model Construction and Parameter Determination
### Environmental Constraints  
Constrained Interactions with External Surfaces  
The simplest method for modeling interactions between body segments and external surfaces such as the ground or sports equipment has been a hinge joint, enabling rotational but not translational movement [134]. However, this method cannot facilitate the nonzero initial velocity of an impact with an external surface. While a hinge joint may be appropriate for a stationary foot-ground contact or hand-held object, alternative solutions are required for more complex interactions involving translation between segment and external surface.  
The most common solution to represent interactions with external surfaces in forward-dynamics simulation models has been to generate ground reaction forces via viscoelastic springs at a finite number of locations. This approach has been used to model specific elastic structures, including the heel pad [69], foot-tumble track interface [8], and hand-high bar interface [15], as well as general foot-shoe-ground interfaces [10; 13; 66]. The constraint complexity has ranged from damped linear springs [8] to highly nonlinear equations [135], and from less than three contact points [35; 66] to as many as 66 during heel-toe running [135]. To ensure the horizontal ground reaction force decays to zero at the same time as the vertical force, viscoelastic spring horizontal force functions have been expressed as a function of the same spring's vertical force [66].  
As an alternative to viscoelastic springs, a frictional solution also has been used to generate horizontal ground reaction forces. Within this approach, the horizontal force is defined as a function of the vertical force and the horizontal velocity of the contact point [136]. Dynamic and static friction has been combined in a model of handspring straight somersault vaulting in gymnastics, with the transition between models at a specified tangential velocity [137]. This combined method was adopted to replicate the visually observed sliding of hands across the vault surface prior to static friction. The two-state approach was compared to more complex pseudo-Coulomb friction, reporting similar results as well as faster simulation and optimization times.  
Since it is not always feasible to measure the viscoelastic or frictional coefficients for each point of contact with an external surface, the parameters are often determined using a similar process to that for wobbling mass viscoelastic parameters (with all viscoelastic parameters often determined simultaneously). The model is driven using experimentally recorded kinematics, with the unknown parameters varied within set bounds by an optimization algorithm to minimize kinetic and whole-body kinematic differences between simulated and experimental performances [66]. The magnitude of compliance permitted is restricted using penalties within the optimization process cost function. While maximum deformations of 11.5 mm and 12.7 mm have been reported experimentally at the shoe sole and human heel pad, respectively [138], simulation viscoelastic foot-ground interfaces have been allowed up to 56 mm of compliance, not only at the heel but also at the toe and metatarsophalangeal joint [60]. This increased compliance likely compensates for the lack of compliance elsewhere in the body, such as within the medial longitudinal foot arch [139; 140], joint structures [61; 62], or vertebra [141]. The effects of foot-ground compliance limits on the ability of a whole-body forward-dynamics simulation model of triple jumping to match experimentally recorded performances and ground reaction forces were previously investigated [60]. It was concluded that an unrestricted model is appropriate for simulating kinematic performance, but compliance is required elsewhere in the link system (e.g., within joint structures) to accurately calculate internal forces. This may also improve the timing of modeled elastic wave transmission [60], which is typically instantaneous in rigid systems, but not in vivo [142].