## 3 Simulating Design Modification
#### Active Functional Joint  
For the actuated element, a damping element is included in the simulation and is defined over the translational joint, parallel to the spring, previously defined in the mechanical link; see Figure 7. The element is inactive at the start of the cycle and activated at mid-stance (0.3 s). It is then turned off shortly before the end of the cycle, at 0.56 s (93% of stance), allowing for the spring energy to be released. The resulting rotational stiffness curves for four values of damping coefficients for the active element are shown in Figure 6, compared to the FE simulation of the original prosthetic foot and the simulation of the compliant model with no active element. The damping coefficients are set to 25, 50, 100, and 300 N s/mm. The rotational stiffness approaches the original rigid link model as the damping coefficient is increased. Rotational stiffness evaluated at maximum moment in dorsiflexion increases up to 51% when applying 300 Ns/mm damping compared to the compliant setup (from 4.0 to 6.1 Nm/\({}^{\circ}\)). In Figure 6, the curves for actuated damping are cut off at peak ankle angle to clarify the plot, excluding the return curve showing the hysteresis due to damping. The energy dissipation is shown and quantified in more detail in Figure 8.  
To track the effect of the energy dissipation in the actuated element, the energy and work is calculated for model components. Figure 8 shows the stored and dissipated energy in the model for the simulation of the actuated damping element for three damping coefficients. The lowest damping coefficient (25 Ns/mm) is disregarded, as it induces the least change in stiffness. The plot  
Figure 6: Design modification—Ankle moment vs. ankle angle results from the FE model. Comparison between original foot simulation (light grey) and resulting curves for the modified designs; compliant mechanical link (dark gray) where a new spring-loaded joint is introduced and actuated damping with four different damping coefficients (dashed black x 4). Damping element is activated at mid-stance at 0.3 s.  
Figure 7: Schematic representation of the linear spring and active damping element over the translational joint defined in the FE model. shows the recoverable energy and damping energy for the three cases. The recoverable energy is the combined strain energy from the strain in the CF blades and the spring energy from the spring element defined over the new joint. The strain in the CF blades increases with higher damping coefficients. The difference between the combined strain energy curves is primarily the higher spring energy, as a result of increased displacement of spring element in the transient joint for lower damping coefficients. The damping energy from the actuated damping model rises at mid-stance, as the element is activated, showing the total dissipated energy at the end of the cycle. Dissipated energy for the cycle increases when increasing the damping coefficient from 50 to 100 Ns/mm but decreases when damping coefficient is further increased to 300 Ns/mm. This confirms a maximum dissipation for the given system and boundary conditions at a damping coefficient between 100 and 300 Ns/mm. The dissipated energy reduces the strain energy available for foot propulsion in late stance phase, decreasing the efficiency of the foot as an energy returning spring system. The sum of the strain energy and damping dissipation equals the work done on the system at the boundaries. As the simulations are investigated under constant displacement conditions, the dissipated energy adds to the boundary work rather than decrease the recoverable strain energy. The efficiency can be represented by a ratio between recoverable energy and work at the boundaries. This ratio between peak values at roughly 80% of the stance phase show that efficiency is in line with the absolute value of dissipated energy, or 77.6%, 75.6%, and 79.6% for 50, 100, and 300 Ns/mm damping, respectively.