Theoretical Hill-Type Muscle and Stability: Numerical Model and Application

Figure 3

(a) Ten 𝐹(𝑡) and 𝑣(𝑡) plots for quick-release contraction experiments using 19 different external forces were recorded. Based on those 𝐹(𝑡) and 𝑣(𝑡) plots the force-velocity curve (crosses) was calculated. In direct comparison with the biological experiments (rat gastrocnemius muscle [20]) and the predictions from theory, the artificial muscle data shows a good match for both, with 𝜅_𝑣=0. A hyperbola fit of the artificial muscle data results in 𝑅²=.97 [13, 15]. (b) The strength of the presented approach is shown by a comparison of 𝐹(𝑣) curves calculated for different biological muscle parameters. The respective 𝐹-𝑣 curve can be plotted by just taking 𝐴 and 𝐵 values from experiments and calculating the parameters 𝑅_PDE and (1−𝜅_𝑣)𝐷_PDE. The latter two parameters are necessary to build a technical muscle of that respective type.

(a)

(b)