To simulate the contraction dynamics of a Hill-type muscle, we need to model two main features: the force—length and force—velocity relationships. The force—length (FL) part models the function of both active and passive forces in terms of the muscle length, and the force—velocity (FV) part describes how the contraction force varies with respect to the muscle’s contraction velocity.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{CE}={F}_{max}\,\ast \,{a}_{t}\,\ast \,{F}_{L}\,\ast \,{F}_{V}$$\end{document}FCE=Fmax⁎at⁎FL⁎FV8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{L}=exp(-{|\frac{{L}_{ce}^{\beta }-1}{\omega }|}^{\rho })$$\end{document}FL=exp(−|Lceβ−1ω|ρ)9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${F}_{V}=(\begin{array}{ll}({V}_{max}-{V}_{ce})/[{V}_{max}+({c}_{V0}+{c}_{V1}{L}_{ce}){V}_{ce}], & {\rm{if}}\,{V}_{ce}\le 0\\ \left[{b}_{V}-({a}_{V0}+{a}_{V1}{L}_{ce}+{a}_{V2}{L}_{ce}^{2}){V}_{ce}\right]/({b}_{V}+{V}_{ce}), & {\rm{if}}\,{V}_{ce}\, > \,0\end{array},$$\end{document}FV=((Vmax−Vce)/[Vmax+(cV0+cV1Lce)Vce],ifVce≤0[bV−(aV0+aV1Lce+aV2Lce2)Vce]/(bV+Vce),ifVce>0,where at is the activation signal from Equation 6. The variables Lce, Vce are the length and contraction velocity of the muscle. To simplify the model, we set Lce = 1 in the equation of Fv, which means that the change of muscle length is ignored when computing the force-velocity relationship. This assumption simplifies the model parameters as: cV = cV0 + cV1, aV = aV0 + aV1 + aV2. The parameters Ω = (Fmax, β, ρ, ω, Vmax, cV, bV, aV) are muscle-specific and determine the overall performance of a muscle.