**Author details**

334 Viscoelasticity – From Theory to Biological Applications

**Iteration Foot** 

**Table 5.** Five sets of the optimised parameters

**Standard deviation** 

**4. Discussion** 

**5. Conclusion** 

**Mass (kg)** 

Second, the optimised segmental masses are validated by repeating the same optimization process for further four times. The five sets of the optimised parameters emanating from five different runs of the GA routines are shown in Table 5. The results of the optimised anthropometric inertia parameters from different simulation runs exhibit acceptable repeatability with only a slight difference between each other with small standard deviation.

> **Moment of inertia (** <sup>2</sup> *Nm* **)**

**0.0016 0.01 0.00006 0.00036 0.00083** 

1 0.95 3.5 0.35823 0.0350 0.220 2 0.948 3.51 0.35830 0.0352 0.221 3 0.951 3.49 0.35828 0.0355 0.220 4 0.949 3.51 0.35815 0.0351 0.222 5 0.952 3.49 0.35820 0.0345 0.221

**Mean 0.95 3.5 0.3582 0.0351 0.2208** 

In this approach the passive properties have been divided into two parts; First, mathematical model is used to represent the combination of knee joint inertial ( *M*<sup>i</sup> ) and gravitational ( *M*<sup>g</sup> ) moments. Second, fuzzy model is applied to represent the combination of the elastic moment ( *M*<sup>s</sup> ) and the viscous moment ( *M*<sup>d</sup> ) as viscoelastic moment of the knee joint. Mathematical model has been used because of the availability of this model and accessibility to estimate anthropometric inertia parameters. This could be an easy method to estimate these parameters without go through complicated clinical experiment since these parameters vary for each subject. The system such as viscoelasticity could be difficult to model due to complexity and nonlinerity. Therefore, fuzzy model is used to eliminate the development of complex mathematical model and helps to simplify the modelling task. These passive properties model then need to be integrated with active properties of the knee joint model to have a complete model of the knee joint. Finally, these models can be utilized

A new approach of estimation of the anthropometric inertia parameters and model of the passive viscoelasticity of the knee joint has been presented. Fuzzy model has been used to model the passive viscoelasticity and could be an effective tool for the modeling of uncertain nonlinear systems without represents using complicated mathematical model. The

as platform for the simulation purpose of the control system development.

**Position of COM of Foot (m)** 

**Position of COM of Shank (m)** 

Therefore, it can be concluded that the optimised masses obtained are valid.

**Shank Mass (kg)** 

B.S. K. K. Ibrahim, M.S. Huq, M.O. Tokhi and S.C. Gharooni *Department of Automatic Control and System Engineering, University of Sheffield, United Kingdom* 
