Studies for a new prosthesis design for the work capacity rehabilitation.

Lovasz, Erwin-Christian ; Modler, Karl-Heinz ; Draghici, Anca 等

1. INTRODUCTION

The social investigations done for the incapacited workers showed that the psychological stress experienced by them from the pressure exercited by the family, the society, the collectivity (at organizational level) affecting the health, the wellbeing of other members of society. The developments in the field of prosthesis improve the work capacity of the employers affected by some particular occupational risks. The disabilities can affect the mobility of the upper and lower limb. For the knee joint prosthesis (Fig.1a) there are a lot of mechanical and hidraulical solutions for insurance of the movement stability. Considering the mathematical model of the biological movement, the movement force is proportional with the square of movement velocity. This dependence can be realised with a double acting hydraulic cylinder (Fig.1c) which have in parallel a drosel (Hutten, 1992). This actuator is usual used in an inverted slider-crank (Fig.1b) which has a non-linear transmission function and allows a limited swivel angle between the thigh and the leg.

In order to eliminate the disadvantages of the classical solutions which use an inverted slider-crank is recomanded to be used a geared linkage with linear displacent actuator. In the field of this type of mechanism, the relevant references (Lovasz et al., 2002; Modler et al., 2005) about studies of the kinematic and kinetostatik analysis and the dimensional synthesis of the geared linkages with linear actuators were used in the following research. The virtual optimization of the linkages and some typs of geared linkages are also, presented in (Gnasa et al., 2002).

[FIGURE 1 OMITTED]

Some geared linkages with linear displacement actuator are able to realise an approximated constant ratio (first order transmission function) for a very large swivel angle. This propriety can be used succesfull to generate an optimal movement of the active knee prosthesis.

2. SYNTHESIS OF THE GEARED LINKAGES

Through the type synthesis of the geared linkage with linear displacement actuator result 6 mechanisms structures (Lovasz et al., 2002). The geared linkages with inverted slider-crank as basic structure can be used successfull for the proposed active knee prosthesis design. This type of mechanism contain a inverted slider-crank as basic structure and a planetary gear, which had the satellite gear connect with the slider (Fig. 2).

Through the optimum synthesis will be determined the links length the geared linkages for a desired generating function. The input parameters for the optimum synthesis problem are: the desired function, the given stroke [s.sub.H] and the gear ratio [rho]. The geometrical function [chi](s) of the geared linkages is obtained in form:

[chi](s) = (1 - [rho]) x [psi](s) + [rho] x [phi](s), (1)

where [rho] = [+ or -][r.sub.3]/[r.sub.5] is the gear ratio, [phi](s) and [psi](s) are the geometrical parameters of basic linkage. The first order geometrical function will be:

[chi]'(s) = (-([s.sub.0] + s) + [rho] x [l.sub.1] sin [phi](s))/([l.sub.1][l.sub.4] sin [psi](s)). (2)

As vector of the variable will be considered x = [([[lambda].sub.2], [[lambda].sub.4]).sup.T] where nondimensional variables are:

[[lambda].sub.2] = e/[l.sub.1], [[lambda].sub.4]]] = [l.sub.4]/[l.sub.1]. (3)

The desired function for the geared linkage with linear displacement actuator will be chosen as constant, which means a constant ratio:

[[chi]'.sub.desire](s) = [[chi].sub.max]/[s.sub.max] = const. (4)

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

where [[chi].sub.max] is the maximal swivel angle of output gear and [s.sub.max] is the maximal stroke of input element.

The difference between the first geometrical function and the desired function will chose as target function, which must be minimized, in order to realize a motion with approximately constant ratio. This target function is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)

The restrictions are given as inequation, which described the start and end of the geometrical conditions:

[([[lambda].sub.4] -1).sup.2] - [[lambda].sup.2.sub.2] - [([s.sub.0]/[l.sub.1]).sup.2] < 0, -[([[lambda].sub.4] + 1).sup.2] + [[lambda].sup.2.sub.2] + [(([s.sub.0] + [s.sub.H])/[l.sub.1]).sup.2] < 0., (6)

The condition for a convenient transmition angle [mu] > [[mu].sub.min] at the start position will be used to determine the start unitary displacement [s.sub.0]/[l.sub.1] :

([s.sub.0]/[l.sub.1]) = -[[lambda].sub.4]sin [[mu].sub.min] + [square root of 1-[([[lambda].sub.2]-[[lambda].sub.4]cos [[mu].sub.min]).sup.2], (7)

For a convenient start value, the variables vector is:

[x.sup.(0)] = [([[lambda].sub.2.sup.(0)], [[lambda].sub.4.sup.(0)]).sup.T] (8)

will be given, generally, local optimum values. These values are the optimum ones for the links length.

The knee can be substituted with a joint (Fig. 3). This joint has to allowe a rotation motion with an angle of 120[degrees] (30[degrees] flexion, 90[degrees] extension). Servo hydraulic cylinder, servo-pneumatic cylinder or electrical actuator can be used as motor. The control of the motion is realized with sensors and the command is performed by a microprocessor.

The lead parameters for the optimal synthesis are the gear ratio [rho] = 0.5 and the minimal transmission angle [[mu].sub.min][degrees] = 30[degrees]. The optimal maximum unitary stroke is determined from the optimisation of the reaction force in the joint [B.sub.0] (Modler et al., 2005) as [s.sub.H]/[l.sub.1] = 0.8. One local minimum value at the synthesis optimization, for the unitary links length results from the contour line diagram is shown in Figure 4, [[lambda].sub.2] = 0 and [[lambda].sub.4] = 0.395.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

The links length are [l.sub.2] = 0 mm and [l.sub.4] = 59.25 mm for the value frame length of [l.sub.1] = 150 mm. This mechanism allows a maximum rotation angle of [[chi].sub.max][degrees] [congruent to] 270[degrees] for a start position [s.sub.0] = 90.75 mm and a stroke [s.sub.H] = 118.5mm. The rotations angle will be limited to 120[degrees] symmetrical in respect to the flat point (Figure 5). The new displacements [s.sub.1] and [s.sub.2] are determined with the conditions:

[chi]([s.sub.2])[degrees] - [chi]([s.sub.1])[degrees] = 120[degrees] [chi]'([s.sub.2]) = [chi]'([s.sub.1]) (9)

The new displacements are [s.sub.1]=23.23 mm and [s.sub.2]= 100 mm, that means, for the knee-joint, the start position and the stroke are [s.sub.0]=113.98mm and [s.sub.H]=76.77 mm, respectively.

3. CONCLUSION

This new active prosthesis with geared linkages with linear displacement actuator will quicklier improves the work capacity of the employers affected by some particular occupational risks that can cause diseases on their knees. The correlation between the synthesis and kinetostatic optimisation method allow the obtaining of an optimal links length for the geared linkages taking into account the constructive constrains.

In the future we shall build a prosthesis prototype that will be tested and validated in the real environment.

4 REFERENCES

Gnasa, U., Modler, K.-H., Richter, E.-R. (2002). Kinematische und dynamische Kennwerte fur Gelenkarmmechanismen (Cinematical and dynamical characteristic values of the joint mechanisms). Vol. 47. Internationales Kolloquium, pp. 318-319, ISSN 0943-7207, 23-26 Sept., TU Ilmenau

Hutten, H. (1991). Biomedizinische Technik, Biomedical Technic, ISBN 3-540-52538-6, Springer, Graz

Lovasz, E.-C., Modler, K.-H., Hollman, C. (2002). Auslegung der Raderkoppelgetriebe mit linearem Antrieb (Synthesis of geared linkages with linear displacement actuator). Vol. 47. Internationales Kolloquium, pp. 316-317, ISSN 0943-7207, 23-26 Sept., TU Ilmenau

Modler, K.-H., Hollmann C., Lovasz, E.-C., Perju, D. (2005). Geared Linkages with Linear Displacement Actuator Used as Function Generating Mechanisms, Proc. of the 11-th World Congress on TMM, pp. 1254-1259 ISBN 7-111-14073-7/th 1438 Tian Jin, 01.04-05.04.2004, China Press