# Modelling of force interaction in the stump-socket of the prosthetic limb of the human Övrigt konferensbidrag, 2002

At present time development of mathematical models for calculation of a force field in the "stump-reception socket" system of leg prosthesis of a person becomes a more and more actual direction in the field of biomechanics and prosthetics. Usage of these models alongside with possibilities of modern computer systems allows operatively, in real time, to calculate and estimate force loading on a stump, purposefully to select parameters of a socket with the purpose of improving its comfort and functionality. The locomotion of the person is modelled by a spatial system of absolute rigid bodies. A surface of a socket of prosthesis is approximated to isosceles trapezoids. An influence of a stump on a socket is changed by a force field {Fi}. It is supposed, that the forces operating within the limits of one trapezoid, are peer among themselves, orthogonal planes of the given trapezoid and are directed outside. A resultant vector of supporting responses of a plane of walking and a point of its application are considered to be given (known from experiments). For a regularization of statically acritical problem the quadratic functional constructed on a hypothesis about uniform distribution of pressure of a socket on a stump is used: Ф=∑Fi2→min. For a solution of the formulated problem standard methods of constraint optimization were used. Initial data for modelling were: geometry of prosthesis, weight of units of prosthesis, magnitude and a point of application of a vector of supporting responses. In result the field of the forces influencing on a stump in above-knee prosthesis and below-knee prosthesis was calculated, that has allowed estimating influence of geometrical parameters of prosthesis and a spatial position of prosthesis on character and magnitudes of the pressure originating in the stump-socket system. The obtained outcomes of mathematical modelling have the important value at development of computer systems of the automized estimation of quality of the lower extremities prosthetic management of the person.

## Författare

### Viktor Berbyuk

Chalmers, Institutionen för maskin- och fordonssystem, Mekaniska system

### Myroslav Demydyuk

National Academy of Sciences in Ukraine