Study On The Algorithm Of Multifunctional Bone External Fixator

This paper discussed the problem that parameters of bone external fixator are difficult to calculate in the practical application. Positive solution is described in detail. We used MATLAB software to make simulation experiment. The innovation lies the development idea of using inverse position to verify the accuracy of positive solution. Forward displacement analysis was mainly developed using analytical method, which has many advantages, such as small dependence to the inverse solution and the higher precision. With further software development, we will have the algorithms; research model and interface program connected and form high precision smart compliance multifunctional bone external fixator products, which will greatly enhance the overall level of bone external fixation technology and clinical application treatment.


Introduction
In order to increase the level of clinical application of the bone external fixator, this title discuss the problem of the solution in calculating parameters in the background of related software of bone external fixator which has self-property right.
Bone external fixator uses the Taylor structure in practical application.It has six flexible studdles that connected to the stationary hoop.And it can rotate freely in the joint.When adjusting the length of the studdle, the relative location of the two hoops changes.This Taylor structure can regard as Stewart platform [1][2].Therefore, this study can regard as the inverse solution and positive solution of the Stewart platform [3][4][5].Fig. 1 shows the application of Stewart platform in femur correction.).we can get some relationship:   [S S S S S S ] T .
[x y z] T is the location vector of the upper platform; [x y z] T is the attitude angle vector of the upper platform;

Positive solution algorithm
When knows the six inputs, we just use the analytical method to solve.Here we establish the upper platform's coordinate system: O XYZ and establish the lower platforms coordinate system: O XYZ .They have the relationship: > @ ' = X T X P In the eq.( 3), T is the direction cosine matrix of the upper; P is the position vector of the upper's center in the fixed-coordinate system.
With the spatial geometric relationship of the parallel mechanism, when know the sizes, we can solve the coordinate value of each hinge point of the moving platform in the O XYZ system.Then the vector of the driver's length in the fixed-coordinate system is: ( )

. . i 4
The equation of the inverse solution of the parallel mechanism is as follows: Solve the equations with the optimization theory.Its objective function is composed by least square principle.
It is:

Summary
At the present stage, the technology of bone fixing in the external has been the important part in the field of bone's cure.This study is working on solving the problem that the parameters of bone external fixator are difficult to calculate in the practical application.
In the study of the Stewart platform, the analysis of positive solution is the basement of its application.The paper study mainly study the forward displacement analysis used analytical method that with many advantages, such as programming faster, calculate easier, higher precision, especially the initial value calculatio-n is more easier to get.We can get the pose of the upper platform through inputting the length of six bars.By this way we can make the bones rest orate gradually.And this method supply a sufficient way about the application of positive solution.

Fig 1 .0
Fig 1.The application of Taylor

Fig 2 .
Fig 2.The define of the coordinate.

Fig 3 .
Fig 3.The joint angle of the upper.

Fig 4 . 2 pr
Fig 4.The joint angle of the lower.
S S S S ] T is the six studdles.Till then, the mathematical model of the parallel structure is done.

Table 1 .
Experimental data