The Study Of Multifunction External Fixator Based On Stewart Platform

The article develops the model of bone deformities, making 6-DOF Parallel Mechanism have widely applied to correction of deformities. The platform’s positional direct solution is the posture of the motion platform. Malformation can be measured by X-ray, based on the space coordinate transformation can find the final posture of the motion platform. Regarding the reverse solution to platform kinematics the paper gives a quick arithmetic program, six actuators to realize motion requirements. For the computer-assisted fracture reduction, we produced an application interface.


Introduction
Stewart platform is a kind of 6-DOF parallel mechanism, which has a stable and compact structure and high precision [1][2][3].It is very suitable for those work situation where the work space is limited or the work space is not large enough but the load is very heavy [4].

MATEC Web of Conferences
Because of the particularity in structure of the St ewart platform,it is needed to regulate 6 studdles si multaneously in order to accomplish the movement of single degree of freedom [5].However, if doctors make adjustment only depend on the subjective ex perience, it will be almost impossible to reach the goals, and even leading to more severe malformatio n.This paper studies on the Stewart platform Compli ance and Multifunction External Fixator correspondi ng software.

Modelling
We definite two coordinate systems,which are socle      3 Bone model experiment

Conclusion
Through the experiment of bone model, we can see the efficacy of disposable reduction is advisable.But because of some external factors such as patient's movement and so on, in order to reach the best efficacy, doctors should shoot X-ray after a period of time, remeasure distortion parameters, make a rejigger for treatment prescription, and use a method of continuous correction to minimize the deviation.

Fig. 1
Fig.1 shows the femur correction process in use of Stewart platform.Firstly, doctors install the fixation frame through operation: first, put the bone blocks where the two ends of the site to be corrected fixed in

Fig 1 .
Fig 1.Femur correction diagram coordinate {B} and upper platform {P}.The origin of the socle coordinate {B} is located in the center of the socle O b ,and the center of the upper platform O p is the origin of the upper platform coordinate {P},as shown in Fig.2.

Fig 2 .
Fig 2. The definition of space Set the moving platform {P} rotates the angle of γ along X b axis,β angle along Y b axis and α angle along Z b axis.Then we obtain the transfer matrix on coordinate {B} along three axes in use of aforesaid definition.
O O RBO O B i (2)Therefore,if we obtain the position vector [X P Y P Z P ] T and the vector of attitude angle [α β γ] T of the moving platform after orthopaedic,we can get the final lengths of six studdles by Eq.1.Firstly,put the six independent equations in Eq.2 into three groups i.e. carries out the calculation of addition or subtracting between the two equations in one group and obtain six independent equations in other forms.Expand each term in the equation and make use of relations as follows: we get six independent equations as follows ).( elimination, there are three unknown quantities X P , Y P , Z P in the six equations, besides,each direction consine has been denoted by the function of X P , Y P , Z P .Thus,if the lengths of six studdles (i.e.inputs) given,we can adopt optimization theory to solve this equation system,and obtain the initial position and pose of the upper platform.Therefore, according to the malformation parameters and the installation framework parameters which are measured by doctors,we obtain the final position vector in use of coordinate frame and get the final lengths of six studdles through Eq.2.

Fig 3 .
Fig 3. Shows the demonstration framework of malfo rmation model of left femur.We can read the length s of six studdles as follows:180mm,184mm,169mm,1 68mm,190mm,197mm.Through shooting orthophoria, we obtain the malformation parameters as follows:va lgus10°,medial displacement 12.9mm.Besides,we get other malformation parameters from the side positio n image as follows:flexion10°,anterior displacement 15mm,overlength 11mm.The installation parameters a re as follows:the center of the ring is located in 5 mm in front of the initial point,and breakpoint is 6 5mm to the proximal femur.Then put the aforeside parameters into the software,and we can obtain the treatment prescription.According to the final frame,w e adjust the lengths of six studdles as 166mm,178m m,173mm,167mm,158mm,162mm.Fig 4. shows the e fficacy of orthopaedic.

Fig 4 .
Fig 4. The framework after orthopedic

Fig 5 .
Fig 5.Before the operation