# Numerical Measurement of a Virtual Model for the Knee Prosthesis Geometry
###### Abstract  
The human knee joint usually suffers progressive deterioration with time. The conventional cure of this issue is to replace it with an alternate knee by applying the prosthesis implant. The reason is that the process causes the abrasion of the different materials rather than just sliding or rolling. This study aims to develop the numerical measurement of the knee prosthesis's geometry, which fulfils the mechanical requirements of the human knee. The MSC.ADAMS programme was applied to demonstrate the movement of the human knee joint in terms of rotation and flexion. The changes between the condyles of the developed multibody of the prosthesis related to the flexion angle ranging from 20-120\({}^{\circ}\) were investigated and presented. The boundary conditions were determined, and simulations performed using the ADAM's programme. An average value of 0.7 was reached for the slip ration, with the maximum getting up to 0.79. An angle between 110-120\({}^{\circ}\) for the flexion angle was obtained. It can be said that the application of the multibody model saves time as there is no involvement of the tibia and the femur as required for the knee prosthesis. More importantly, as the application of the test machine is omitted in our process, our model's approximations to a human knee are carried out directly. Without cost, several measurements for the knee prosthesis could be made and repaired. The study results provide the necessary insight for future tests regarding the movement of the knee joint. m odelling; knee joint; rotation; flexion; kinematics; MSC ADAMS +
Footnote †: journal: Applied Sciences  
11 February 2021  
18 March 2021  
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**C.O. The test machine for measuring the prosthesis by [PERSON], 2019, was created by the Biomechanical Research Group of Szent Istvan University. With this machine, they made many different sizes of the prosthesis by using the 3D model of knee prosthesis. The developed prosthesis model was produced by the CNC milling technology [12]. The test machine is multipurpose, making it ideal for evaluating the knee prostheses. Its suitability for different types of loads is also significant. Unfortunately, in using the method of machine milling with 3D printing, designing and developing the knee prosthesis is time-consuming, and a high cost is incurred. Since it is a try and error method, and there is no predefined procedure, a significant quantity of knee prosthesis model material will be lost with these measurements [13; 14]. [PERSON] et al. used the 3D computational model in the MSC.ADAMS software to examine the forces that connect the surfaces of the femur, tibia, and the patella. They applied the equilibrium equations by defining the forces relating to the femur, tibia, and the patella. In the end, hey obtained the force functions as inputs for the isometric motions. However, the internal forces connecting the surfaces as a function for flexion were not investigated [15; 16; 17]. The application of the MSC.ADAMS software for our study made use of the linear or non-linear ordinary differential equations simultaneously with the non-linear differential algebraic equations. To find a solution with these equations, an initial value is determined from which the final trajectory would be determined [15]. Thus, the appropriateness of using the ADAMS programme to design the knee prosthesis as a faster, more efficient and accurate procedure without having to go through the several testings attempts to arrive at the appropriate design as done in the procedure by [12]. This study aims to develop the numerical measurement of the knee prosthesis geometry by applying the MSC.ADAMS program. The forces that relate to the femur, tibia, and the patella would be investigated. The 3D CAD printing procedure will be applied to create the initial knee prosthesis, and then the ADAM software used to model and obtain the final product.