Preprocessing a static finite elements simulation for a transtibial prosthesis using cae tools

This document focuses on the approach of a computerized motion analysis to structure the preprocessing of a static finite element simulation, used in the design of a transtibial prosthesis for a Paralympic cyclist, and thus evidence the behavior of the proposed prosthesis model under the charges present during competition.

Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=12 ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

PREPROCESSING A STATIC FINITE

ELEMENTS SIMULATION FOR A TRANSTIBIAL PROSTHESIS USING CAE

TOOLS Juan Sebastián Lasprilla, Hoffman F Ramírez, Mauricio Mauledoux

DAVINCI Research Group, Mechatronics Engineering Department,

Military Nueva Granada University, Bogota, Colombia

ABSTRACT

People with physical-motor disabilities who make use of prosthetic devices, have the need for these prostheses to be designed to fulfill the tasks of their daily lives, regardless of the level of physical activity they maintain This particular problem can

be approached from the mechanical design of the prostheses, having as a critical stage, the validation of the components designed for its operation Therefore, to improve the designs, a stage of determining the forces that the device must withstand

is necessary For this reason, a stage where all the forces affecting the prosthesis are determined is necessary For this work, simulations can be used in specialized programs and finite element analysis methods to detail the behavior of virtual models under specific conditions critical to the design This document focuses on the approach of a computerized motion analysis to structure the preprocessing of a static finite element simulation, used in the design of a transtibial prosthesis for a Paralympic cyclist, and thus evidence the behavior of the proposed prosthesis model under the charges present during competition

Keywords: Mechanical design, finite element analysis, CAD modeling, transtibial

prosthesis, motion analysis

Cite this Article: Juan Sebastián Lasprilla, Hoffman F Ramírez, Mauricio

Mauledoux, Preprocessing a Static Finite Elements Simulation for a Transtibial

Prosthesis Using CAE Tools International Journal of Mechanical Engineering and

Technology 10(12), 2019, pp 311-322

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=12

1 INTRODUCTION

When talking about prostheses for Paralympic athletes, it should be considered that physical activity levels are much more exhausting and intense than those of a normal person Therefore, to correctly design a transtibial type prosthesis for an Olympic athlete in a condition of disability it is necessary to carry out studies and analyses that validate these designs, with the aim not only of positively impacting the athlete's physical performance but also in minimizing physiological impacts of the use of prostheses

and the socket

Initially, it is necessary to categorize the type of socket necessary for the desired application since there are currently different ways of attaching the socket to the stump In the study [1], they show detailed uses of the different types of prosthetic sockets with the representative restrictions for certain types of activities Thus, by validating the objective of the final function of the prosthetic device, it is possible to slightly delimit the analysis process

of the forces exerted on the socket Similarly, in the study [2], it is detailed, according to the stump profile, how the forces applied on the socket should be distributed

However, these studies are based on a uniform distribution from the socket „s reaction forces, an event that shows no correlation with reality An experimental method is necessary

to determine the reaction forces that are generated on the system through instrumented sockets, which allow to experimentally measure the pressures generated between the stump and the socket when external forces are applied to the system An example of this is sockets instrumented with pressure measurement systems, such as the one used in the study [3] This socket (figure 1), is made up of 4 lines of transducer arrays, forming more than 350 measuring points in the system, which allows having a percentage of more than 90% of stump coverage

Figure 1 Instrumented socket with transducer array

This process carries expenses in terms of time and money, not only because of the repetitiveness involved in the construction of test sockets to implement them, but also, for the acquisition of sensors with the ease for being adapted to the irregular shape of the socket model and the capability of withstanding pressure measurement levels

To improve and optimize these physical prototype design and validation processes, a computational simulation can be used, such as motion analysis, which facilitates the stress distribution determination presented in a model, and thus subsequently be able to perform different independent analyzes of each element of the model [4] [5] [6] This process is detailed in the study titled [7], where they show the process of designing and simulating a socket for a transtibial amputation In this design, the maximum pressure points are determined using FEA (finite element analysis) with the objective of using compliant mechanical designs to minimize the mentioned pressure points

This type of simulation is also useful when material studies are required, since by using the simulation environments, it is possible to apply specific material properties and, therefore, determine, according to established methodologies and simulation parameters, behaviors from

different types of materials for a specific design These types of simulations can be seen in the study [8], where they are based on four simulation elements: carbon fiber, polypropylene, HDPE (High Density Polyethylene) and LDPE (Low Density Polyethylene) This process is carried out in order to determine which material has the best behavior in terms of the types of force and boundary conditions used for the definition of the simulation model

As a last resort to consider in the process of a transtibial prosthesis correct design and analysis, it is the mechanical model and free-body diagrams of the system This part determines the principles of mechanical movement for the prosthetic device, taking into account variables such as the weights of the components, forces, torques, movement angles, among others so that it is possible to determine equations that characterize the movement and can be used to determine the boundary conditions or critical times in which the system must

be exposed to maximum forces, pressures or torques that affect the integrity of the design itself In the study [9], they propose a free-body diagram for a transtibial prosthesis, considering mainly the weights of the orthopedic components, the forces, and torques generated by the characteristic movements of a lower limb (leg), to determine the equivalent forces, and the torques generated on the prosthesis joints [9] Likewise, different studies propose an analysis of free body diagrams to determine the specific behavior that describes the mechanical contact between the socket and the stump, making use of different mathematical approaches with optimization methods to minimize and delimit the scope of the variables used in the models proposed [10] [11]

In conclusion, the purpose of carrying out the necessary studies that validate the design process and analysis of the prosthetic device under certain conditions is to validate and give scientific support to the proposed design, so that it is accepted by the community and can be viable for future implementations

2 DESCRIPTION OF THE PROSTHESIS

Initially, to guarantee a proper design, it is necessary to establish a control process on some of the anthropometric and biomechanical parameters that are most important for the design

objective (Table 1)

Table 1 Anthropometric and biomechanical design parameters

Stump length

(Long transtibial amputation)

Based on the proposed anthropometric characteristics and the considerations for low-cost and modularity design, an assemble that not only complied with these parameters but was also designed under modularity components and high mechanical strength was proposed

This design is composed of eight main pieces, which have the possibility of being modifiable in terms of prosthesis height, characteristic angles of the ankle joint and the implemented foot model

The general design consists of three major sections (Figure 2) This is mainly to facilitate mechanical maintenance, assembly, and have high adaptability for different tasks and usage environments, by changing the prosthetic foot and adjusting the tibial axis length

Figure 2 Sectional side view of the final prototype

Section one (Figure 3), consists only of the socket, which is the piece that connects the affected part of the person with the prosthesis In this case, the socket is a rigid revolution structure made from Ultra High Molecular Weight Polyethylene [12] This material was chosen due to its high mechanical performance, low weight, ease of machinability and price accessibility

Figure 3 Isometric view of the socket

It should be taken into account that the socket model presented in this study is unique for

a given test subject, and in order to scale the scope of the implementation of this prototype, it

is clarified that each socket must be custom-made for each subject test

Figura 4 Isometric view of the tibial region

Section two (figure 4), is composed of five pieces that replace the tibia and the ankle This

is how the link between the socket and the prosthetic foot is formed In this mechanical assembly, an articulated mobile joint was implemented using a ball joint between two

threaded parts, in order to achieve fixed dorsiflexion and plantarflexion angles In this section,

it is also possible to vary the tibial axis length, allowing its implementation for the three different types of transtibial amputations (long, medium and short)

Section three (figure 5), is composed of two pieces that replace the foot, and due to the physical properties of the material, create a spring effect that supports and facilitates the walking cadence The material used for these two pieces is carbon steel due to its elastic mechanical properties, and due to the shape of the folds, it is possible to generate a passive feedback force when walking, allowing some mobility ease to the whole prosthesis

Figure 5 Isometric view of the prosthetic foot

For this design, the plantar flexion (figure 6, right) and dorsiflexion measurements (figure

6 left), have a maximum angle, in both cases, of approximately 15.22º This measure is mechanically controlled by the threaded adjustment between two parts on the kneecap, so that the angle described for plantar flexion and dorsiflexion is fixed for any environment

Figure 6 Characteristic measures of plantar flexion (Right) and dorsiflexion (Left)

In order to correctly execute the static finite elements simulation, it is necessary to determine the magnitude and direction of the forces involved in the movement that the cyclist applies to the system during the pedaling process; for this reason, it is necessary to perform a motion simulation in which these values can be determined

3 MOVEMENT ANALYSIS

For the movement simulation, it was necessary to generate an environment in which there was

a constant high demand level For this purpose, a velodrome was modeled (figure 7) with the characteristic measures regulated by the UCI through the sports facilities manual [ 13]

Figure 7 Isometric view of a section of a competition velodrome

The ultimate purpose of this model is to be used, together with the simplified model of a track bike, based on the actual standard dimensions and weights (figure 8), to generate a simulated environment of high mechanical stress to validate the proposed design

Figure 8 Simplified track bike model

Only three parts were used in this model: frame (# 1), plate and connecting rod (# 2), and wheel (# 3) For the reliability of the simulation, the following parameters were taken into account:

 The weight of the front wheel is incorporated into the rear wheel, along with the weight

of the sprocket and the chain

 The weight of the front axle, consisting of the handlebar and fork is added to the weight

of the frame

After defining the principles and objectives for the movement analysis, it is necessary to assemble the modeled pieces to verify that they work together without any relation or indeterminate mechanical connection problems The entire CAD design for the transtibial prosthesis, in conjunction with the simplified bicycle model, is shown in Figure 9

Figure 9 Model implemented for motion simulation

It should be clarified that despite being a simplified model and not using all the pieces involved in the movement mechanics, these models have the necessary pieces to describe the movements that are required for this study; Similarly, the implemented parts simulate the total weight, for both the human and mechanical parts of the bicycle, and the location of the mass centers of the lower axle of a cyclist

In order to show the similarity in the way of implementation of the models presented in the motion study for the validation of the transtibial prosthesis design, the comparison between the positions of the mass centers for a professional track cyclist with those of the implemented model is shown (figure 10) In this case, it is seen that the cyclist´s lower axle mass centers are congruent, but since the upper axle is not used in the proposed simulation, these weights are replaced and positioned on the waist part

Figure 10 Graphical comparison from the mass center positions for a professional cyclist and the

implemented model

To mathematically support this study and make a proper implementation of the forces exerted on the proposed system, it is necessary to arithmetically determine the relationship between the force exerted by the prosthesis user and the reaction forces between the crank-pedal set and the prosthesis

Depending on the mechanical conditions in which the prosthesis is used, different types of forces are generated within it Since the prostheses are used in such variable environments, it

is not possible to accurately determine all the components of all the forces generated in the movement, for this reason, it is necessary to parameterize the global forces that affect the prosthetic apparatus performance With the approach from this premise, it is clarified that the forces with the greatest impact on the prostheses, according to the study of manufacturing processes from KAFO type prostheses [14], are:

1 Tensile force on the traction phase

2 Pressure force with patient´s vertical load

3 Forces on the traction phase (balancing phase)

4 Bending Moment is anteroposterior and antero-medial

5 Rotation Moment, especially on joints

6 Torque around the vertical axis

For representative visualization purposes, the force types that are executed on the prosthesis user´s axial plane are six (Figure 11)

Figure 11 Graphical representation of the forces exerted on a prosthesis

For this study´s purpose, focused on preprocessing the static finite element simulation, only the tensile force on the traction phase is considered

4 LOADING VECTOR

To determine the magnitude and direction of a single force, we can make use of (1), established and shown in [15], which expresses, according to angle and speed parameters, the total force exerted by the cyclist on the bicycle´s crank

( (( ) ))

( ) (1) The mentioned article presents the dynamic behavior analysis for the reaction forces on the connecting rod, starting from the study on the movement angles of a track bike in a velodrome Obtaining, as a result, values that show that the maximum peak of effective force exerted by a cyclist on the connecting rod is approximately 803.6 N per leg Similarly, they show the results of the maximum peaks of effective forces experienced by two specific parts

of a transtibial prosthesis (Table 2)

Table 2 Results of magnitude and direction of the effective forces on a transtibial prosthesis

Newton

To verify this result, the method proposed in [16] is used, where it is shown that depending on the type of prosthesis categorized by the OTTO BOCK® system, a weight correlation factor is generated, which relates the person´s weight with the force exerted on a particular activity, therefore, for this project, which is categorized as K4, due to its level of mobility, the weight correlation factor is between 1.1 and 1.4; To simplify the model, the average of these values will be used, from which a value of 1.25 times the bodyweight is obtained These values are expressed in Table 3:

Table 3 Force parameters for simulation

Making a comparison between the two models, to compare the variation between the force values and assuming the real maximum effective force value as 803.6 N, a value of 0.8% error exists

5 RESULTS

On this stage, to perform the movement simulation, it was necessary to delimit the movement that the ensemble could have, so contact relationships were applied between the track and the bicycle´s wheel; also, to achieve the bike´s movement on the velodrome, additional trajectories that relate the ensemble to the track were implemented, so that the movement that was made is congruent with the one described by the cyclists in a track cycling competition The final ensemble´s arrangement used to perform the motion simulation can be observed for the validation of the design of the transtibial prosthesis (Figure 12)

To measure the force exerted by the cyclist during a certain trajectory, it is necessary to make two analyzes: an inverse kinematic analysis, in which the femur´s displacement angular measurements from its rotation point (the hip) are made This analysis is based on a previously defined trajectory and is the one that the bicycle will follow during a certain time How the bicycle follows this trajectory can be easily obtained from measurements made on cyclists during real trials or practices For experimental purposes, a random trajectory and time is set, only to verify the ability of the analysis to effectively measure the femur‟s angle and rotation speed from to the hip rotation point

Figure 12 Final set for movement simulation of the transtibial prosthesis design

According to the implemented study parameters, for the movement analysis, the following traces (figure 13) of displacement and angular velocity´s leg from the hip rotation point were obtained

Figure 13 Leg´s Displacement and angular velocity from the hip rotation point

Once the reverse kinematic analysis was done, the direct kinematic analysis was carried out In this analysis, all possible factors allowed by the simulation (friction and gravity) are taken into account The results of the inverse kinematics are loaded in this new analysis, by using a rotational motor applied directly on the femur and using as rotation axis, the same that the femur has with the hip Applying materials, masses, and inertia to the different parts of the set, the simulation is carried out, and it is verified that the bicycle effectively, in the virtual environment, follows the trajectory as it had been defined for the inverse kinematic analysis The applied motor‟s torque used to achieve the ensemble‟s movement can be measured, obtaining figure 14

The above graph shows the motor‟s torque that activates the cyclist's femur over the simulation time The graph shows that some values are negative, this is due to the motor´s orientation, and that during the simulation, the values vary from negative to positive This is because the bicycle‟s movement on the velodrome is not constant, it accelerates at first, and subsequently slows down The maximum torque values generated during the simulation can also be determined from the graph, and with the respective measurement of the femur´s angle from the calf, the load is applied as a force applied to the part that fits with the socket of the prosthesis (figure 15)

Figure 14 Torque exerted by a cyclist femur to generate movement