Lower Limb Prosthetic for Children

Lower Limb Prosthetic for Children Jose Gomez, Crystal Guerrero, Daniel Castellanos, Tomika Walkin, Christopher Mojica, Frank De La O, Sabri Tosunoglu Department of Mechanical and Materials Engineering Florida International University 10555 West Flagler Street Miami, Florida 33174 jgome099@fiu.edu, cguer071@fiu.edu, dcast139@fiu.edu, twalk011@fiu.edu, cmoji002@fiu.edu, fdela031@fiu.edu, tosun@fiu.edu ABSTRACT This paper highlights considerations and ideas for the specific design and manufacturing of an affordable and adjustable prosthetic which can simulate growth for child users, between the ages of 6 to 16 years, with lower limb deficiencies. Keywords: Prosthetic, lower limb prosthetic, adjustable prosthetic system for children. 1. INTRODUCTION All over the world, there exist men, women and children who are living without one or more limbs due to birth defect, accidents, etc. Luckily, through the use of prosthetics or an artificial replacement of a body part, these limb deficient persons can live a normal life to the fullest extent possible. In the case of adults who no longer experience significant body growth, it is far less complicated to design prosthetics to fit their needs for an extended period of time. However, in the case of growing children, the challenge arises when the prosthetic needs to be constantly configured to adjust to the child s varying fit and comfort level. Because of this, children require replacement limbs are repairs between up to the age of about 16 years. Specifically, children between the ages of 5 to 16 years require prosthetic replacement every 6 to 12 months attributed to their natural development. The most dominant limb deficiency is that of the lower leg, representing approximately 75 percent of all amputation worldwide. Lower limb prosthetic costs can vary from $5,000 to $15,000 per year depending on the amount of replacements a child must undergo during their childhood to adolescent years. For these reasons, it is worthwhile to have adjustable and affordable prosthetics that can simulate growth for child users. Concentrating on the lower limb deficiency, the designs considered in this paper are limited to three sections: below the knee, knee disarticulations and above the knee. These sections are depicted in Figure 1. Prosthetics, as any other medical device, must undergo certain testing and comply with various related standards to ensure user safety to the fullest extent possible. This is because part failure, as well as improper use can cause injury and/or discomfort to the user. Prosthetics are placed into classes by the FDA which designate their likelihood of causing risk to the user. To be in Class 1, which is where lower limb prosthetics fall into, means the risk involved are low to moderate. The FDA requires documented record of any and all bodily injuries that occur to users of Class 1 prosthetics. The prosthetic must also be tested repeatedly by different users to determine its strength, adjustability and durability. Figure 1. Lower Limb Prosthetic Test situations should be those that can occur every day, including but not limited to level walking, abrupt stopping, abrupt sidestepping, stepping on or over an obstacle and swinging of the knee extension. Testing should take into consideration material properties, and the motion and stresses of the prosthetic limb should be analyzed. Once these tasks are completed, following the safety standards, design considerations and testing methodology, a final product should be manufactured. Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 90

2. DESIGN SPECIFICATIONS The design specifications for the lower limb prosthetic shall include the ability to simulate growth since the target group is growing children between the ages of 5 and 16 years. The prototype must be modular so to accommodate three-dimensional body changes as well affordable for users. The prototype considered in this paper will be a lower limb prosthetic consisting of a food, a calf-shaft, knee joint and a socket. The calf-shaft shall be adjustable in length to simulate growth with the child. The limb must be able to support the child s increasing weight as he or she grows and should be resilient enough not to fail under daily fatigue or stress. The socket should allow for virtually no fatigue or irritation to the child and his or her skin. 2.1 Design Overview There are four main components which make up the lower limb prosthetic. These are: the foot-ankle, the shank, the knee and the socket. Figure 2 below depicts these components. the straps which are fitted to the user s thigh to increase in diameter as her or she grows. Materials that can facilitate these requirements are those of thermoplastics. They are also corrosion resistant, antifungal, moldable, compoundable and machine-stable, making them perfect candidates for a prototype such as this. Thermoplastics also bond well with other thermoplastics, which means their properties can be altered slightly to fit the needs of the user once they are mixed together. Three thermoplastics that can be considered for a prototype include ABS, high-low density polyethylene and flexible PVC. ABS properties include being light-weight, high-impact resistivity and high mechanical toughness. However, whether or not it can achieve the flexibility needed for this prototype is not clearly defined. ABS is, however, used in many other applications known to consumers worldwide which can make it appeasing to consumers. Polyethylene can vary in density from extremely high to low. Those characterized with high density are much stronger, however, low density polyethylene is much more flexible. The two extremes must be varied, one with the other in order to produce a material that can fit this prototypes needs effectively where strength and flexibility must be considered. PVC properties include being strong, impact-resistant and resilient with regard to creep compared to most other thermoplastics. It is also very rigid and it is mixes well with other substances. However, PVS is not suitable for injection molding. Other substance can be added to PVC to increase flexibility while retaining strength. Table 1 shows the values of select properties for each material considered previously. Table 1. Material Properties for Socket Property ABS LDPE HDPE PVC Figure 2. Lower Limb Main Components Density [g/cm 3 ] Rockwell Hardness 1.21 0.941 0.976 1.42 R 97 R 56 R 71 R 115 The design incorporated in the paper is one that enhances several different ideas based on two overall goals, i.e., adjustability and affordability. 2.2 Socket Design The socket design incorporated in this paper is one that allows some of the weight of the user to be loaded to the thigh, above the knee. This design cups the bottom of the prosthetic limb and continues up the thigh becoming thinner on its way up. The semi-flexible cup shall be securely fitted to the thigh of the user by straps. This set-up will allow for a high degree of adaptability simultaneously decreasing the impact of pressure experienced by the skin surrounding the limb. In order to decrease pressure even further, memory foam shall line the bottom of the socket. The foam thickness shall depend on the size of the child, i.e. smaller children shall have thicker foam layers to provide comfort as well as adjustability for the user. The socket material used shall be one whose strength will sustain the stresses involved in handling the user s weight, as well as allow Yield Strength [psi] Flex Modulus [psi] Izod Impact [ftlb/in] 7650 2020 4600 7500 320,000 148,000 251,000 481,000 4 6.6 9.5 1 The material selected for the socket is high density polyethylene. Based on cost and material properties, it was determined to be the most suitable for the task at hand. The socket is made with four large, evenly-spaced slits. These slits allow for about 3 of deformation on the top diameter. The strap will be placed around the top portion of the socket, essentially fastening the socket to the residual limb of the child. A depiction of this design can be seen in Figure 3. Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 91

Figure 3. Socket Design 2.3 Knee Design The knee joint of the prosthetic should have the ability to withstand the child s weight without buckling, whether standing or walking. Therefore, a spring based knee is incorporated in this design. The spring will create a torque in the opposite direction that the knee is forced to bend. This means, the knee will bend, open or close, when sufficient torque is supplied counter-clockwise to the center of rotation of the knee. This action facilitates standing, walking or sitting. To achieve this, tensional springs are placed in a semi-circle, where one end of the spring is attached to the top pin above the hinge and the other is attached to the bottom pin. The axis of the hinge is the center of the rotation of the knee. In order to minimize vibrations and allow for a smoother walking experience for the user, the k value of the springs shall be optimized as well the number of springs used in each knee. Also, the friction factor associated with the hinge. The knee shall be able to achieve an angular displacement between 0 and 90 degrees. A locking system will be incorporated for such times when the user is sitting or when he or she desires to lock the limb to any position within its range of motion. This will be useful if the user is required to stand for an extended period of time, he or she can lock the limb position at 0 degrees. This knee joint design is effective due to the fact that even though the child will gain weight causing the torque that is supplied to the axis of the knee to increase with time, the springs can easily be replaced with stronger springs to account for this change. Therefore, a spring based knee is more feasible than other knee considerations, such as the hydraulic knee joint. Figure 4 depicts the spring design of the knee which will be incorporated in this prototype. The material used for the knee is aluminum 1060 alloy. It is a strong, lightweight material with properties that fit the needs of this design. Figure 4. Spring Knee Design 2.4 Shank Design The shank design shall include various levels designated by holes in the calf of the limb so that pins are able to lock in place. This will allow for adjustment of the prosthetic as the child grows. This pinbased shank is more affordable and attainable as will be show later in this paper by stress simulations performed on the shank model. The simulation will verify that fractures will not occur at the weak points of the bearing/pin interface. The shank will comprise of two aluminum hollow shafts which will fit one within the other. The outer shaft will have an outer diameter of 1 inch and an inner diameter of ¾ inch. The inner shaft will have an outer diameter of ¾ inch and an inner diameter of ½ inch. Each shaft will have a series of 3/16 inch holes spaced at varying lengths from each other. At the top of the inner shaft, there will be 4 holes, each spaced ¼ inch apart. These holes will connect with the knee allowing for minimal adjustment if needed. For larger adjustments, the outer and inner shaft will have holes spaced 1 inch apart. In Figure 4, the two shafts are depicted. Figure 5. Shank Shaft Design 2.5 Foot-Ankle Design The foot/ankle shall be a spring-pin based design which is easy to manufacture as well as it is cost effective. It will easy to adjust, Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 92

making it more appealing for child users. In Figure 5 below, steel bars are shown which are 2 inch wide and ¼ inch thick. Metal forming shall be used to bend the bars into the desired shape. The bottom of the foot will have a 3 inch diameter bend at the heel, as well as a series of 0.15 inch diameter holes spaced ¼ inch apart. There will be two 45 degree bends with 2 inch radii at the top of the food. Also at the top shall be a series of holes spaced ¼ inch apart. This design shall be incorporated because it is very cost effective to manufacture a hollow bar, rather than hollow out an existing solid bar. One bar on top of the other shall be used. The bars shall be shaved in half at the connection point to ensure both are flush with the bottom. 5.1 Shank Force Analysis The shank force analysis is the most straightforward of the force analysis that will be evaluated to the prosthetic. During this analysis, the shaft of the shank will undergo compression due to the force of the weight of the child. When the child is on both feet, the force felt on the bottom of a single foot is equivalent to half the weight of the child. In this position, the center of gravity of the child is directly above the legs as demonstrated in Figure 7, the Standing Reaction Force Diagram. If the child chose to stand on the prosthetic alone, it would bear the full weight of the child. But what happens when the child is walking? As the child begins to walk, their center of gravity will begin to move away and will no longer be collinear with the axis of the shaft. This will of course create moments at the end points. This moment must be analyzed and simulated to ensure shank remains structurally sound. Figure 6. Foot-Ankle Design 3. DESIGN FEASIBILITY Using the simple, yet practical designs methods outlines above, a prototype geared to fulfill the requirements of this project is easily attainable. Basic mechanical mechanisms, standard material sizes and components as well as 3-D printing technology can go a long way in completing a final product of this proposed design. 4. KINEMATIC ANALYSIS OF THE KNEE Kinematic Analysis of the knee was undertaken which demonstrated little difference between the angular ranges of the knee with three springs in comparison to the knee with one spring, as long as the k-value of the single spring is equivalent to the sum of the k-value of the three spring system. The maximum velocity of the single spring system with a 1.75 inch spring and a 0.333 lb/in k-value is 206 deg/sec. Figure 7. Maximum Angular Velocity of Knee 5. ENGINEERING ANALYSIS Analyzing the forces involved in human gait is essential for understanding the different types of forces applied on a human leg in order to create a prosthetic leg. The forces on the shank, foot, knee, and socket will be evaluated in determining if the prosthetic will function under certain loads and conditions. Figure 8. Standing Reaction Force Diagram 5.2 Foot Force Analysis The foot of the prosthetic is designed to replicate that of a human foot and ankle. Based on the round design, the foot will be impacted by three different stages of pressure. The first is when only the heel portion of the foot is in contact with the ground. At this stage, the reaction force that the heel will be impacted by will be perpendicular to the tangent line of the point on the rounded heel that is in contact with the ground. In the second stage, the whole bottom of the foot will be in contact with the ground. In this stage, the weight is assumed to be evenly distributed about the foot. At this stage, the heel of the lead foot (the user s foot) is also in contact with the ground. Although there will be less weight felt by the prosthetic foot, more weight will be on the front portion of the foot, creating a moment. 5.3 Knee Force Analysis Considering that the knee will be consist a spring on the hinge of the knee, taking into account Hooke s Law will be evaluated. According to Hooke s Law, the relationship between the force that is exerted by a spring and its deformation is linear. This is only valid before the elastic limit of the spring is reached. The rate at which the spring deforms relative to the force is the spring constant. This spring constant is a physical property of the spring based on its elasticity. Now the elasticity of the spring is based on the spring s material, shape, diameter, thickness, and other physical properties. Equation 1 is the Hooke s law equation where F is the force that is being exerted by the spring, k is the spring constant or spring rate, and x is the linear distance that the spring has deformed. Figure 8 displays a Force vs. x curve, as it shows; the relationship is linear until it reaches its elastic limit where it begins to curve off. Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 93

Figure 10. l Knee Diagram Figure 9. Spring Force vs. Elongation Diagram (3) (4) (1) Due to the nature of the design, calculating the deformation of the spring is not a straightforward task. The spring takes the path of the dotted line that is shown in Figure 8, which is a perfect half-circle. Therefore, when the knee is closed and the two inner faces of the knee are touching, the length of the spring will be equal to half of the circumference of the circle. Equation (2) is the formula for calculating lc which is just half the circumference of a circle. Now, this length, (lc) may not necessarily be the un-deformed length of the spring (l0). However, they were equivalent in the preliminary sample calculations made. c = πr (2) 5.4 Socket Force Analysis The socket s relevant forces must be analyzed using different methods than the rest. The socket is designed to fully cup the residual limb and more than that, is tightened to ensure it handles the stresses and doesn t come loose. Due to this, the socket will also be exposed to pressure. Due to the sockets shape, cylindrical pressure tank theory will be used to model and analyze the forces and stresses in the socket. 5.5 Shank Stress Analysis The shaft will generally be under compression as the weight of the child pushes down on the shaft. In order to analyze the stresses, the shaft will first be modeled as a simple hollow shaft under an axial force at the top with the bottom fixed. Equation 5 should be used to calculate the stress in the modeled shaft. Now, as the knee opens, the spring will no longer deform tangent to the circle. Instead, it will begin to deform linearly. This is clearly displayed in Figure 9. The distance of this deformation may be calculated using the law of cosines. The length (l ) is unknown and is to be solved for using the radius of the circle (r) and the angle (θ). The derivation of the law of cosines for the length l is displayed in the Spring Torque Sample Calculations, the result is equation 3. Equation 4 calculates x using the known and calculated lengths, where l is the total length ( l + lc ) and l0 is the original or undeformed length of the spring. Finally, equation 4 produces the torque that is supplied by the spring on the hinge of the knee. While designing the holes of the shaft they created adjustable every inch but causing high stress at the hole as shown in Figure 11. This resulted in choosing an extremely strong material and lightweight to withstand the stress from the hollow tubing and holes on the tubing. The stress of the shaft undergoing 200 lbs. of force simulated using a material of Aluminum 6061. The von Mises stress is 3,650 psi that is well within range of the material s yield strength of 40,000 psi. (5) Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 94

Figure 11. Stress on Shaft with a 200 lbs. Force 5.5 Foot Stress Analysis The foot experiences different levels of stress during different stages of a single step completed by the user. When the step is firm and controlled, the forces are evenly distributed at the bottom of the foot. At the heel and on the top portion of the foot however, are weak points. SolidWorks simulations shall be run to analyze the contact between the heel and the ground. Figure 13. Stress on Socket with a 200 lbs. Force and 15 psi Pressure Outwards 5.7 Knee Stress Analysis Analysis was run on the knee with a 100 lb load on the top surface of the pin. The maximum stress in compression experienced was 998.463 psi. The Von Mises stress was 3999.3 psi and the safety factor for the material under this loading was 4.0. The highest stresses occur at the pin because of its small surface area to the high load. This part overall is well within range of safety standards and will not yield. Figure 12 shows the model of this part. Figure 12. Stress on Foot with a 200 lbs. Force 5.6 Socket Stress Analysis The stress analysis for warping demonstrated that the socket would not fail and the maximum Von Mises stress was calculated to be 2130 psi. Thus proving this part under specified parameter to be very resilient. Figure 11 depicts the Von Mises Stress levels of the socket. Figure 14. Stress on Knee with a 200 lbs. Force 6. PROTOTYPE DESIGN The prototype comprises of a 3D printed socket, a pin-based shaft link, a spring-based knee joint and a screw-based foot joint as Figure 15 shows. The final prototype assembly are for the most part true to the design specifications outlined in Section 2. However, slight changes were made to the foot and knee design in order to accommodate the manufacturing process. Each component is designed to have maximum adjustability. The shank ranges from ¼ inch to 9 inches to allow for extension or shortening as needed. The Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 95

springs in the knee can be replaced as necessary to facilitate the growth of the child. The foot is designed to extend as needed as well. 6.2 Foot Prototype The prototype of the foot was constructed from several pieces of aluminum bars, machined the specified cuts and contours. Holes were drilled into the various pieces to that they can be connected together, then they holes were threaded. All the pieces were assembled to the extension piece of the foot and was fastened to the bottom. The top of the foot was then fastened to the extension. Figure 15 shows the assembled prototype whereas Figure 17 depicts the foot. Figure 15. Lower Limb Prosthetic Prototype Assembly Figure 17. Foot Prototype 6.3 Socket Prototype The prototype of the socket was constructed using PLA plastic and took a total of 19 hours to 3D print. Figure 18 shows the prototype of the socket. 6.1 Shank Prototype The prototype of the shank was constructed from two hollow shafts of different radii. The shaft with the larger radius was cut to 5 inches and the other was a slightly longer than that to facilitate the connection of the two shafts. The end of the smaller shaft was placed in the larger and holes in accordance with the design specifications were drilled in both shafts. Figure 16 shows the prototype of the shank. Figure 18. Socket Prototype 6.4 Knee Prototype The prototype of the knee was 3D printed. The top and bottom were fastened together by a 2.5 inch hinge and the springs were threaded through the spring holes. Figure 19 illustrates the assembly of the prototype of the knee. Figure 16. Shank Prototype Figure 19. Knee Prototype Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 96

6. TESTING Each component of the prosthetic was tested separately and was an overall success. The spring of the knee was tested under a supplied torque, with k values ranging from 14 lb/in to 42 ln/in. It was also tested with different springs (Figure 20). An error of approximately 7.5% was obtained with regard to experiment vs theoretical torques. Height (inches) Table 2. Knee Experiment Results (k=42 lb./in) θ (degrees) Force (lbs.) Experimental Torque (lb*in) Theoretical Torque (lb*in) ε (%) 0.5 9.594 11.5 20.47 22.257 8.027 1 19.471 24.5 43.61 45.006 3.101 1.5 30 36 64.08 68.884 6.973 2 41.810 50 89 94.967 6.282 The socket sustained a crack when a residual limb was used as a test limb. This occurred due to the size of the limb, not in fact the weight of the limb which was 20 lbs. The limb was made from aluminum which is much tougher than the 3D printed plastic socket. Therefore, when the pressure of the aluminum limb was applied, the crack on the socket was sustained as seen in Figure 22. Figure 22. Socket Crack Figure 20. Testing of Knee The shaft and foot were tested in compression with a maximum weight of 180 lbs. They were both able to sustain this weigh with no fractures inflicted. This weight was within a 90% range of the 200 lbs which the simulations were ran with. Figure 21. Testing of Foot/Shank Figure 23. Testing of Socket Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 97

7. SUMMARY In designing this prosthetic leg, the motive was to eliminate abandonment, provide a more cost effective prosthetic, and increase comfort for users of ages 6 to 16. With the assistance of 3D printers, the parts were fabricated at a much lower cost compared to prosthetic legs in the market. With the prosthetic leg designed, we are hoping to encourage others to participate in this new upcoming movement for 3D printed prosthetics. Not only will this provide amputees with the proper prosthetic at low cost, but it will create a friendly way of living for amputees. 8. REFERENCES [1] Hsu, John D., John W. Michael, and John R. Fisk. AAOS Atlas of Orthoses and Assistive Devices, 4 th ed., Philadelphia: Mosby/Elsevier, 2008. [2] ASM. "ASM Material Data Sheet." ASM Material Data Sheet 3000 Series".[Online].Available: http://asm.matweb.com/search/specificmaterial.asp?bassn um=ma6061t6. [3] Besier, Thor F., Michael Fredericson, Garry E. Gold, Gary S. Beaupré, and Scott L. Delp. "Knee Muscle Forces during Walking and Running in Patellofemoral Pain Patients and Pain-Free Controls," in Journal of Biomechanics. [Online], Available: http://www.ncbi.nlm.nih.gov/pmc/articles/pmc2671570/. [4] ASM. "ASM Material Data Sheet." ASM Material Data Sheet 6000 Series Aluminum. [Online]. Available: http://asm.matweb.com/search/specificmaterial.asp?bassn um=ma6061t6. [5] Smith, Douglas G. "InMotion Easy Read: Ways Children Adjust to Limb." InMotion Easy Read: Ways Children Adjust to Limb. [Online]. Available: https://www.amputeecoalition.org/easyread/inmotion/mar_apr_06/congenital_p art2-ez.html. [6] "Limb Loss Statistics." Amputee Coalition. [Online]. Available:https://www.amputee-coalition.org/limb-lossresource-center/resources-by-topic/limb-lossstatistics/limb-loss-statistics. [7] "Amputee Statistics You Ought to Know AdvancedAmputees.com." Amputee Statistics You Ought to Know, AdvancedAmputees.com. [Online]. Available: http://www.advancedamputees.com/amputee-statisticsyou-ought-know. [8] "See How Your Baby Grows: Age-by-Age Growth Chart for Children." Parents.com. [Online].Available:http://www.parents.com/toddlerspreschoolers/development/physical/age-by-age-growthchart-for-children/. [9] DA, Taylor, Dikos GD In, and Loder RT, Long-Term Lower Extremely Prosthetic Costs in Children with Traumatic Lawnmower Amputation. In Natural Center for Biotechnology Information. [Online] Available: https://www.ncbi.nih.gov/pubmed/15583104. Proceedings of the 29th Florida Conference on Recent Advances in Robotics, FCRAR 2016, Miami, Florida, May 12-13, 2016. 98