Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 8872362, 14 pages https://doi.org/10.1155/2020/8872362 Research Article Development and Performance Verification of a Motorized Prosthetic Leg for Stair Walking 1 2 2 2 Kiwon Park , Hyoung-Jong Ahn, Kwang-Hee Lee, and Chul-Hee Lee Department of Mechatronics Engineering, Incheon National University, Incheon 22012, Republic of Korea Department of Mechanical Engineering, Inha University, Incheon 22212, Republic of Korea Correspondence should be addressed to Chul-Hee Lee; firstname.lastname@example.org Received 12 April 2020; Revised 3 August 2020; Accepted 25 September 2020; Published 27 October 2020 Academic Editor: Wei Wei Copyright © 2020 Kiwon Park et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The present study emphasized on the optimal design of a motorized prosthetic leg and evaluation of its performance for stair walking. Developed prosthetic leg includes two degrees of freedom on the knee and ankle joint designed using a virtual product development process for better stair walking. The DC motor system was introduced to imitate gait motion in the knee joint, and a spring system was applied at the ankle joint to create torque and ﬂexion angle. To design better motorized prosthetic leg, unnecessary mass was eliminated via a topology optimization process under a complex walking condition in a boundary considered condition and aluminum alloy for lower limb and plastic nylon through 3D printing foot which were used. The structural safety of a developed prosthetic leg was validated via ﬁnite element analysis under a variety of walking conditions. In conclusion, the motorized prosthetic leg was optimally designed while maintaining structural safety under boundary conditions based on the human walking data, and its knee motions were synchronized with normal human gait via a PD controller. The results from this study about powered transfemoral prosthesis might help amputees in their rehabilitation process. Furthermore, this research can be applied to the area of biped robots that try to mimic human motion. 1. Introduction with user intentions. Hence, the powered type is considered to replace the passive and variable-damping types. Powered A prosthetic leg is a basic rehabilitation device that helps prosthetic legs are enabled by advances in computers, robot- rehabilitation of limb amputees, and the number of lower- ics, and battery technology . Powered prosthetic legs can limb amputees was estimated at approximately 7 million be classiﬁed based on their method of torque generation as worldwide . The development of prosthetic legs for three linkage types or direct-drive types. Conventional three linkage types are an easy way to convert the linear motion lower-limb amputees is becoming an important issue. The above-knee amputees and particularly the lower-limb ampu- to the rotating motion at the knee joint. However, a longer tees’ face increased diﬃculties in natural walking when com- linkage is required to generate a large angle at the knee joint pared with lower-knee amputees. This is because of the due to kinematics and leads to issues with the dimensions. absence of the knee joints that are mainly responsible (50% Additionally, the center of mass shifts when the translation linkage shortens. The direct-drive type directly transfers the of the importance) for the walking mechanism. The develop- ment of prosthetic leg that can create the natural knee motion rotational motion of the motor to the joint. However, it is required for above-knee amputees. requires an additional device to amplify the torque, which The prosthetic leg can be classiﬁed as passive, variable- can increase the size and weight of the prosthesis. damping, or powered [2–4]. Prosthetic legs were traditionally There have been diﬀerent kinds of studies about the classiﬁed as passive or variable-damping due to limitations of development of powered prosthetic leg. Some researcher power generation and battery life. Passive and variable- used electrohydraulic actuator for making the knee motion damping types do not result in a natural motion in keeping . Due to advances in motor and battery technology, the 2 Applied Bionics and Biomechanics motor is introduced as an actuator of a prosthetic leg. Three 2. Design of the Motorized Prosthetic linkage type powered prosthetic leg was developed using a Leg System motor and ball screw system [7, 8]. As motors become more compact and are enable to produce high torque, direct-drive 2.1. Design Torque-Generating System. A transfemoral pros- type prostheses have been developed. DC motor was used for thetic leg is a rehabilitation apparatus for above-knee ampu- the drive system [9–11] or a harmonic drive and belt pulley tees. Thus, it is necessary for a prosthetic leg to implement system to amplify the torque applied to the knee joint . the functions of the knee and ankle joints. Furthermore, it Studies were performed on the kinematic structure design is necessary for a powered prosthetic leg to imitate the of an active prosthetic leg with a motor system [13, 14]. motion of each joint and to also possess dimensions similar The extant research examined control mechanisms of knee to the body size to ensure user comfort. In this study, the and ankle joints to mimic a natural human gait [15, 16]. walking mechanism and lower-limb structure were analyzed However, most previous studies focused on the kinematic to determine the dimensions and performance of a prosthetic walking mechanism or control for the level walking. Only a leg. A target user included a 28-year-old male with a body few studies carried out for control mechanisms under stair size involving a height of 176.6 cm and weight of 82 kg. walking condition . A previous study indicated that the speciﬁc weight of the Most of the study of the powered prosthetic leg focused shank and foot should correspond to 5.99% of the total body on overground walking, but for the disabled to move freely, mass . Therefore, the weight of the prosthetic leg should a prosthetics capable of overcoming various obstacles should be less than 4.912 kg, which is set as the user’s body weight. be developed. Typical walking obstacles include ramps and The length of the lower knee leg is measured for design. stairs, of which obstacles requiring greater power are stairs. Figure 1 shows portions of the lower knee leg segment in In order to climb the stairs, it should be considered for var- which the shank possesses a length of 37.3 cm from the knee ious dynamic loads and requires more power than when to the ankle, and the foot is of the length of 6.5 cm. Based on a walking on the overground. Therefore, it is inevitably previous study, the highest knee torque of human gait occurs required to be lightweight and an optimum structure that during stair descent, and the normalized value at that point is is as stable as possible under limited weight conditions. approximately 1.3 Nm/kg . Given a user weight of Existing studies focus on control to overcome the staircase, approximately 82 kg, the knee joint of a prosthetic leg can and research on optimizing the structure itself is insuﬃ- produce a torque of up to approximately 106.6 Nm for cient. The purpose of this study was to perform the optimi- functions similar to the human knee. Similarly, the highest zation of a motorized prosthesis capable of walking on plantarﬂexion moments of human gait occur during level stairs. walking, and the maximum normalized value was approxi- Several major factors inﬂuence the behavior of a pros- mately 1.55 Nm/kg . That is, the ankle joint could sup- thetic leg and include the alignment, mechanical properties, port a torque of 127.1 Nm. length, and the weight of the components of a prosthetic The core of the prosthesis that can climb stairs should be leg . Although the weight of the prosthesis is one of the light, creating a torque that is strong enough to support the important factors for performance, researches to improve human weight. When selecting torque, safety factor was the structure of the prosthesis are rarely carried out. In order considered excessively. Since the weight diﬀerence due to to overcome obstacles such as stair, it is necessary to study the reducer was not large compared to other parts, safety the optimization of the structure of prosthetic legs. Recently, was prioritized over weight reduction of the motor within studies about a prosthetic leg for walking stairs have been the range that satisﬁes the weight requirement. actively carried out, but little research has been implemented Two types of torque generating systems exist at the knee to design optimal structures for stair walking. joint, namely, the three linkage type and the direct-drive type. This study focuses on the development of a powered Conventional linkage types can easily convert linear motion transfemoral prosthetic leg that can imitate the human walk- to rotation motion, but the size cannot be reduced due to ing motion and is optimized for stair walking. A structural the geometry limitations. In this study, a BLDC (brushless design with two degrees of freedom at the knee and ankle DC) motor was used because the three linkage-type mecha- joint was proposed. The power system of the knee joint is nism involves performance and weight limitations due to most important because the knee joint plays a major role the dimensions of the linkage structure . The concept (exceeding 50%) in the walking mechanism. In order to pro- model is shown in Figure 2. EC 45 BLDC motor made by duce a higher torque for a stair walking, a larger motor and Maxon (136211) was selected as the knee joint motor, given gear set should be applied, and the prosthetic leg must be rel- a maximum power production capacity of 250 W. The torque atively heavy due to their weight. The prosthetic leg structure constant and nominal current of the motor corresponded to was optimized with topology optimization to reduce its 0.0328 Nm/A and 10.2 A, respectively. If the maximum cur- weight. Additionally, the ankle joint consists of a spring sys- rent was assumed as the nominal current, then the maximum tem to obtain a driving force to shift the body. The structure torque of the motor corresponded to 0.3346 Nm. Therefore, a of the prosthetic leg was optimally designed with topology reduction gear with a gear ratio of 318.5 : 1 was used to optimization to minimize weight while maintaining the achieve the maximum required torque of 106.6 Nm for the safety of the structure. FE analysis was performed to verify knee joint. the safety of the structure, and unlocked prosthetic leg test During stair walking, the speciﬁc aim was to control the was carried out for testing the controller. joint angle along the reference motion. It was important to Applied Bionics and Biomechanics 3 was followed by designing a model and improving the model <Unit : cm> by topology optimization to reduce weight. Topology optimization involves a mathematical method 38.0 Thigh to obtain the optimal distribution of material for given design conditions including boundary conditions. The topology optimization problem was formulated in 1988 using a homogenization method . Homogenization and solid isotropic material with penalization (SIMP) are widely used 37.3 Lower leg methods to solve optimization problems. These methods allow discrete design variables with intermediate density values ranging from 0 to 1. Speciﬁcally, SIMP is an extension 6.5 of the homogenization method that has gained popularity in structural optimization because of its conceptual simplicity 4.1 14.6 6.8 and ease of implementation . Figure 1: Dimensions of the lower knee leg. Design variables, constraints, and an objective function are required to deﬁne an optimization problem. The problem for minimizing mass can be expressed as follows : check motion stability, not to control in 0.1 degree units like a Minimize: mass. precision mechanical system. To conﬁrm the feasibility of operation of the entire lightweight prosthetic system (3D Subject to FðÞ σðÞ x ≤ 0, ∀x ∈ Ω: ð1Þ printing structure), the experiment was conducted to see if the designed motorized prosthesis can properly follow the The material failure function F depends on the stress reference motion. It has been conﬁrmed that the error of ﬁeld σðxÞ and strain ﬁeld εðxÞ, which are deﬁned with respect the angle and delay was shown at the degree level. to an original domain Ω. The failure function is deﬁned with The spring system was introduced to create the required the von-Mises criterion, which is normally used as a failure torque without the addition of a motor and electric devices criterion. The failure function F is expressed as follows: at the ankle joint. The plate spring was used for the ankle joint because it was advantageous in terms of space applica- tions. Additionally, FE analysis was used to determine the FðÞ σ = − 1, ð2Þ spring coeﬃcient. The maximum required torque corre- sponded to 127.1 Nm, and the knee ﬂexion angle at that point where σ denotes the equivalent stress, which is usually was approximately 15 . The geometrical relationship indi- regarded as the yield stress of the material, and σ denotes cated that the displacement of the spring δ is based on the fol- the eﬀective von Mises stress that is computed as follows: lowing equation: δ = d sin θ, in which θ =15 and d =35mm. That is, the value of δ was approximately 9 mm. The thick- 2 2 2 2 ness of the plate spring was determined by comparing the σ = ðÞ σ − σ +ðÞ σ − σ +ðÞ σ − σ v 11 22 22 33 33 11 2 ð3Þ result of the FE analysis and the theoretical displacement δ 2 2 2 +3 σ + σ + σ : at which they coincided. Figure 3 shows the proper thickness 12 23 31 of the plate spring calculated by FE analysis. The property of the spring was assumed as SAE1045, which is typically used The density approach was used for topology optimiza- for spring. This material possessed a density (ρ)of tion. The standard format of a linear static topology optimi- 7,700 kg/m , elastic modulus (E) of 207 GPa, Poisson’s ratio zation problem is expressed as follows: (v) of 0.266, and a yield stress of 1515 MPa. Finally, the N :E: proper thickness of the spring was determined, and the value Minimize : m = 〠 ρ Ω corresponded to 0.5 mm. i i=1 The design speciﬁcations are summarized in Table 1. The design of the active transfemoral prosthetic leg utilizes the Subject to F σ ≤ 0 ðÞ ð4Þ BLDC motor designed for the knee joint. A motor with plan- N :E etary gear and helical bevel gear actuated the knee joint. The 〠 ρ V ≤ V i 0 spring system generated torque for the driving force from the i=1 ground at the ankle joint. The knee joint was capable of 100 0< ρ ≤ ρ ≤ 1 min i of ﬂexion at the knee. Additionally, the ankle was capable of ° ° 25 of plantarﬂexion and 15 of dorsiﬂexion at the ankle. The number of elements in the design domain is denoted by N.E., and Ω represents the region occupied by a ﬁnite ele- 2.2. Design Process and Topology Optimization. First, the ment. Furthermore, V denotes the volume of the design space, and it denotes the index of the elements. The design speciﬁcations of the knee joint were deﬁned to satisfy the reported boundary conditions for walking on stairs based variable corresponds to the bulk material density, which on a previous study . The major components, such as can be expressed using relative material density and material the motor and torque ampliﬁer, were then determined. This properties of each element in the SIMP method. The 4 Applied Bionics and Biomechanics Max. torque: 106.6 Nm Absolute encoder Knee joint Planetary gear Gear ratio 318.5:1 Pin connection 360 mm BLDC motor Load cell Torque constant: 0.0328 Nm/A Nominal current: 10.2A Maximum torque: 0.3346 Nm Plate spring 12 mm 12 mm Ankle joint 65 mm 35 mm Figure 2: Concept modeling of a powered transfemoral prosthetic leg. Displacement (mm) 0.000 35 mm -1.152 -2.303 -3.455 Rigid -4.606 -5.758 24 mm -6.909 -8.061 T = 127.1 Nm -9.212 Thickness = 0.5 mm -10.036 <Boundary condition> <FE analysis result> Figure 3: FE analysis to obtain the proper thickness of the plate spring at the ankle joint. Table 1: Design objectives considering body dimensions. The optimization process and particularly topology opti- mization converge during the process of developing an active Speciﬁcation Value transfemoral prosthetic leg. ° ° Knee range of motion 0 to 100 The objective of optimization involved determining the ° ° Ankle range of motion −25 to 15 optimized structure while ensuring structural safety under Maximum knee torque 106.6 nm working conditions. There are three design optimization Maximum ankle torque 127.1 nm methods, namely, shape optimization, size optimization, and topology optimization. Shape optimization involves Peak knee power 250 W determining the optimum shape by adjusting the positions Height (below knee) 438 mm of each node on the outer surface of the structure under Maximum total weight 4.912 kg boundary conditions. Size optimization involves a process of determining the properties of structural elements such as elasticity tensor (E) includes the following relationship: shell thickness, beam cross-sectional properties, spring stiﬀness, and mass. Finally, topology optimization involves ﬁnding an optimized structure by utilizing internal strain EðÞ ρ = ρ E , ð5Þ energy density distributions and removing any portion that does not contribute to the structural strength. These optimi- where n denotes a penalization factor, and ρ denotes the zation processes were applied to design the structure of an density (0 ≤ n, 0 ≤ ρ ≤ 1) [20, 24]. active transfemoral prosthetic leg. Applied Bionics and Biomechanics 5 1205.4 N 1205.4 N 1205.4 N 127.1 Nm 120.54 N 160.72 N (a) Heel strike (b) Toe oﬀ (c) Mid-stance Figure 4: Boundary conditions for foot optimization. Additionally, NX 9.0 was used for 3D CAD modeling. Shape optimization was implemented by Optistruct Solver of Altair Hyperworks, and Inspire of SolidThinking was used as the solver for topology optimization. The optimization process commenced with the deﬁnition of the design space. It was necessary to maximize the design space while mini- mizing the space for other components and interference (a) Design space (b) Topology optimization caused by the rotating motion of joints. The nondesign space, such as connections to bearings and bolts, in which optimiza- tion is not performed, was deﬁned. The FE model was intro- duced for optimization, and properties of the material and the boundary conditions including external load were applied. The design parameters for optimization were set and included design variables, objective function, con- straints, and the minimum or maximum size of the structure. Following the preprocessing, an optimization process was (d) Manufacturing (c) 3D modeling performed to determine the optimal structure while satisfy- ing the constraints. This was followed by performing optimi- Figure 5: Optimization process for the foot structure. zation with iterations until the performances satisﬁed the objective function. After the optimization process, the opti- corresponded to 0.15 times the body weight, and the other mized shape was designed given the optimization results. Finally, the optimized model was veriﬁed by FE analysis. point involved the toe-oﬀ phase in which the magnitude corresponded to 0.2 times the body weight. The peak values 2.3. Structural Design of Artiﬁcial Foot. A prosthetic foot at these points were considered as a boundary condition. includes malleability to accommodate variation in the physi- The medial/lateral ground reaction force is relatively small and is therefore negligible. The boundary conditions for opti- cal terrain in conjunction with rigidity to enable transmission of the body weight with adequate stability . Therefore, mization were determined considering the abovementioned plastic nylon was used to develop the artiﬁcial foot because walking characteristics and are shown in Figure 4. There it possesses suﬃcient ﬂexibility to absorb shocks while are three load cases for the boundary condition, and optimi- supporting the body weight. It is necessary for the artiﬁcial zation was performed by simultaneously applying all three cases as each case was considered independent. The load leg to look similar to a human foot because several amputees desire to be perceived as normal. Therefore, it is important was imposed on the ankle joint, and ﬁxed boundary condi- that the shape of the artiﬁcial foot is similar to that of a tions were applied to the ball of the foot and heel that were human foot and for the size to not exceed real foot size. directly in contact with the ground. The foot material corre- A few conditions involving the peak ground reactant sponded to plastic nylon, which possessed ﬂexibility and robustness. The material had a density (ρ) of 1,230 kg/m force were considered to design the foot structure. According , to the previous study , the peak ground reaction force an elastic modulus (E) of 2.91 GPa, a Poisson’s ratio (v)of appeared during stair descent walking with a magnitude that 0.41, and an yield stress of 75 MPa. corresponded to 1.5 times the body weight of a human. The Following the deﬁnition of the boundary condition and maximum ankle moment corresponded to 1.55 Nm/kg and materials, topology optimization was performed to design occurred at the end of the stance phase and was also consid- the optimal shape of the structure. Figure 5(a) shows the ered as a boundary condition. Additionally, the anterior/pos- maximum designable space, which was maximized while terior ground reaction force was also considered as a avoiding the space for other components and interference boundary condition. Two notable points occurred at 20% caused by the rotating motion of the ankle joint. The nonde- and 85% of the stance phase of level walking. One of the sign space where optimization was not performed was points involved the heel-strike phase in which the magnitude deﬁned at the contact surface and joint. The design space 6 Applied Bionics and Biomechanics 1205.4 N 106.6 Nm Rigid element Pin Pin joint joint Rigid element Figure 6: Boundary conditions for lower-limb optimization. tion as the shin. Additionally, the torque imposed on the was used for topology optimization using boundary condi- tions, as shown in Figure 4 and applying a material corre- knee joint was supported by the structure of the lower limb sponding to plastic nylon. Figure 5(b) shows the topology and the gear system. Constraints were applied at the end of optimization results. The unnecessary mass was eliminated the bottom of the prosthetic leg, which was connected to an while maintaining the robustness under the boundary condi- adapter and was assumed as a ﬁxed joint. The boundary con- tion. However, it was too complicated to directly manufac- dition for optimization was determined considering the ture the shape by machining, and thus, 3D printing was abovementioned load conditions and is shown in Figure 6. used to realize the model. 3D printing is advantageous as it It is necessary for the material of the lower-limb structure can create complicated shapes. Therefore, the result of opti- to exhibit robustness for safety and ensuring weight lightness mization can be applied in a very similar manner by using with respect to user comfort. Thus, 7075 aluminum alloy was 3D printing. Figure 5(c) shows the optimized model that used as the design material for the lower-limb structure. This was designed based on the topology optimization results material is usually used for prostheses and is lighter than steel and manufacturing method. Finally, the optimized foot was alloy. This material includes a density (ρ) of 2,800 kg/m ,an manufactured by a 3D printer and is shown in Figure 5(d). elastic modulus (E) of 75 GPa, a Poisson’s ratio (v) of 0.33, and a yield stress of 95 MPa. 2.4. Structural Design of the Lower Limb. It is necessary for Similar to the structural design, the optimization process the lower-limb structure of a prosthetic leg to sustain the was implemented to design the optimal structure by consid- ering boundary conditions. Figure 7(a) shows the maximum body weight of the user and bear an approximate torque of 106.6 Nm for the same function as the human knee when a designable space for the lower-limb structure. It was neces- sary for the maximum designable space to not exceed the user’s weight corresponds to 82 kg. The body weight is assumed as the maximum ground reaction force, which cor- dimensions of a human leg and to avoid interferences with responds to 1205.4 N. A previous study  indicated that other components such as motors and gearbox. The bearings and bolts deﬁned the nondesign space in which optimization the resultant ground reaction forces were directed towards the center of gravity. Therefore, the resultant force of the was not performed. The design space was used for topology optimization using boundary conditions based on Figure 8 ground reaction forces was assumed to be in the same direc- Applied Bionics and Biomechanics 7 Shape change (mm) 5.900E+00 5.244E+00 4.589E+00 3.933E+00 3.278E+00 2.622E+00 1.967E+00 1.311E+00 6.555E+01 0.000E+00 (a) Design space (b) Topology optimization (c) Shape optimization (d) 3D modeling Figure 7: Optimization process for lower-limb optimization. Bevel helical Encoder gear Knee joint Planetary gear Load cell BLDC motor Plate spring 3D printed foot Figure 8: Developed active prosthetic leg system. and an aluminum alloy. Figure 7(b) shows the topology lower structure were considered as a design variable. The constraints and external force were the same as the boundary optimization results. In this phase, geometrical symmetry was considered for the balance of the prosthesis. The result conditions for topology optimization. The objective function indicated that the shape of the structure did not signiﬁ- involved minimizing the mass. The contour showed the cantly diﬀer from that of the previous model despite displacement of the shape change versus the original model. changes in the thickness and edge. Following the topology The results indicated that it was necessary to reduce the thickness to approximately 6 mm. The optimal thickness of optimization, shape optimization was implemented to obtain a better model by determining the thickness as shown in the structure was determined based on the results. Finally, Figure 7(c). The degree of freedom of nodes placed on the the advanced shape of the lower-limb structure was obtained outer face of the upper structure and the inner face of the while maintaining robustness under boundary conditions. 8 Applied Bionics and Biomechanics Figures 7(d) and 8(d) show 3D modeling and the model manufactured by machining, respectively. 2.5. Design of the PD Controller. An important point in the development of active transfemoral prosthetic leg involves implementing the motion of natural gait using a power source. It is important to analyze human gait to determine the walking phase and to implement the motion of the aﬀected side that is similar to that of the normal side. In this study, a walking phase was identiﬁed through a mechanical sensor for knee joint control, and the PD controller based on the knee angle position was applied to actively cope with various walking environments. An encoder was used to collect the walking motion data of the knee joint to analyze the walking behavior. The mea- suring system is shown in Figure 9. The gait data of each walking situation were collected by walking around stairs and ﬂat ground. The data were measured ﬁve times for each case. The noise was removed by ﬁltering, and the standard Figure 9: Measuring system of the knee motion. gait data was determined by averaging. The data of a level and the stair walking are shown in Figure 10, and this was 𝜃 3 eq used as a trajectory to implement the walking motion. 𝜃 3 eq The swing motion was implemented by entering the 𝜃 4 motion to track on the motor for tracking obtained from eq Figure 10. The dynamic relationship of the walking system 𝜃 3 eq is as follows : 𝜃 1 eq 𝜃 2 𝜃 2 eq 30 eq 𝜃 4 𝜃 1 eq 𝜃 1 eq eq τ = k θ − θ + bθ, ð6Þ 10 𝜃 2 𝜃 4 eq eq eq 020 40 60 80 100 Cycle time (%) where τ denotes the torque of the knee and ankle joint, and k and b denote the linear stiﬀness and damping coeﬃ- Level walking Stair ascent cient, respectively. Additionally, θ denotes the angle of the Stair descent knee joint, and θ denotes the equilibrium angle during the eq transition between phases. A position-based PD controller Figure 10: Measuring result of the knee motion. was constructed to control the active prosthetic leg and applied to the developed prosthesis. Based on previous studies, the parameters were tuned using a combination of strike or forefoot strike was detected through the load cell feedback from the user and from visual inspection of the joint attached to the middle of the structure, then the walking angle, torque, and power data . phase was changed from the prelanding phase to the stance In the PD controller, a control loop feedback mechanism phase. that is commonly used in industrial control systems is used Phase 2 constitutes the preswing phase. This phase for control. The control system is shown in Figure 11. The immediately preceded the detachment of the sole from the PD controller is used to mitigate the stability and overshoot ground, and the load on the knee moved to the opposite problems that arise when a proportional controller is used leg. The heel fell from the ground while the knee bent over at a high gain by adding a term proportional to the time a certain angle, and this was followed by changing the walk- derivative of the error signal. The value of the damping can ing phase into the preswing phase. be adjusted to achieve a critically damped response. Phase 3 constitutes the swing ﬂexion phase. When the The decomposition of the joint behavior into passive seg- sole was completely separated from the ground, the load on ments requires division of the gait cycle into modes or “ﬁnite the knee was completely free because the load was supported states” . The walking phase was distinguished by the load by another side leg. When the load cell conﬁrmed that the cell and the encoder signal. A ﬁnite state machine was con- foot was completely separated from the ground, the walking structed as shown in Figure 12 to further divide the walking phase changed from the preswing phase to the swing ﬂexion step into four steps. The ﬁnite state machine of the prosthetic phase. leg was based on previous studies [9, 27, 28]. Phase 4 constitutes the swing extension phase. The knee Phase 1 constitutes the stance phase. If the knee was joint began to naturally expand. If the direction of the angu- extended over a certain angle in swing ﬂexion, then the phase lar velocity of the knee joint was reversed in the swing ﬂexion switched to the stance phase. The sole had contact with the phase, then the walking phase changed into the swing exten- ground, and the load was applied to the knee joint. If the heel sion phase. Degree (°) Applied Bionics and Biomechanics 9 Desired input Motion output K e(t) Error P 𝜃 (t) 𝜃 (t) eq O e(t) + Motor system 𝜏 = 𝜅 (𝜃 − 𝜃 ) + b𝜃 – eq de(t) dt Controller Encoder Figure 11: PD controller for the knee motion control. 3.2. Lower-Limb Structure Analysis. In order to verify the Phase2: Heel rise Phase3: safety of the structure, FE analysis was performed under a preswing swing flexion F(load cell) < threshold boundary condition similar to that shown in Figure 6. Figure 15(a) shows the 3D mesh for the analysis. A tetra Toe off Leg swing mesh was used owing to its advantages in meshing a complex 𝜃k > threshold 𝜔k : +→ − solid shape. The number of elements corresponded to 365,724, and the number of nodes corresponded to 84,988. Heel strike (forefoot strike) Phase1: Phase4: The body weight was applied to the nodes located at the stance swing extension F(load cell) > threshold center of the bearing holes that supported the knee shaft. The twelve bolt connections between the support and bevel Figure 12: Finite state machine. gearbox were considered as rigid link components based on the assumption that the bolts were nearly rigid bodies with An experimental method was used to perform coeﬃcient little deformation. Fixed constraints were applied to the bolt adjustment of the controller to optimize the walking perfor- hole located at the bottom of the leg that was bolted with a mance of the active prosthesis system. pyramid adaptor. All the materials were modeled as linearly elastic, isotropic, and homogenous. The results of the FE analysis of the lower-limb structure 3. Validation of the Developed Prosthetic Leg are shown in Figure 15(b). The maximum stress was exhib- ited in the area near the bolt hole. The value was 80.71 MPa 3.1. Artiﬁcial Foot Structure Analysis. It is necessary for the lower than 95 MPa, which corresponded to the yield strength artiﬁcial foot to support body weight while walking. There- of the 7075 aluminum alloy. This implied that the structure fore, FE analysis was performed to validate its structural was safe under the load condition. Furthermore, the bolt safety. The abovementioned boundary condition was holes were simpliﬁed to a rigid element, and it displayed a applied. FE analysis was performed for each of the boundary characteristic indicating a stress that exceeded the real stress conditions. Figure 13 shows the 3D mesh and boundary con- because the rigid element acted as a load point. Therefore, it ditions for the analysis. The quality of the mesh was impor- was expected that the actual stress at the point was lower than tant for obtaining an accurate result. A tetra mesh was used 80.71 MPa. due to its advantages in meshing a complex solid shape. The outer surfaces and geometrical corners involved com- 3.3. Unlocked Prosthetic Leg Test. An experimental setup for pact meshes for accurate analysis. The number of elements the unlocked prosthetic leg test was introduced to create the corresponded to 141,898, and the number of nodes corre- motion of the knee joint. The experimental setup is shown sponded to 38,047. The model included three load cases con- in Figure 16, and it was designed to ensure that the pros- sisting of heel strike, toe oﬀ, and mid-stance. The external thetic leg could move freely. The coeﬃcient adjustment of loads and moment of each load case acted on the center of the controller to optimize the walking performance of the the ankle joint, and constraints were applied to the ball of active prosthesis system was performed through an experi- the foot and heel. All the materials were modeled as linearly mental method. Given the reference walking data and user elastic, isotropic, and homogenous. Figure 14 shows the feedback, the value that could mimic the walking motion in results of the FE analysis of the foot structure. Table 2 the most natural manner possible was selected as the coef- summarizes the peak stresses of each phase. The highest ﬁcient value. Tables 3, 4, and 5 show the coeﬃcient of the von Mises stresses appeared in the heel strike phase, which controller for level walking, stair ascent, and descent, was located at the lower surface of the heel. The maximum respectively. The controller coeﬃcients for each phase were stress obtained in the results was compared with the tensile obtained through the experimental method. The equilib- strength of the materials used to check the stability with rium angle θ was selected as the peak angle of each phase respect to the applied load. The maximum stress corre- eq sponded to 65.51 MPa, which was lower than the yield or the angle at which the ground reaction force was strength of the material (75 MPa). imposed. 10 Applied Bionics and Biomechanics 1205.4 N (a), (b), (c) (a) Heel strike 127.1 Nm (b) Toe off (c) (c) Mid-stance 160.72 N 120.54 N (b) (a) (a), (c) (b), (c) Figure 13: A 3D mesh of the foot structure and the boundary conditions. VonMises VonMises VonMises stress (MPa) stress (MPa) stress (MPa) 5.561E+01 5.456E+01 4.925E+01 Max 5.023E+01 5.730E+01 4.391E+01 5.095E+01 5.021E+01 3.834E+01 4.367E+01 4.304E+01 3.206E+01 3.639E+01 3.587E+01 2.736E+01 2.911E+01 2.870E+01 2.191E+01 2.184E+01 2.152E+01 1.845E+01 1.468E+01 1.436E+01 1.096E+01 7.279E+01 7.180E+01 5.477E+00 1.017E+00 7.157E-03 4.856E-04 Max Max Max (a) Heel strike (b) Toe off (c) Mid-stance Figure 14: Results of the FE analysis of the foot structure. plays an important role in supporting the torque caused by Table 2: Peak stresses of each walking phase. the body weight. The spring system is simple and involves a general system to generate torque without a motor system. Walking phase Max stress Yield stress The ankle joint was composed of a spring system to generate (a) Heel strike 65.51 MPa 127.1 Nm torque and angle. (b) Toe oﬀ 64.56 MPa 75 MPa In order to evaluate design eﬃciency, speciﬁcations of the (c) Mid-stance 49.29 MPa prosthetic leg system and desired speciﬁcations were com- pared, and the comparison results are shown in Table 6. 4. Discussion The objects of comparison included the maximum torque and operating angle of each joint, power of the knee joint, 4.1. Performance Evaluation of Prosthetic Leg. Consequently, height, total weight, and maximum stress. These variables an active transfemoral prosthetic leg system was developed as were selected for the following reasons. shown in Figure 8. The three linkage type includes certain First, it is necessary for the prosthetic leg to make a speciﬁcation disadvantages, and thus, a direct-drive type proper motion to mimic the gait of a normal person. There- was applied to the knee joint, and a spring system was applied fore, it is necessary for the prosthetic leg to implement the to the ankle joint. The structure was then designed using the range of motions similar to a human leg in conjunction with optimization process. The active prosthesis was designed supplying the necessary power to overcome obstacles that with two degrees of freedom in the ankle and knee. The knee could be encountered by the amputees while walking. The range of the joint angle, target torques, and power was based joint plays an important role and is accountable for more than 50% of the walking mechanism. It consists of an AC on speciﬁcations listed in a previous study. The prosthetic leg motor system and can generate 106.57 Nm torque and was designed to meet the speciﬁcation based on this design ° ° proper motion in a range from 0 to 100 . The ankle joint parameter. Applied Bionics and Biomechanics 11 VonMises Max stress (MPa) 8.071E+01 7.174E+01 6.278E+01 5.382E+01 4.486E+01 3.590E+01 2.693E+01 1.797E+01 9.010E+00 4.827E-02 (a) 3D mesh (b) FE analysis Figure 15: Result of the FE analysis of the lower-limb structure. Table 5: Coeﬃcient of controller for stair descent. Phase k (nm/deg) b (ns/m) θeq (deg) 18 0 28 2 6.5 0 26 3 0.1 0.02 81 4 0.1 0.03 13 Table 6: Comparison between the desired and prosthetic leg Figure 16: Experimental setup for the unlocked prosthetic leg test. speciﬁcations. Table 3: Coeﬃcient of controller for level walking. Prosthetic leg Requirement Speciﬁcations Phase k (nm/deg) b (ns/m) θeq (deg) ° ° ° ° Knee range of motion 0 to 100 0 to 100 ° ° ° ° 16 0 25 Ankle range of motion −25 to 15 −25 to 15 24 0 13 Maximum knee torque 106.6 nm 106.57 nm 3 0.1 0.02 59 Maximum ankle torque 127.1 nm 127.1 nm 4 0.2 0.03 9 Peak knee power 250 W 250 W Height (below-knee) 438 mm 444.5 mm Table 4: Coeﬃcient of controller for stair ascent. Maximum total weight 4.912 kg 4.779 kg Max. stress Foot: 65.51/75 MPa Phase k (nm/deg) b (ns/m) θeq (deg) Allowable stress Lower limb: 80.71/95 MPa 12 0 17 210 0 24 0.920 kg for the reducer, 0.209 kg for the foot, and 2.5 kg for 3 0.1 0.02 87 the body (including cover and joint gear), totaling 4.779 kg. 4 0.5 0.03 72 In addition, the experiment was conducted by supplying power by wire without a battery. Although the weight of the motor and gearbox exceeds 2 kgf, the total weight was Second, weight is the most important factor because the eﬀectively reduced by introducing an optimization process user can feel fatigue or discomfort if the prosthetic leg is with respect to the structure. Similarly, it was necessary for heavier than their original leg. Hence, it is necessary to the total length of the prosthetic leg to be similar to the length minimize the weight to ensure the comfort of the amputees. of the original leg of a user. The developed prosthetic leg had a length of 444.5 mm, which corresponded to 101.5% of the The developed active transfemoral prosthetic leg has a total weight of 4,779 g, which corresponds to 97.3% of the target target length (438 mm). weight (4,912 g) obtained by considering the user’s body size. Finally, it was necessary to ensure the safety of the user The weight of the prosthesis is 1.150 kg for the motor, while using the prosthetic leg. Therefore, the safety factor is 12 Applied Bionics and Biomechanics 70 100 Phase1 Phase2 Phase3 Phase4 Phase1 Phase2 Phase3 Phase4 0 0 0 10203040 50 60 70 80 90 100 0 10203040 50 60 70 80 90 100 Percent of stride (%) Percent of stride (%) Measured joint angle Measured joint angle Desired joint angle Desired joint angle (a) Level walking (b) Stair ascent Phase1 Phase2 Phase3 Phase4 0 10203040 50 60 70 80 90 100 Percent of stride (%) Measured joint angle Desired joint angle (c) Stair descent Figure 17: Comparison between the desired motion and the actual drive motion. important in designing a prosthetic leg. The yield stress of delay. This phenomenon was due to the limitations of the the used material was compared with the maximum stress experimental system. The supplied voltage was lower than predicted by FE analysis. Plastic nylon (which is the foot the nominal voltage and reduced the torque below the target structure material) has a yield strength of 75 MPa. The torque. It was considered that the torque estimated by the maximum stress of the foot structure was expected as inﬂuence of relatively low power supply had a slight delay 65.51 MPa, and the safety factor at this time was estimated when compared to the objective data and would thereby as 1.15. In a similar manner, the 7075 aluminum alloy, aﬀect the walking speed. which was used to design the material of the lower-limb Figures 17(b) and 17(c) show the comparison between structure, possesses a yield strength of 95 MPa. The maxi- the desired motion and the actual drive motion with stair mum stress of the lower limb was expected as 80.71 MPa, ascent and the descent controller obtained by the unlocked and the safety factor at this time was estimated as 1.18. prosthetic leg test. They also indicated that the objective The maximum stresses of each part were lower than the function was followed in a similar manner. However, they yield strength of each material. exhibited slight inconsistencies. It involved a position-based The developed prosthesis was heavier than the prosthesis control, and a delay occurred when each phase went to the next phase. This appeared to be the cause of showing the sold on the market, although it was lighter than the dimen- sions of an actual human body. The weight of the motor actual knee motion follow slightly refracted curves. and the gearbox exceeded 2 kg. It was necessary to introduce The active prosthetic leg and controller exhibited behav- a suitable motor and gearbox to reduce the weight. Hence, ior that was considerably similar to that of a normal gait. The the implementation of the research on optimizing motors PD controller implemented a knee motion similar to normal walking. The experimental result of control based on the and gearboxes will help in developing a better prosthesis. position data showed the feasibility of the level and stair 4.2. Performance Evaluation of Controller. The comparison walking of the active prosthetic leg using the PD controller. between the desired motion and the actual drive motion with Additionally, it allowed the framework of the walking test the level walking controller obtained by the unlocked pros- to mimic the motion of a normal individual. Finally, the developed prosthetic leg was controlled by a thetic leg test (Figure 17(a)). The knee angle of the prosthesis was measured while tracking the normal walking data. The PD controller that generated human-like walking motion, actual motion of the prosthetic knee joint exhibited a similar and the resulting joint kinematics were compared with a tendency with the desired motion. The knee angle of the captured human gait to verify the control performance. It is prosthetic leg indicated a smooth swing curve, but was rela- expected that the study results with respect to the active transfemoral prosthetic leg will help in the rehabilitation of tively smaller than the desired angle and experienced a slight Angle (degree) Angle (degree) Angle (degree) Applied Bionics and Biomechanics 13 amputee subject,” IEEE Transactions on Neural Systems and amputees. Furthermore, this study can be applied to the area Rehabilitation, vol. 19, no. 1, pp. 71–78, 2011. of biped robots that imitate the human motion.  W. C. Flowers and R. W. Mann, “An electrohydraulic knee- torque controller for a prosthesis simulator,” ASME Journal 5. Conclusions of Biomechanical Engineering, vol. 99, no. 1, pp. 3–8, 1977. In this study, an active transfemoral prosthetic leg was opti-  K. H. Lee, J. H. Chung, and C. H. Lee, “Design and optimiza- mally designed and controlled with a PD controller. The tion study of active trasfemoral prosthesis leg,” Korean Journal weight of the prosthetic leg is an important factor in the of Rehabilitation Welfare Engineering & Assistive Technology, vol. 7, no. 2, pp. 41–46, 2013. design because it is related to user fatigue. An optimization process was used for foot and lower-limb structures to obtain  F. Sup, A. Bohara, and M. Goldfarb, “Design and control of a powered transfemoral prosthesis,” The International journal optimal shapes and reduce the weight. Topology and shape of robotics Research, vol. 27, no. 2, pp. 263–273, 2008. optimization were implemented in the design. As a result,  B. Lawson, H. A. Varol, A. Huﬀ, E. Erdemir, and M. Goldfarb, the shape of a prosthetic leg was developed without exceeding “Control of stair ascent and descent with a powered transfe- the dimensions of the human body. 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Applied Bionics and Biomechanics – Hindawi Publishing Corporation
Published: Oct 27, 2020