a methodology for the development of active ankle … · methodology for the functional design of...

http://www.iaeme.com/IJMET/index.asp 221 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 2, February 2018, pp. 221–234 Article ID: IJMET_09_02_022 Available online at http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=2 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed

A METHODOLOGY FOR THE DEVELOPMENT

OF ACTIVE ANKLE PROSTHESIS

Michele Gabrio Antonelli, Stefano Alleva, Pierluigi Beomonte Zobel

and Francesco Durante

Department of Industrial and Information Engineering and Economics, DIIIE, University of L’Aquila, L’Aquila, 67100, Italy

ABSTRACT

In the present work a methodology for the functional design of ankle prostheses is

presented. This methodology is applied to the functional design of an innovative active

prosthesis for the lower limb able to guarantee the physiologically correct movement

of the ankle. This new prosthesis, described in this paper, is based on a mechanism

with two links: one replaces the tibia and the other, coupled together with a hinge at

the ankle level, replaces the foot. For the functionality of the device, an active shock

absorber is placed between the two links and acts for damping and for accumulating

potential elastic energy; furthermore, the anchoring point of the shock absorber on

the tibia is adjustable by means of a motor that acts on a rocker arm. The

methodology for the functional design of ankle prosthesis is based on 4 steps: 1) the

analysis of the gait of able-bodied men with the definition of a dimensionless model of

the lower limb in a numerical computing environment; 2) the analysis of the force

exchanged with a sensorized treadmill in a virtual ambient; 3) the functional design of

the prosthesis able to adjust the pitch of the ankle and at the same time able to store

and provide the mechanical energy; 4) the preliminary draft of the control system of

the actuators able to define the law of motion to reproduce the physiological gait.

Keywords: Active ankle prosthesis, methodology, energy recovery, gait analysis.

Cite this Article: Michele Gabrio Antonelli, Stefano Alleva, Pierluigi Beomonte Zobel and Francesco Durante, A methodology for the development of active ankle prosthesis, International Journal of Mechanical Engineering and Technology 9(2), 2018. pp. 221–234. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=2

1. INTRODUCTION

During the gait, the motion of an inverted pendulum is described by the center of mass of an able-bodied men; the harmonic motion of the arms, combined to the action of the muscles, provides for this innate behavior [1]. The latter, in addition to the structure of the body with bones, muscles and tendons, permits to have a continuous exchange of energy from the muscular to the kinetic one. For this reason, the design of assistive devices should consider the human factor and the human physiology to restore the correct gait proprieties. It follows

A methodology for the development of active ankle prosthesis


that the most widespread solutions are obtained by mimicking the human physiology with mechanical systems [2]. In a gait of an able-bodied man, there are two phases: a phase when the structure of the body acquires and stores mechanical energy inside the skeletal muscle apparatus and a phase in which this energy is released. To perform a physiological gait, only a little amount of energy must be provided by the muscles, as an external contribution to the continuous exchange of energy [3]. On the contrary, in the analysis of amputees with a fixed foot, it is possible to notice that all of them show an unnatural gait due to the limited mobility of the ankle caused by a fixed joint; furthermore, there are not any degrees of freedom of the ankle joint and the only relative movement of the foot around the ankle is due to the flexion of the foot. This lack of the harmonic motion of the center of mass and, at the same time, the lack of a system that guarantees the energy recover and release, lead amputees with fixed foot to have a gait that requires more energy than an able-bodied man. A lot of study is conducted to assess the energy consumption (evaluated in CO2 production) during the gait of amputees. The energy cost depends on the anthropometric measurements, the type of amputation, the type of socket used and the type of prostheses [4-8]. As aforementioned, during the gait, the able-bodied men, recover and release energy with muscles and tendons; on the contrary, for the energy storage, amputees require a mechanical system to be charged and discharged.

In the last years, many studies were conducted to improve the perception of a more natural gait for the amputees. To achieve this goal, the research is focused on a different type of energy recovery system able to, at the same time, recover energy and restore it during the gait. The typical system is a foot, properly designed, acting like a bending spring and made of elastic material (i.e. carbon fiber); the hinge of the foot can be placed on the ankle [9] or on the tibia [10]. These prostheses are called “energy-storing-and-returning” (ESR), different from the normal conventional feet (CF) prosthesis that has not the ability to store energy inside it. On the one hand, these types of solutions permit to reduce the cost in CO2; on the other, they cannot provide for the control of the plantar-dorsi flexion of the ankle joint, the pitch and the control of the gait phase for the energy storage or release. For this reason, these solutions do not require electronic control systems and external power [11].

More recently, the researcher focused their aim to produce a prosthesis able to replicate the gait of an able-bodied man as natural as possible. To achieve this behavior, the solution of the ESR with an electromechanical system able to change the angle of the ankle, hereinafter called pitch, during the gait and during the change of slope or ground condition, is used. The most widespread mechanical systems adopt leverages with one or more coil springs or pneumatic muscle actuators [12, 13], acting like human tendons, joined to the ankle hinge [14-18] and widely adopted for their variable stiffness actuation [19], or other smart pneumatic device [20]. The mobility of the foot and the restoring of the kinematics of the ankle are enhanced by these solutions. Proprio Foot (Össur), the Elan foot (Endolite) and Motion and Raize Foot (Fillauer) are prostheses commercially available; they adopt hydraulic and electric actuators for the stabilization of the ankle-foot system, moreover they allow a natural kinematics of the ankle and the adaptability to different ground conditions. The last types of prostheses are called bionic ankle (BA) and actually there are not commercially available models that provide the control of when the energy stored inside the foot must be released and, also, there are not models that provide the little lack of energy that is missing to obtain a natural stride [11].

The goal of this paper is the development of a methodology for the functional design of ankle prosthesis, shown in designing an innovative active ankle prosthesis. The first step consists in the definition of a complete dimensionless model of the gait on a flat ground condition. This model allows to change the input parameters to adapt the simulation to the anthropometric measurements of the patient. The model is extended to obtain the trends of the

Michele Gabrio Antonelli, Stefano Alleva, Pierluigi Beomonte Zobel and Francesco Durante


force exchanged with the ground and the trend of the torque of the ankle, second step. The third step consists in the functional design of an innovative active ankle prosthesis based on a mechanical system hinged to the foot that can be able to store, release and produce power and, at the same time, able to change the pitch of the ankle. The innovative ankle prosthesis is based on a 5 bars linkage, this kinematics has 2 degrees of freedom (DOF). Two elements of the prosthesis can change its length: one is a shock absorber, that is able to store and release energy, the other is a linear actuator that is able to produce power and change the angle of the foot. The innovative architecture proposed, with 2 reserved elements if compared to [21], is applied to the dimensionless model of the gait as an ESR foot to assess the law of motion of the linear actuator (LA). Finally the fourth step with the architecture of the electronic control system: the control system detects the foot position and adjusts the operating parameters.

2. MATERIALS AND METHOD

2.1. Theoretical background

The goal of an ankle prosthesis is to replicate the behavior of the physiological ankle during the gait and at rest. The passive ankle-foot prostheses use an integrated system to store elastic energy during the early stage of the gait: usually, a flexion spring is integrated in the foot structure. The energy stored inside the foot allows the user to have a less energy expensive gait thanks to the recovering of all the potential energy, that in the physiological gait would be stored in tendons and muscles. The frequent problem in the passive ankle-foot prostheses is that the energy recovered during the single gait is not enough to allow a natural behavior: there is a lack of energy that must be provided to allow a natural propulsion.

In Figure 1 there are 3 pictures:

a. phases of a single gait

b. pitch

c. dimensionless trend of the power provided by a physiological ankle.

In a patient with a foot prosthesis equipped by an energy recovery system, the angle of the replaced joint of the ankle is not the same of the physiological one. With reference to Figure 1a, in correspondence of the point X, the prosthesis loses contact with the ground, so it is impossible to exchange any force with the ground. With reference to Figure 1c, it’s possible to distinguish 3 areas. The first area (I) starts from the phase of the heel strike: it is the area with the negative power. The area describes the amount of energy stored inside the muscle and tendons in the physiological ankle or inside an elastic element in the prosthesis. The second area (II) is the one with positive power, where the user starts the propulsion phase. In this phase, the energy previously acquired is released. The areas I and II are almost the same. As shown in Figure 1c, there is a third area (III) divided from the area II by the projection of the point X. The area III is not present in the case of a user with a prosthesis with an energy recovery system because at the point X the loss of contact with the ground occurs. The consequent lack of energy exchange has an impact on the gait, forcing the amputees to adopt a different gait from the natural one.



Figure 1 a) phases and sub-phases of the gait in able-bodied people; b) angle of the ankle (pitch); c) power (dimensionless) on ankle during a single gait

To replicate the gait of able-bodied men more natural as possible two aspects are important: obtain a gait that is comparable to the natural one in terms of torque/power and restoring the behavior of the ankle joint in terms of mobility during all the situations.

2.2. Dimensionless model

It’s the first step of the design methodology and consists in studying for the gait of able-bodied men with the construction of a dimensionless model of a lower limb in a numerical computing environment. Starting from experimental data acquired from a representative sample of able-bodied men, it is possible to obtain the graph of the angles of the lower limb during a gait on a flat ground. The data is acquired by a simulation conducted on a treadmill whose speed is automatically regulated by the users walking on it. The information is acquired by the technique of stereophotogrammetry with the pad placed on the lower limbs and the trunk. For this analysis, only three angles were detected: dorsi-planta flexion of the foot, corresponding to the pitch; flexion of the knee; flexion of the hip joint. From the acquired data, an average trend was deducted for the 3 joints. The detected angles are relative to the 2 bones of the joint taken into account. With reference to Figure 2a, the angle α used is converted to refer them to a reference system, centered on the hip joint, that maintains the horizontal and vertical direction respectively for x and y axes. β and γ are the angles between, respectively, femur and tibia and tibia and foot. Using the detected trends for the 3 joints of the lower limb, a parametric dimensionless model of the lower limb was implemented in a numerical computing environment. The model can replicate the dimension of the person of which it is necessary to replicate the gait. The parameters of the model are the dimensions in mm of: femur (AB), tibia (BC), foot (DE); the dimensions are to be considered as the distance between the characteristic hinges of the different links for femur and tibia, while for the foot



is intended its length, with the center of the ankle joint placed at 1/3 of its total length

2 / 3 DC CE⋅ = .

The dimensionless model is used for a simulation of one gait on a flat ground starting from the position of the heel strike and ending in the same position.

The simulation is divided in 100 steps: for each of them, the position of all the key points (A, B, C, D and E of Figure 2a of the virtual structure of the lower limb is calculated; hence, the values of the angles are calculated, as shown in Figure 2b.

Figure 2 a) schematic structure of lower limb; b) angles of joint of lower limb

2.3. Forces exchanged with the sensorized treadmill

Using the model developed by Kevin Deluzio in the C-Motion Software [22], it’s possible to analyze the force exchanged during all the phases of the gait, i.e. the step 2 of the design methodology. By means of Visual3D reader it is possible to calculate the force acting on the foot and the location of the application point. Conducting an image analysis, it is possible to determine the position of the application point of the force applied to the foot during the stance phase. The analysis is implemented inside a numerical computing environment and the model was implemented as a dimensionless analysis. The latter is conducted using the key points as the input data. With reference to Figure 3, the foot is schematized as a triangle whose vertexes are ABD: A is the heel, B are the fingers, D is the ankle joint. Finally, F is the application point of the force applied by the treadmill, C is the intersection of the direction of the tibia with the foot line AB and CF direction is considered orthogonal both to the direction CD and to direction of the force F. This direction and the direction CD of the tibia are also considered parallel each other. The distance L�� between the application point F of the force and the point C is made dimensionless by the expression:



Figure 3 Schematic model of foot analysis

The distance L�� between the application point F of the force and the point C is made dimensionless by the expression:

force

CFL

AB=

(1)

To obtain the direction of the torque, the direction of the vector ��was evaluated. It was analyzed only the stance phase. To obtain the torque as dimensionless trend, the input trend of the forces has been made dimensionless by dividing each value of the trend by the mass of user. The torque is calculated by the expression:

dimext

non force

user

CFFTorque L

M g CF−

= ⋅ ⋅

⋅

uuur

(2)

The analysis has been done by applying the equation (2) for every integration step of the stance phase (approximately 60% of total gait). Then, the collected data relative to the different integration steps were used to obtain a mathematical expression for an easier use in the next analysis. The mathematical expression was obtained with a curve fitting method made of a sum of 4 sine functions. To better obtain a torque trend like the physiological one, 20 points before and 20 points after to the calculated torque trend equal to zero were added. These points help to simulate the swing phase, where the torque of the ankle is zero, not represented by the previous trend. The obtained expression of the torque is:

dim 0.3824 sin(0.03235 0.4782) 0.1698 sin(0.1113 1.284)

1.422 sin(0.1908 4.113) 1.315 sin(0.1947 1.085)

non fitTorque x x

x x

− −= ⋅ − + ⋅ + +

+ ⋅ − + ⋅ − (3)

In Figure 4a the visual reconstruction of the simulation is shown: the foot and the tibia are represented with the blue segment, the C point with a black circle, the position of the force F with a red asterisk. The expression of the torque for standard anthropometric dimensions is:

dimnon fit user footTorque Torque M L− −

= ⋅ ⋅ (4)

where Lfoot is the length of the foot, distance AB in Figure 3. Figure 4b shows the trend of the torque during the gait.



Figure 4 a) visual reconstruction of the simulations; b) normalized ankle torque (dimensionless) during the gait

3. RESULTS AND DISCUSSIONS

3.1. Functional design of the active ankle prosthesis

To obtain a correct design of the ankle prosthesis, step 3 of the design methodology, this one should control at the same time the torque of the ankle and the pitch. The model of the prosthesis adopts the kinematics described in [21], but with two reversed elements. The kinematics is based on a structure made of a 5 bars linkage with 2 DOFs. With reference to Figure 5, the first replaces the tibia, element 4, and is connected by a hinge to the other, element 1, replacing the foot. The linkage is equipped with the element 5, corresponding to the motor, connected by 2 hinges to the elements 1-4 and 3. The shock absorber is represented by the element 2.

The active ankle prosthesis, Figure 5, is so composed by:

1. foot

2. shock absorber (SA)

3. rocker arm

4. prosthetic tibia (fixed to the stump of the user)

5. linear actuator (LA)



Figure 5 The kinematic chain of the active ankle prosthesis

Finally, since LA has a defined law of motion, the linkage has just 1 DOF. Tanks to this kinematics the upper attach point of the SA can modify its position, due to this aspect, hereinafter the prosthesis is called SAVAP (Shock Absorber Variable Attach Point). Without any interaction with the environment, the current configuration depends on the lengths of LA and SA. These elements can change their length to adapt to different situations, graded according to the gait phases:

• When the foot-ground contact occurs (stance phase), the foot exchanges force with the ground: it means that it is necessary to control the prosthesis with the correct torque;

• When the foot-ground contact does not occur, it is necessary to control the pitch to prevent stumbling.

• Due to these requirements, the problem has been studied as 2 sub-problems:

• The control of the pitch during the swing phase (no torque exchangeable with the outside world);

• The control of the torque of the ankle during the stance phase (pitch, when the foot is in contact with the ground, is automatically controlled).

Once the physiological torque is detected, there is the need of finding a way for the prosthesis to reproduce the same torque at the ankle level. It has to be noted that the architecture of the proposed prosthesis is able to give to the device the behavior of a passive prosthesis just by blocking the length of the LA, or giving an assigned law of motion. In this case, the prosthesis has 1 DOF and the foot is able to move with respect to the tibia under the elastic reaction of the SA. Hence, the idea is to perform a simulation by imposing the physiologically correct angles for the limb with the LA blocked and to detect the torque acting at the ankle level in these conditions. The torque will differ from the physiologically correct one detected as in the previous paragraph and this difference has to be provided in order to obtain the correct torque at the ankle joint. The compensation torque can be applied by the LA able to control its own length which, by means of the rocker arm 3, acts on the attachment point of the shock absorber.

The simulation activity to detect the torque acting at the ankle level with the LA blocked is here presented. The simulation is performed in the already considered numerical computing environment. The simulation is made commanding the element foot (1) and the element tibia (4) with the physiologically correct trends presented in Figure 2b. It is possible to change the parameters of the model to obtain more detailed results; besides the anthropometric



dimensions of the lower limb, it is possible to specify the mass of the human body and the stiffness of the shock absorber. After the inclusion of the parameters, the simulation starts and all the gait is evaluated in 100 steps.

The content of the simulation is explained in the Figure 6:

6a) the visual simulation of a complete gait, with the LA fixed in length and the SA that changes colour if the rod is inward (green) or outward (red);

6b) the length of the SA during the gait, for a fixed dimension of the LA;

6c) the speed of the rod of the SA during a gait. The speed is evaluated as mm/1% of gait. Introducing the duration of a single gait, it is possible to calculate the speed in mm/s;

6d) the resultant of the force exchanged with the ground, made dimensionless by the weight of the user.

This analysis permits to evaluate the force developed by each component. The contribute of the damping effect was neglected in the present analysis. Analyzing the results shown in Figure 6, it is possible to notice that if the LA changes its length, it changes the configuration of the device: the position of the attachment point of the SA changes, by changing the angle between the element 3 and 4, with the resulting change of the pitch. The adjustment of the length of the LA, during the swing phase, allows to adjust the pitch to better fit the trend of a physiological gait.

Figure 6 The behavior of the prosthesis design at a fixed LA during the gait: a) visual simulation of the lower limb; b) length of the SA; c) speed of the SA; d) force reaction with the ground

Meanwhile the goal of controlling the pitch is reached by controlling the length of the LA during the swing phase, to reach the goal of controlling the torque of the ankle during the stance phase, it is necessary to detect the differences between the physiological torque and the one provided by the passive prosthesis obtained by blocking the LA length. The first analysis is conducted starting from a comparison of two trends: the first trend, the blue one of Figure 7, is the trend of the torque of the ankle of able-bodied men; the orange one of Figure 7 is the trend obtained from the prosthesis with LA fixed in length and the foot following the same positions as in the simulation of Figure 6. The trends in Figure 7 is obtained from the previous



dimensionless model, but considering a body of 80 kg, a 42 (EU) foot and a stiffness of the spring of 75 N/mm.

Figure 7 Torque comparison between physiological torque and torque provided by the spring

As shown in Figure 7, the two trends are completely different. A simple spring cannot be used to obtain a natural gait in terms of torque. To achieve the last goal, it must be found the law of motion of the LA capable to obtain a trend of torque similar to the physiological one. To do this, the difference of torque of the two trends was calculated. This difference is the “differential torque” that must be provided by the LA of the SAVAP; changing its length, the LA can increase or decrease the compression of the spring of the SA. This action modifies the energy stored inside the SA; hence, the force expressed by it. Therefore, the difference of torque must be provided by the LA. The knowledge of the differential torque allows to achieve the law of motion of the SA by (5), where D is the lever arm of the shock absorber and K is the stiffness of the SA.

real springTorque TorqueDisplacement

D K

−

=

⋅ (5)

Figure 8 shows the obtained trend of the linear actuator to be considered only for the stance phase of the gait. The resulting trend is too complex for a motor: the continuous change of speed combined with the fact that the motor must produce enough torque to sustain the gait has forced to adopt a simpler trend that can be sustained by the LA. This trend is composed by 3 straight lines computed by (6). The behavior of the torque of 3 distinct types of ankle is analyzed:

• physiological ankle

• energy recovery foot

• biomimetic ankle with SAVAP presented in this work

The torque comparison shown in Figure 9 (dimensionless) has considered the energy recovery foot and the biomimetic ankle with equal stiffness, not considering any damping effects with an elastic constant for both prostheses coherent with the mass of the user.



Figure 8 Length of SA vs. gait phase to obtain a physiological gait

( %) /10 ( %) 40

1.45 ( %) 62 40 ( %) 60

5 ( %) 325 60 ( %) 65

Displacement stride for stride

Displecement stride for stride

Displacement stride for stride

= <

= − ⋅ + ≤ <

= ⋅ − ≤ <

(6)

Figure 9 Torque comparison with the prosthesis solution

As shown in Figure 9 the innovative ankle prosthesis design presented in this work has a better fitting of the physiological trend compared to the energy recovery foot. The filled area indicates the lack of torque of the SAVAP prosthesis compared to an energy recovery foot. This lack is provided by the LA that changes the configuration of the device during the gait, increasing or decreasing the energy stored inside the spring and, hence, modifying the force expressed by the SA.



3.2. Control system

Following the step 4 of the design methodology, it is necessary to define a preliminary draft of the control system for the actuation of the LA and of the SA during all the phases of the gait. To know in real time the gait phases, an approach of using two types of sensors, respectively for the two phases of the stride, has been embarked: in the stance phases, two sensors located under the foot will be used; in the swing phase, an inertial measurement unit (IMU) fixed to the frame of the prosthesis is chosen. The sensors under the foot are pressure sensors. By the analysis of the difference of these two sensors, it is possible to know the different pressure applied to the soles of the foot; hence, it is possible to distinguish the gait position during the stance phase. During the swing phase, because there is no contact with the ground, the IMU is used to calculate the approach angle of the lower limb, more specifically the angle of the tibia. This angle is unambiguous; hence it is possible to know also during the swing the gait position. The signals, at the same time, of the two pressure sensors and the IMU help to distinguish the types of ground in which the user is walking.

The system is developed, at this stage of drafting the control system of the active ankle prosthesis, as a functional blocks scheme, Figure 10. All the signals are acquired by a central processor unit that analyses the acquired data, processes them and, in real-time, adjusts the parameters of the two types of actuation: the control of the LA is made by a position control; the LA is controlled in closed loop and receives the length as input parameter. As regards the SA, the microprocessor unit must control the speed valves to perform a dumping effect or to block the prosthesis in a defined position.

Figure 10 Functional scheme of the control system

4. CONCLUSIONS

In this paper a methodology in 4 steps for the functional design of angle prosthesis is presented. The methodology is described as applied to an innovative active ankle prosthesis. The dimensionless model helps the user to fit as accurately as possible the simulation to the real behavior. The proposed kinematics of the ankle prosthesis should be able to control at the same time the pitch and the torque of the ankle. The result of the gait analysis, carried out on a flat ground, is used to identify the trends of the angles of lower limbs and to construct a dimensionless model able to reproduce the correct gait of an able-bodied man. The model is



broadened with the trends of torque and power. These trends are used as final goal: obtain the trends of angles, torque and power as close as possible to the physiological ones.

The mechanism of the prosthesis is made of a 5 elements linkage. Two of these elements can change the length: a linear actuator and a shock absorber. The first element provides the control of the pitch during the swing phase; in the stance phase, it changes its length to adapt the torque of ankle to the required one. The second element can store energy by one or two springs. The simulation is made only on a flat ground not considering the dumping effect/control. The analyses are carried out in the two phases: in the stance phase the aim of the prostheses is to copy the trend of angle; the torque is zero during the swing phase. To copy the physiological trend of the pitch, the law of motion of the LA is proportional to the pitch, due to this fact is not carried out in this work. In the stance phase, the analysis is carried out considering the prosthesis as an ESR and the trend of the torque is compared to the physiological one. The aim has been achieved by changing the length of the LA that can increase or decrease the energy stored inside the SA; for this phase, the law of motion of the LA is identified.

The control system is based on a central micro-controller unit. It detects in real-time the signals of three sensors. A closed loop control system has been conceived for the control of the actuator.

REFERENCES

[1] Koceska, N., Koceski, S., Beomonte Zobel, P. B, and Durante, F., Control architecture for a lower limbs rehabilitation robot system, Proceedings. IEEE International Conference on Robotics and Biomimetics ROBIO, Bangkok, Thailand, 2008, pp. 971-976.

[2] Renjewski, D., and Seyfarth, A., Robots in human biomechanics a study on ankle push-off in walking, Bioinspiration & biomimetics, 7(3), 2012, 036005.

[3] Donelan, J. M., Kram, R., and Kuo, A. D., Mechanical work for step-to-step transitions is a major determinant of the metabolic cost of human walking, Journal of Experimental Biology, 205(23), 2002, pp. 3717-3727.

[4] Waters, R. L., Perry, J., Antonelli, D., and Hislop, H., Energy cost of walking of amputees: the influence of level of amputation, J Bone Joint Surg. Am., 58(1), 1976, pp. 42-46.

[5] Nielsen, D. H., Shurr, D. G., Golden, J. C., and Meier, K., Comparison of Energy Cost and Gait Efficiency During Ambulation in Below-Knee Amputees Using Different Prosthetic Feet-A Preliminary Report, Journal of Prosthetics and Orthotics, 1(1), 1988, pp. 24-31.

[6] Schmalz, T., Blumentritt, S., and Jarasch, R., Energy expenditure and biomechanical characteristics of lower limb amputee gait: The influence of prosthetic alignment and different prosthetic components, Gait & posture, 2002, 16(3), pp. 255-263.

[7] Traballesi, M., Porcacchia, P., Averna, T., and Brunelli, S., Energy cost of walking measurements in subjects with lower limb amputations: a comparison study between floor and treadmill test, Gait & posture, 27(1), 2008, pp. 70-75.

[8] Versluys, R., Beyl, P., Van Damme, M., Desomer, A., Van Ham, R., and Lefeber, D., Prosthetic feet: State-of-the-art review and the importance of mimicking human ankle–foot biomechanics, Disability and Rehabilitation: Assistive Technology, 4(2), 2009, pp. 65-75.

[9] Arbogast, R. E., and Arbogast, C. J., US Patent No 4,865,612 Washington, DC. US Patent and Trademark Office, 1989.

[10] Nolan, L., Carbon fiber prostheses and running in amputees: a review, Foot and ankle surgery, 14(3), 2008, pp. 125-129.



[11] Cherelle, P., Mathijssen, G., Wang, Q., Vanderborght, B., and Lefeber, D., Advances in propulsive bionic feet and their actuation principles, Advances in Mechanical Engineering, 6, 2014, 984046.

[12] Versluys, R., Desomer, A., Lenaerts, G., Van Damme, M., Beyl, P., Van der Perre, G., Peeraer L., and Lefeber, D., A pneumatically powered below-knee prosthesis: Design specifications and first experiments with an amputee, Proceedings 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics, Scottsdale, AZ, USA, 2008, pp. 372-377.

[13] Antonelli, M. G., Beomonte Zobel, P., Durante, F., and Raparelli, T., Numerical modelling and experimental validation of a McKibben pneumatic muscle actuator, Journal of Intelligent Material Systems and Structures, 28(19), 2017, pp. 2737-2748.

[14] Au, S. K., Weber, J., and Herr, H., Biomechanical design of a powered ankle-foot prosthesis, Proceedings IEEE 10th International conference on rehabilitation robotics 2007, Noodwijk, The Netherlands, 2007, pp. 298-303.

[15] Hitt J., Bellman R., Holgate M., Sugar T., and Hollander, K., The sparky (spring ankle with regenerative kinetics) project: Design and analysis of a robotic transtibial prosthesis with regenerative kinetics, Proceedings ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference 2007, Las Vegas, US, 2007, pp. 1–10.

[16] Bellman, R. D., Holgate, M. A., and Sugar, T. G., 2008, SPARKy 3: Design of an active robotic ankle prosthesis with two actuated degrees of freedom using regenerative kinetics, Proceedings 2nd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics 2008, Scottsdale, AZ, USA, pp. 511-516.

[17] Hitt, J., Merlo, J., Johnston, J., Holgate, M., Boehler, A., Hollander, K., and Sugar, T., Bionic running for unilateral transtibial military amputees, Military academy West point NY, 2010.

[18] Belforte, G., Eula, G., Ivanov, A., Raparelli, T., and Sirolli, S., Presentation of textile pneumatic muscle prototypes applied in an upper limb active suit experimental model, The J. of Textile Institute, 2017, 1-10. http://dx.doi.org/10.1080/00405000.2017.1368111.

[19] Antonelli, M. G., Beomonte Zobel, P., Durante, F., and Gaj, F., Development and testing of a grasper for NOTES powered by variable stiffness pneumatic actuation, The International Journal of Medical Robotics and Computer Assisted Surgery, 13(3), 2017, e1796.

[20] Ferraresi, C., Maffiodo, D., and Hajimirzaalian, H., A model-based method for the design of intermittent pneumatic compression systems acting on humans, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 228(2), 2014, pp. 118-126.

[21] Antonelli, M. G., Alleva, S., Durante, F., and Beomonte Zobel, P. B., Ankle Prosthesis with an Active Control of the Pitch and the Release of the Energy, Proceedings RAAD17 International Conference on Robotics in Alpe-Adria Danube Region, Torino, Italy, 2017, pp. 825-832.

[22] C-Motion Research Biomechanics www.c-motion.com.

[23] Kashif Wani, Suspension Based Kinetic Energy Recovery System. International Journal of Mechanical Engineering and Technology, 7(6), 2016, pp. 142–157

[24] Abhishek Mohan Menon, Ananthapadmanabhan S.R, Ullas Innocent Raj, Wind Lens Energy Recovery System, International Journal of Advanced Research in Engineering and Technology (IJARET), Volume 5, Issue 8, August (2014), pp. 70-78

a methodology for the development of active ankle … · methodology for the functional design of...

Documents