Abstract
Current commercially available prosthetic feet have succeeded in decreasing the metabolic cost and increasing the speed of walking compared to walking with conventional, mostly solid prosthetic feet. However, there is still a large discrepancy when compared with a non-disabled gait, and the walking pattern remains strongly disturbed. During the stance phase of the leg, these prostheses store and return energy using a spring element. This spring returns to its neutral position, which generates a push-off, but the foot extends much less than with a non-disabled gait. The walking pattern may improve with a more extended push-off. In this paper, we present a passive ankle-foot prosthesis that aims to deliver an extended ankle push-off using a specific planetary gearbox arrangement and locking mechanisms in order to release the energy in the spring over the full natural stretching of the ankle. In recent years, both powered and passive prosthetic devices have been developed. The prosthetic foot presented in this paper is a passive system, such that it has the possibility to be made lighter and more robust than, for example, one driven by an electric motor. Preliminary walking experiments were conducted with a transfemoral amputee.
1. Introduction
A variety of prosthetic feet are currently available that aim to restore the walking abilities of transtibial amputees. The SACH foot (Solid Ankle Cushion Heel) is the most basic prosthetic foot and is usually made of wood and rubber [1]. More active individuals generally wear an energy-storing-and-returning (ESR) foot [2], also called a “dynamic elastic response” (DER) foot [3], which is essentially an ankle-foot prosthesis with elastic and damping characteristics. This foot enhances the comfort of disabled individuals; nevertheless the capability of an ESR foot in mimicking the human ankle-foot complex is limited. Amputee gait speed remains lower than in normal walking [4] and many studies show that ESR feet have not solved the increased metabolic energy consumption which leads to early fatigue [5, 6]. In addition, the natural walking pattern remains greatly disturbed, which results in medical pathologies in the long run [7, 8].
Recent years have seen the development of various prosthetic devices that restore – to some extent – able-bodied ankle kinematics and kinetics [2]. Some are passive while others have active components. The prostheses of the SPARKy Project (Arizona State University) are electrically powered. They use an electric drive in series with helical springs to provide the required push-off power [9, 10]. Another is the powered ankle-foot prosthesis developed at the Massachusetts Institute of Technology, which uses a rotary series elastic actuator (SEA) with a 150W DC motor [11]. The system is constructed to deliver the characteristics of a natural ankle. These advanced prostheses are very promising, but they also entail a high degree of complexity and have limited autonomy. It is likely that, for these reasons, active ankle-foot prostheses are – at present – mainly at the research level and not available to a broad range of users. In contrast, advanced passive prostheses are also being developed, such as the CESR foot by Collins et al., which regenerates impact energy at the heel strike that is returned in the push-off [12]. To yield an increased return, the CESR foot must regenerate significantly more energy in the heel strike than the energy related to the heel strike in a natural gait. We developed an advanced passive prosthesis based on an essentially different approach which regenerates energy in the dorsiflexion phase and releases this energy over the entire push-off phase. As such, we aim to regenerate the energy in the same phase where a natural gait also regenerates most of its energy.
Under normal conditions, 93% of the work done by the ankle is related to motion in the sagittal plane (in the side view of a person) [13]. It is therefore reasonable to assume that the ankle function in the sagittal plane outweighs those in the frontal and transverse planes. In this work, only the sagittal motion of the ankle is taken into account. The ankle-foot complex is abstracted as a single rotational joint. The relative (in-plane) rotation between the foot segment and the lower leg segment is described by the terms dorsiflexion and plantarflexion. Dorsiflexion implies the bending of the foot towards the knee. On the other hand, plantarflexion is the rotation of the foot away from the knee. The angle between the foot and the leg will simply be called the ‘ankle angle’. When the leg is perpendicular to the foot's sole, the ankle angle equals zero and the angle is defined positive in figure 1.
Torque-angle plot of the human ankle in a natural gait. The values are averaged and can vary significantly between subjects. Data originates from [14].
An ESR foot stores energy in the stance phase of human gait as the elastic element is tensioned while the forward motion of the body is slowed down. Similar to a natural gait, the prosthetic ankle stores energy up to approximately +10°. In the late stance, the energy is returned in the “push-off” when the prosthetic ankle plantar flexes and the spring returns to its neutral position, so that the foot is perpendicular to the leg. In a natural human gait, however, the ankle plantar flexes three times more, up to approximately −20°. This discrepancy is hypothesized as a significant cause of the disturbed walking pattern seen with an ESR foot. This paper comprises the development of an ankle-foot prosthesis which delivers an extended push-off while the device remains a principally passive system. The prosthesis uses a specific planetary gearing arrangement combined with linear springs and pawl-ratchet mechanisms. This setup allows for the change of the equilibrium position of the springs and, consequently, generates an extended push-off. A passive device means that there is no need for electric drives or battery packs, which add bulk mass to the prosthesis. Secondly, a passive system is believed to be more reliable, which is crucial for disabled individuals. This prosthesis can be categorized as almost passive, since the locking of the pawls requires a minimal amount of power.
2. Requirements for the Prosthetic Design
2.1 Ankle-Foot Behaviour under Normal Conditions
Figure 1 shows the natural torque-angle data of the ankle [14], averaged over multiple gait cycles and individuals for a natural walking speed (about 1 Hz gait cycle or 120 steps/min). It is seen that after initial contact (IC), the ankle angle of able-bodied individuals evolves to about – 5° while a dorsiflexion torque builds up to roughly 0.05 Nm per kg body mass about the ankle joint. This part of the ankle characteristic realizes a quick and controlled foot-flat (FF) as the body weight is accepted by one leg. From FF onwards, the dorsiflexion torque gradually changes into a plantarflexion torque, while the ankle makes a dorsiflexion movement. When sufficient plantarflexion torque is built up about the ankle joint, the heel lifts off the ground. The maximum dorsiflexion angle (MDF) has now been reached. Immediately after MDF, the plantarflexion torque builds up even more, achieving a maximum of about 1.7 Nm per kg body mass. Next, this torque rapidly declines with the plantarflexion of the ankle. At toe-off (TO), the ankle torque approaches zero while the ankle angle is about −20°. The foot finally returns to 0° with a negligibly small torque. This motion provides foot clearance and prepares for the next IC.
The cyclic torque-angle curve indicates that mechanical energy is generated by the ankle joint. Clinical studies report that the ankle generates 250 W of peak power and 36 J of energy per step (80 kg subject at 0.8 Hz walking), which is significantly more than what is required at the knee and hip joints [15].
2.2 Ankle Characteristic and Prosthetic Design
From a mechanical point of view, figure 2 is very useful for the design of the prosthesis as it reveals the mechanical functions of the ankle-foot complex in a natural gait. It is hypothesized that establishing similar characteristics with a prosthesis is of major importance in improving the gait of individuals with a lower-limb amputation. The following behaviour is observed:
Between IC and FF, the ankle joint behaves as a quasi-linear spring where joint torque is proportional to joint position. The impact accounts for only a very small amount of energy, which is considered insignificant for storage and so unimportant for our goals. Therefore, this phase is not comprehended by the mechanism and neither does the abstraction account for the small torque. The mechanism freely allows for ankle rotation during IC to FF, but does not provide any torque.
Between FF and MDF the ankle joint behaviour is consistent with that of a nonlinear spring. 1 This phase is further called the “loading phase” since elastic energy is stored in the ankle joint, which will be returned in the subsequent phase.
The “push-off” phase from MDF to TO can be abstracted as a different nonlinear spring1 with a different equilibrium position that releases its elastic energy as it generates a plantarflexion ankle torque.
Abstraction of the natural torque-angle characteristic of the human ankle. Full curve: averaged biomechanical data of a natural gait, curve regenerated from [14]; Dashed curve: abstraction for the prosthetic design.
Since the amount of work generated during the push-off phase is higher than the amount of energy stored during the loading phase, additional work is supplied by the flexor muscles.2
2.3 Equilibrium Position
In figure 2, one notices that the angle range in which energy is released (push-off) is significantly larger than the range in which energy is stored (loading) in the ankle joint (ã 30° vs. ã 15°). Considering the abstraction with springs, there has been a change in the equilibrium position during stance: at the start of the loading phase (IC) the ankle angle and torque are almost zero, whereas the ankle angle approximates −20°, again with zero torque, at the end of the push-off phase (TO). The loading and push-off phase have a different equilibrium position. This phenomenon is crucial with regard to the design of the prosthesis as the proposed mechanism will effectuate the change in equilibrium position during the gait cycle.
3. Concept and Design
3.1 Working Principle
The working principle of the prosthetic device is shown in figure 3, where the system is depicted at four important instants in the gait cycle: IC, FF, MDF and TO. The mechanism consists of a leg segment, a foot segment and a lever arm, all of which rotate about the ankle joint axis. The respective angles are defined in the figure. The foot segment of the prosthesis is drawn horizontally to gain an insight into the concept. One end of a linear spring is attached to the lever arm, which is based on principles of the MACCEPA actuator [16], a compliant actuator with energy saving capabilities. The other end is fixed to the foot segment.
Mechanical set-up/working principle of the prosthesis. Naming of parts and definition of the leg angle and lever arm angle. Approximate values of the leg angle (in degrees) are indicated; from biomechanical data of a natural gait [14].
At the instant of IC, the leg segment is perpendicular to the foot segment (dashed line), resulting in an ankle angle of 0°. While the toe is nearing the ground, the rotation of the lever arm is disconnected from the leg and the lever arm is aligned with the spring. No torque is generated about the prosthetic ankle joint from IC to FF when the ankle angle is about −5°.
2 The amount of work/energy can be calculated using the area below the curve.
From FF onwards, the leg moves in the dorsiflexion direction (clockwise in figure 3). The lever arm is now linked to the leg through a transmission ratio n = ωleverarm / ωleg > 1, where ωi defines the derivatives of the respective angles. As the spring is increasingly extended, the torque about the prosthetic ankle joint builds up. The angular velocity of the lever arm is higher than that of the leg segment, which results in a high torsion stiffness.
The torque will increase sufficiently to raise the heel and subsequently the ankle's angular motion will change direction at MDF (ã+10°). In the plantarflexion direction, however, the gear ratio between the lever arm and the leg segment is set to 1 by the locking/unlocking system. The spring force returns the lever arm to its neutral position and the leg segment rotates with the same angular velocity as the lever arm. The energy stored in the spring now provides a push-off until TO is reached. After TO, in the swing phase of the foot, a soft reset spring (not drawn in the figure) drives the foot to its initial (perpendicular) position in anticipation of the next IC.
It is important to note that at FF (ã-5°), the system generates no torque about the ankle joint. The mechanism is in its first equilibrium position. At TO (ã-20°), the spring generates no torque about the ankle joint either. This is the second equilibrium state of the system. The prosthesis is able to shift the equilibrium position of the spring, which generates an extended push-off.
3.2 Mechanism
A planetary or epicyclical gearing [17] is a gear system consisting of essentially 3 elements: the central sun gear, the outer ring gear and the carrier with one or more planet gears (depicted in figure 4). Of these three elements, one can choose which element is the driving input and which is the output such that the third is then considered fixed. Different arrangements are possible that lead to different gearing ratios.
Classic representation of planetary/epicyclical gearing.
The central element of the prosthesis is a lockable planetary gearing, which allows the setting of a transmission ratio between the leg angle and the lever arm angle. Through the actuation of two pawls, either this transmission ratio can be set or else the leg and lever arm can be locked to each other, yielding a unity ratio. Figure 5 depicts the technical design of the gearings and lockings. Note that the pawls are bidirectional in order to allow for other strategies, but only one direction is used in this study. The planetary gearing is configured with the planet carrier as the input and the sun gear as the output while the ring gear is locked to the foot. This mechanism allows a compact design because the lever arm and the foot rotate about the same axis and a good quarter of the ring gear is sufficient for the range of motion.
Technical aspects of the planetary gearing and locking mechanism (lengths in mm).
The loading phase, from FF (ã −5°) to MDF (ã +10°), accounts for approximately 15° of the ankle motion (see also figure 6). The unloading phase, from MDF to TO (ã −20°) accounts for ã 30°. Thus, for the loaded spring to exercise this plantarflexion, a change of transmission ratio of 30/15 = 2:1 is theoretically needed – hence, n = 2. The ring, sun and planet gears were constructed with a transmission ratio of n = 2.33 for technical reasons. The planetary gearing and the locking mechanism are schematically drawn in figures 6 A and B. Figure 6A shows the working of the gear and locking mechanisms during the loading phase, whereas figure 6B shows the push-off phase. The swing phase and the phase from IC to FF are not shown, as the planetary gearing has no specific function there: both pawls stay released and the gears are semi-free to move, softly guided to the rest position by the reset spring. For simplicity, the foot is depicted fixed while the motion of the leg, gearing and lever arm are discussed. This is most practical, since one end of the spring is fixed to the foot. The sun gear is connected to the lever arm. The satellite gears are anchored on the leg segment. Note that pawlleg is connected to the leg and locks the sun gear, whereas pawlfoot is connected to the foot and locks the ring gear. At the start of the loading phase (indicated by FF), servo actuators press pawlfoot towards the ring gear and pawlleg towards the sun gear. From FF to MDF, the leg moves in a clockwise direction. Pawlfoot locks the ring gear to the foot while the sun gear is driven by the rotation of the leg through the planetary transmission. The sun gear rotates n times faster than the leg, which makes pawlleg ratchet over the sun gear ratchet. When MDF is reached, the leg starts moving in a counter-clockwise direction, driven by the spring force. In this direction, pawlleg locks the sun gear to the leg. The satellite gears' shafts are fixed to the leg; therefore, the ring gear will also rotate with the same speed as the leg and the sun gear. Pawlfoot ratchets over the ring gear ratchet.
Key instances of the mechanism during the gait cycle and the ratcheting behaviour, which changes the gear ratio. Approximate values of the ankle angle are indicated at the key instances. The spring is loaded over a range of ã15° and unloaded over a range of ã30°. A: Ratcheting of pawlleg while pawlfoot locks during the loading phase, ωsun > ωleg; B: Ratcheting of pawlfoot while pawlleg locks during the push-off phase ωleg = ωring – ωsun.
Essentially, the transmission ratio between the rotation of the leg and the rotation of the sun gear with the lever arm is different for clockwise and counter-clockwise rotation, respectively n and unity. Consequently, the equilibrium position of the spring is changed when the direction of rotation is inverted, which is at MDF or else the intersection of the loading and unloading phases. Evidently, the change in gear ratio yields a reduction of torque.
3.3 Desired Characteristics
The torque about the ankle joint, generated through the lever arm, can be calculated as a function of the angle of the lever arm using figure 7. The torque is given by
Calculation of the torque generated by the spring, definition of parameters.
Ideally, the single joint prosthesis is one that reproduces the natural angle and torque as a function of time when fitted to an amputee. It can be assumed that the prosthesis's torque-angle characteristic should approximate the able-bodied characteristic. This curve is not time-related, but strongly determines the dynamics of the walking person.
To generate the torque-angle characteristic, the torque at MDF is one of the parameters to be set. It is chosen to approximate the torque seen at MDF in an able-bodied gait. It may also be interesting to investigate whether higher torques can be realized, as this will also increase the energy return. The prosthesis is tuned to a body-weight of 90 kg of Mr. A, who is the test subject in this work. The corresponding torque at MDF is about 150 Nm. The spring and the spring pretension were chosen so that the torque at MDF equals 150 Nm at an angle of about +12°, which approximates the energy-storing characteristic seen in an able-bodied gait (for technical reasons, +12° were chosen instead of +10° as was proposed in section 3.2). The start of the loading phase was set at 0° in the calculation. It may be interesting to initiate the loading phase earlier, since this possibly increases the energy storage, but the limited speed of the mechanical set-up does not allow this: the limited speed of the servo motors implies a locking delay after FF and, thus a few degrees of dorsiflexion, before the loading phase is initiated. The resulting torque-angle characteristic is plot in figure 8. A theoretical torque change at MDF of a factor 1/2.33 is visible. This is an inherent consequence of the passive nature of the device. The subsequent push-off extends to about −17° at TO, where the resulting torque has decreased to virtually zero.
Simulated torque-angle characteristics.
3.4 Sensors and Actuators
In the previous sections, key mechanical parts such as the gearing, spring and pawl-ratchets are described. The complete prosthetic device includes several other components to make the system work, as indicated in figure 9. The pawls are actuated by standard servos of the type HS-7955TG from Hitec. One can note that the actuators (servos) are rather large. This is chosen to increase the versatility for testing. The servos are, for example, able to release a pawl under load. A Microchip PIC16F876A controls the locking and unlocking of the pawls according to the phase of the gait that is detected. The key instances that need to be detected to make the mechanism work are FF and TO. A switch on the hinged tip plate detects the ground contact of the tip, which is sufficient to detect FF and TO. To evaluate the prosthesis's characteristics, the ankle angle and torque are measured simultaneously. The controller does not need these measurements for the operation of the mechanism, so the sensors can be left out in a commercial product. A potentiometer is fixed to the ankle axle and measures the angle between the leg and the foot segment. A bending beam equipped with strain gauges is calibrated and measures the ankle torque. The microcontroller is battery powered so that the prosthesis is unrestricted.
The prosthesis prototype.
The mechanism changes states as follows: the phase between IC to FF is not comprehended by the mechanism (explained in section 2.2). At IC, and consequently, neither pawl is actuated from the prior swing phase and they stay that way. Next, the tip of the foot reaches the ground and the switch tells the microcontroller to actuate both pawls. Furthermore, the change in gear ratio occurs automatically at MDF, without specific actuation by the microcontroller at this instance. The one-directional ratcheting of both pawls provides the transition from the loading phase to the push-off phase. Note that MDF must not be detected. At the end of the push-off phase, the tip contact is disrupted and the microcontroller releases both pawls.
4. Results and Discussion
The prosthesis prototype was preliminarily tested with Mr. A, who is a transfemoral amputee aged 33. Mr. A has a completely healed, unilateral transfemoral amputation on the right side and is capable of independent ambulation. He is 180 cm tall, 90 kg in mass and has a thin, conical stump of about 17 cm. The developed prosthesis is actually intended as a transtibial prosthesis, but the goal of this test is to evaluate the device itself and Mr. A is very flexible and enthusiastic to experiment. In this section, the captured torque and angle data of slow over-ground walking are analysed.
4.1 Time-based Data
The time-based experimental data of one stride during a test with Mr. A is depicted in figure 10. Angle and torque data is plotted during a one stride, as well as the ground contact signal and the locking state of the pawls. A first remark to be made is that the ankle angle at FF is much more negative than that seen in a non-disabled gait. Mr. A is a transfemoral amputee who tends to take relatively large steps. He also has an aberrant knee angle, which may influence the ankle angle at FF. The range from IC to FF is not comprehended by the mechanism (discussed earlier), so this occurrence should have no influence on the performance of the system. A second remark is that the ankle angle goes out of measurement range around t = 1.4 s, while the torque is zero. This happens because of the rather large weight and inertia of the prosthetic foot. A very soft spring is used to return the foot perpendicular to the leg, which does not prevent the foot to quickly reach a larger angle. Although undesired, this is not expected to influence gait since it happens when the foot is in the swing phase. The energy storage-and-return – which is the range of interest – lies before the swing phase. Thirdly, the large oscillations are also the consequence of the poorly damped mechanism with the soft reset-spring. It is seen that, during the swing phase, the foot has returned to the reset position before the next IC, and so this should not have any further implication for walking.
Time-based ankle angle and torque data of a test with Mr. A, including ground contact signals and pawl actuation signals.
From FF to MDF the angle increases, which indicates dorsiflexion. At t = 0.8 s, the plantarflexion torque starts to rise, which indicates the loading phase. Between MDF and point C, the heel lifts off the ground while the ankle angle remains nearly constant. The ankle joint is virtually immobilized and the foot rotates about the tip. After point C, the angle rapidly decreases, which indicates the push-off or unloading phase. At point C, the torque delivered by the spring becomes sufficient to extend the foot. It can be assumed that at this point the body weight is partially transferred to the other leg. It is noticed in the angle curve that this push-off is delayed in the gait cycle compared with the push-off of an able-bodied person. In the ankle angle data from [14], the plantarflexion due to the push-off occurs very shortly after MDF.
4.2 Torque-Angle Data
The torque-angle plots in figures 11 and 12 of the same experimental data present additional, interesting information. Figure 12 contains the data of multiple gait cycles. This shows that the torque-angle measurements are repetitive for subsequent steps.
Torque-angle characteristics of the test with Mr. A.
Torque-angle characteristics of the test with Mr. A for multiple gait cycles.
Figure 11 represents the data during a single step and the key instants in gait are indicated. Note first that TO is not indicated in the figure because it lies outside of the boundaries of the plot (this is explained in the previous section). It can be seen that the loading curve approximates that of an able-bodied gait (shown in figure 1). In the measured data, the loading phase starts at about −1° (point A), which is only a few degrees further than in an able-bodied gait. At MDF, the torque reaches about 140 Nm, which is close to the value of 150 Nm expected from the able-bodied gait data. There is a discontinuity in the torque at MDF, yet there is no sudden change for the patient since the torque is defined by the direction of rotation and not, for example, by a sudden switching of lockings. The push-off curve follows the same course – as theoretically calculated (see figure 8) – which is lower in torque than the curve of an able-bodied gait due to the passive nature of the prosthesis. The push-off torque gradually decreases to virtually zero at about – 20° (point B), where TO would normally be located. Where conventional ESR prostheses do not provide any torque after 0°, we measured a remaining torque of about 25 Nm at 0° that still provides propulsion. This confirms the extended push-off that is characteristic of the prosthesis. Integration from MDF to TO results in a push-off energy of 11.0 J. This is a very promising value, bearing in mind that this prototype is a passive system and cannot return more energy than is stored. For comparison, an able-bodied individual with the 90 kg body mass of Mr. A has an energy storage in the ankle of 10.8 J (calculated from biomechanical data from [14]).
4.3 Evaluation of the Experiment
The experimental results confirm the theoretical torque-angle characteristics. The torque is slightly lower than the theoretical torque, particularly during the push-off phase. This may be due to elastic deformation of the mechanical components and frictional effects. Similar to the theoretical curve, an extended push-off is generated to about −20° in the experiments.
Mr. A did not really feel the extended push-off. He also indicated that he felt the weight of the prosthesis. The foot is reasonable for walking with, but he did not feel anything near the comfort of his own ESR foot. The latter can be expected since the acclimation period was very short. More extended experiments with multiple transtibial amputees will need to be performed in order to study the clinical effects of the prosthesis.
The preliminary tests have revealed several aspects that should be improved in a second prototype. First, the total mass must be significantly reduced using other materials and structural optimization. The test subject felt uncomfortable with a mass of about 3 kg, despite the fact that this approximates the weight of the body part that it is a substitute for [18]. The large mass also introduced undesired dynamics, visible in the experimental data. Secondly, the relatively low speed of the servo motors turned out to delay the start of the loading phase. A solenoid may be better suited so as to quickly and accurately lock the pawl, which might allow the regeneration of a larger amount energy. It would also be very interesting to lock the pawls without electronics – i.e., pure mechanically – which would result in an entirely passive device.
5. Conclusions
A new passive prosthesis was designed and tested. Unlike other advanced passive foot prostheses, such as the CESR foot by Collins et al., this foot regenerates energy during the dorsiflexion phase and releases its energy over the entire push-off phase. The device incorporates a planetary gearing and pawl-ratchets to change the equilibrium position of a spring. The spring as an energy storing element together with the gear switching generates an extended push-off to about −20°, while ESR feet only return to 0°. The prototype was tested with a transfemoral amputee and the results confirm the theoretical principle. The torque and angle data were measured on the device and the resulting torque-angle characteristics are close to the theoretical curve. The prototype has shown itself to be reliable for prolonged tests, which need to be performed with multiple individuals to study the clinical effects of the extended push-off characteristics.
