1. IntroductionAlthough the passive ankle prosthesis [1] can help the disabled to return a certain amount of energy to help them during walking, it does not have the ability of active output, which leads to greater energy consumption [2] and gait distortion in amputee patients during walking [3]. Compared with the knee prosthesis, designing a powered ankle prosthesis is much more challenging, largely due to the load characteristics of the ankle, which can require up to 1.6 ± 0.2 Nm/kg of peak torque and up to 2.5 W/kg of peak power for medium-speed level walking [4], while the knee joint in the walking process absorbs energy, so it hardly needs excessive power output of the knee prosthesis. Therefore, how to improve the power-volume/mass ratio has become a core topic in the field of dynamic lower limb research.The concept of powered ankle prosthesis was first proposed by Herr [5], who demonstrated the effectiveness of powered prosthesis by measuring human metabolism [6]. Series elastic actuators (SEAs) [7] driven by motors has been the majority power kernel of powered ankle prosthesis. It has been proved that SEAs can amplify the power of the actuator by as much as 1.4 times under ideal load conditions [8]. In addition, SEAs can help enhance the force control ability of the actuator and reduce the shock load of the drive system, which are significant for gearboxes and screws [5]. Since then, a series of designs for ankle–foot prostheses have been proposed. SPARKy is ankle prosthesis with SEA powered by a 150 W DC motor designed by Sugar et al. in Arizona State University, USA. The prosthesis is enough to provide energy consumption and peak power output for an 80 kg subject walking at a speed of 1.8 m/s [9,10]. The later prototype SPARKy 3 introduces a pair of parallel mechanical Achilles tendons, which realizes the movement of ankle prosthesis in the coronal plane [11]. Grimmer et al. designed the Walk–Run ankle with SEA, powered by a 200 W DC motor [12]. The Walk–Run ankle was capable of providing 3 W/Kg in 1.6 m/s walking, 5.6 W/Kg in 2.6 m/s running, and the maximum torque was 2.1 Nm/kg. Herr added a unidirectional parallel spring based on SEA, so that SEA can choose lower spring stiffness to obtain better output characteristics while meeting the force bandwidth need of 3.5 Hz [5]. Their subsequent prototype of ankle and knee prosthesis TF-8 use SEA as their power kernel, which can provide a maximum torque of 160 Nm, a maximum velocity of 6 rad/s on its ankle joint, with an ankle segment mass of 2.6 Kg [13]. They concluded that the SEA can provide power compensation while adapting to more terrain.Parallel elastic actuator (PEA) [14] is another actuation concept, which usually combines the motor with a unidirectional spring to share the force required by the motor. Compared with SEA, PEA can significantly reduce the torque requirement of the motor to the peak power requirement, without any change in speed, and contributes to the force bandwidth improvement of the entire drive system. Verstraten carried out an optimization analysis of the design of ankle–foot prosthesis, and the results show that the unidirectional parallel spring is the optimal result in terms of both power and energy consumption for their selected motor [15]. Frank designed a transfemoral prothesis with brushless DC motors of 200 W used in each joint. The parallel spring is used at the ankle joint to make up for the shortage of output torque. The hole prosthesis is 4.5 Kg, with a maximum ankle torque of 130 Nm and peak ankle power of 250 W, which can meet the needs of daily activities such as walking at medium speed and going up and down stairs for adults weighing about 80 kg [16]. However, PEA is not suitable for those prostheses using mechanical reducers such as gearbox and screw. The PEA, despite the introduction of springs, is a stiff driver. For the mechanical transmission devices (e.g., gear boxes, ball screws, etc.), the shock load during heal strike can cause damage. In addition, for those using mechanical transmission devices, installing force sensors on the end-effector is difficult, while SEA can transform force control to position control, which is more available for mechanical prostheses.Electro-hydraulic actuator (EHA) is an alternative to the motor-mechanical reducer driver. EHA is a power-by-wire (PBW) servo system widely used in aerospace industry [17,18] which is appropriate for wearable robots due to its high output power to mass ratio, high controllability, and robustness. The University of Tokyo was the first to apply the EHA system to humanoid robots [19,20] and they demonstrated the advantages of the backdrivability of EHA over gear transmission in force control. Based on the Elan Foot passive hydraulic ankle–foot prosthesis produced by the company Blatchford, Dr. Yu from the University of Bath led the design of an electro-hydrostatic-powered ankle–foot prosthesis system, which can switch active and passive modes [21]. However, the hydraulic system of this prosthesis is energy-consuming and has a complex sealing structure. Wang designed an EHA-based prosthesis that is similar in function to AMP’s EEA [22]. It can charge the accumulator in advance and release it during the push-off phase. The simulation results show that the accumulator can provide 150 W peak power. Tessari designed a prototype of the EHA knee prosthesis [23] and he demonstrated the potential of the EHA system for high efficiency.According to the literature review so far, EHA has been regarded as a pure hydraulic system, and its excellent performance as a transmission device has never been reflected in the design of prosthetic limbs. PEA also has greater potential in terms of power and energy consumption than SEA. This study attempts to combine EHA and PEA, and provide full play to both advantages via their combination. In our previous work [24], an EHA-driven ankle–foot prosthesis design was proposed where the SEA was pre-defined as the actuation concept of the prosthesis and the spring parameters were designed by the limitation of the force bandwidth. In this article, we combined EHA with a unidirectional spring and design the spring parameter with optimization to minimize the energy consumption in a single cycle.The rest of the paper is organized as follows: Section 2 introduces the design of the ankle–foot prosthesis, including the design of hydraulic circuit and mechanical schematic, the part selection, and the parameter settings of the spring. Section 3 provides the prototype design, including the structure design and the control system. Section 4 is the experiment for validating the performance, and Section 5 is the discussion of the experimental results. Section 6 concludes this article. 5. DiscussionAccording to the above experiments, the prosthesis can meet the load profile with a peak torque of 120 Nm, a maximum speed of 4 rad/s, and a fast recover time of 0.2 s, which is acceptable for a 75 kg male. We emphasize the importance of satisfying the load profile, i.e., the demands of the ankle joint at every moment in the gait cycle, rather than the performance of the prosthesis itself. Therefore, we analyzed the motor model and design the prosthesis parameters with biomechanical data as the target load. A situation can be seen in [13], where the maximum power of the ankle was 552 W, but it cannot provide enough torque compared with the biomechanical data. The load profiles were also not matched in comparable active EHA prostheses [21,22].

From the perspective of power density, the mass of the prosthetic prototype is 2.6 Kg. Although meeting the requirement, the mass can be reduced to a considerable extent on the valve block, with the help of metal 3D printing. The gear pump is possible to be integrated with the motor as one part, so the power density ratio of the prosthesis can be improved.

For EHA system, the parallel spring reduces the torque requirement and therefore the pre-charge pressure. During this experiment, the pressure difference between the two chambers at maximum load did not exceed 40 bar, so a pre-charge pressure of 20 bar was sufficient. It also greatly reduces the flow of external leaks and reduces the requirement for seals. For EHA systems without springs [21], a higher pre-charge pressure is required, which significantly increases the complexity of the sealing device.From an overall design point of view, different choice of motors may lead to various designs. In Section 2.4, we obtained an optimization result of parallel spring in line with [15] which used a motor having similar characteristics to ours. In the selection of motor parameters, the choice of a motor with low inertia and high torque constant can help reduce motor current, thereby reducing motor energy consumption and improving efficiency. The inertial load was obvious, although we only applied an external elastic load, which came mainly from the inertial load of the motor. According to Figure 8, the first current peak was very close to the phase of the mechanical peak, while the second peak was close to the phase of the positive peak of the current, so it was mainly caused by inertial load. This illustrates the importance of choosing a small inertia motor, which is also mentioned in [15].PEA can reduce motor torque requirements as shown in Figure 6, avoiding motors from overcurrent. The optimization result of [13] is a series spring, largely because they choose the torque motor as the power source where the SEA was designed to compensate the speed requirement. In terms of power, we generally consider that torque motor is suitable for SEA, while the high-speed motor is suitable for PEA. A single spring should be chosen as far as possible, rather than the combination of SEA and PEA, otherwise it increases the mass of the system and increases the difficulty of control. If the optimization result is always the combination of SEA and PEA, the main reason may be the unreasonable setting of transmission ratio.