The rotation of the human forearm relies on the ulna and radius turning from a parallel state to an intersecting state. The successful realization of this movement depends on the complete distal radioulnar joint (Neumann, 2016). However, transradial amputation is the most common form of upper limb amputation, which leads to the inevitable destruction of the distal radioulnar joint. As the degree of amputation increases, the rotation ability of the residual limb decreases sharply. Even with a prosthetic hand, the patient’s ADLs are still greatly restricted due to the lack of the most important rotation function of the wrist. In this case, to achieve motion compensation, amputee’s body would inevitably be distorted during manipulation scenarios, which would not only seriously affect the amputee’s comfort, but also bring depression and anxiety to them (Bandara et al., 2014; Semasinghe et al., 2018; Billones et al., 2020). Moreover, it has been discovered that compared with further improving the performance of prosthetic hand, it is more effective to employ a prosthetic wrist to achieve a substantial overall improvement (Montagnani et al., 2015a; Deijs et al., 2016; Bajaj et al., 2019; Lee et al., 2021).

A survey of upper-limb prosthetic users showed that features such as lightweight, durability, and long duration of single charge (more than 12 h) are directly related to whether prosthetic products will be accepted (Mustafa et al., 2006), and among which, lightweight is the most important (Biddiss et al., 2007). Therefore, commercially available prosthetic wrists generally adopt designs those only have a single degree of freedom, retaining the most important rotational freedom to meet the lightweight needs. However, during manipulation tasks, the wrist plays a crucial role in precise positioning the prosthetic hand before the hand comes into contact with the target, and is heavily involved in maintaining stability of the target during the contact, which excessively requires the non-back-drivable ability of the rotating component. To address this issue, various solutions have been proposed, including motor holding brakes, high reduction ratio reducers, and worm gears. However, the motor holding brake only functions after a power outage and cannot continuously prevent torque from the load end (Ann et al., 2000). The latter two solutions may alter the transmission ratio, resulting in reduced movement speed and transmission efficiency. Therefore, how to design a miniaturized non-back-drivable mechanism without changing the transmission ratio so that the forearm rotational freedom can be locked at any position for any duration is a problem to be solved in the research of prosthetic wrists (Controzzi et al., 2010; Kimura et al., 2021; Shi et al., 2021), and is critical to the successful completion of the manipulation task (Gao et al., 2021). In most grasping actions which require to maintain the locking state for a long time, if the actuator lacks a self-locking mechanism, the external load will directly act on the drive motor and drive the prosthetic wrist in the opposite direction, resulting in not only an unstable wrist rotation angle, but also a potential hazard (Guo et al., 2020; Wei et al., 2023). This hazard would be exacerbated in the event of a power failure due to a depleted battery or circuit failure. The unlocked wrist joint will rotate freely under the action of the external load, posing a great danger to amputees. Therefore, prosthetic joints that take into account both miniaturization requirements and self-locking capabilities have become the main development trend, and the key component is the non-back-drivable clutch.

To be specific, the input end of the NBDC is the power system such as the drive motor, and the output end is connected to the hand and the external loads. When the input end receives a motion command and the motor starts to rotate, whether it is clockwise rotation or counterclockwise, as long as the initial torque is greater than the unlocking torque, the transmission system can be activated to achieve efficient power transmission. To the contrary, regardless of whether the external loads apply clockwise or counterclockwise torque to the NBDC, as long as it is within the maximum self-locking torque range, the mechanism will automatically enter the locking state, so that the external loads will not directly affect the drive motor. This feature gives the prosthetic joint the ability to maintain stable grasping at any position for a long time. It also possesses the ability to function without power supply during operation that does not need further rotating, extending the battery life to a certain extent. Therefore, designing advanced NBDC and continuously optimizing its self-locking performance can effectively improve the stability, safety, and endurance of prosthetic joints (Liu et al., 2022).

Researches focusing on how to improve NBDC performance have concluded five optimization directions (Chu et al., 2008; Controzzi et al., 2010; Controzzi et al., 2017; Montagnani et al., 2015b; Hu et al., 2021; Wu et al., 2023): (1) Low cost. In order to meet the large-scale production and implementation of self-locking mechanisms, the cost of related components need to reasonably controlled (Liu et al., 2021) while ensuring the performance and quality (Mota et al., 2023). (2) Simplicity (Zhang et al., 2023), including miniaturization (Ding et al., 2021) and ease of manufacturing and assembly (Controzzi et al., 2010). (3) Safety. Due to the sufficient interaction between humans and prosthetic limbs(Lu et al., 2021), safety is the primary concern in real practice (Hu et al., 2020). If the external load can reversely drive the prosthetic joints, it will cause secondary damage to the amputees. (4) Energy efficiency. How to improve the battery duration of a single charge has always been an important topic in the field of prosthetics (Cirelli et al., 2021; Okafor and Longe, 2022; He et al., 2023). If a single charge cannot satisfy an amputee’s normal use for a day, it will greatly affect its acceptance. As a result, reducing the friction energy loss and inertia would be of great importance (Cirelli et al., 2021). (5) Robustness. As the external load is determined by the actual manipulation tasks, the nominal self-locking torque should be high enough to cover most daily working scenarios.

Focusing on the above five requirements, Marco Controzzi et al. (Controzzi et al., 2010; Controzzi et al., 2017) designed a cylinder-based NBDC and applied it in the SmartHand (Cipriani et al., 2010), enabling it to effectively generate strong gripping force under strict power and weight constraints. Compared with the traditional non-back-drivable mechanism based on worm gears (Kang et al., 2015), this clutch, based on a wedge structure, achieves higher transmission efficiency. Within the load range from 50 Nmm to 150 Nmm, the maximum efficiency of this mechanism is around 0.95. Jun-Uk Chu et al. embedded a self-locking mechanism in the prosthetic finger joint (Chu et al., 2008). The self-locking mechanism adopts a coil spring and cam ball structure to prevent the reverse force of the grasped object on the fingers. However, the springs and cams in this mechanism suffer significant wear during operation, which does not meet the durability requirements of prosthetic devices. Qiqiang Hu et al. (Hu et al., 2021)were inspired by the ratchet spanner and employed an interlock to increase the grip strength of the fingers, enabling them to safely perform high loads and prolonged gripping tasks. However, when the ratchet mechanism is unlocking, it is always in a state of friction with the buckle and is prone to wear. At the same time, there is a certain amount of free travel in the self-locking process, resulting a small deviation at the load end. Xiaofeng Wu et al. (Wu et al., 2023) proposed a compact arc-groove self-locking mechanism with two linear springs embedded in the arc grooves, eliminating the need for additional mounting structures. The whole system is compact, small, and modular, enabling underdriven finger mechanisms to achieve adaptive gripping. However, the groove needs to be regularly filled with an appropriate amount of grease to reduce the impact of friction between the spring and the groove. Federico Montagnani et al. (Montagnani et al., 2015b) designed a non-back-drivable mechanism for miniaturized application scenarios such as finger joints. This mechanism can turn off the power after reaching a stable state, thereby avoiding accidental release of the grasped object, and absorbs the impact generated during grasping. However, this mechanism must also consider the corrosion of lubricants, etc., limiting its application in certain conditions. In summary, for the existing self-locking mechanisms, there are still unsolved problems such as not being able to lock instantly, excessive wear of the system under normal operating conditions, and the need to add grease to the mechanism in a timely manner.

In this study, in order to solve the above problems, a novel NBDC is proposed, which achieves self-locking based on the line-contact between the wedges and the fixed support, and can be applied in prosthetic wrists to realize rotational self-locking. The proposed mechanism consists of a fixed support, a wedge pedestal, four wedges, a pin pedestal and four pins, meriting low cost and simplicity in manufacture and assembly. As to the operating mechanism, it mainly contains three key states: (1) Self-locking state. No matter whether the output end, which is connected to the external loads, moves clockwise or counterclockwise, the loads cannot be transmitted back to the input end. (2) Intermediate state of unlocking. 7° of idle angle exists between unlock state and complete lock state. (3) Unlocking state. When the torque at the input end drives the pin to rotate more than 7° of idle angle and reach 14°, the driving force would be transmitted to the output end, and then the self-locking system start to rotate as a whole. Simulations and Experiments have been conducted and verified that the self-locking structure could resist a reverse torque of 600 Nmm from the output end, and only requires an unlocking torque about 80 Nmm at the input end, making it highly efficient for the implementation in prosthetic wrists or other rotating joints.

The main contributions of this paper are as follows:

(1) A non-back-drivable clutch with self-locking features is designed, which does not change the transmission ratio of the system and can ensure the motion speed of the rotating forearm under the premise of stable manipulation. (2) A wavy spring with suitable stiffness is designed to switch between unlocking and locking modes in the self-locking system, separating the wedges from the support in the unlocking state, reducing the friction and improving the efficiency. (3) Critical working conditions of the self-locking system are analyzed and verified through detailed kinematic analysis, static analysis, transient dynamic simulations and experiments, proving the performance of the proposed system that the self-locking ability reaches 600 Nmm.

The rest of this study is organized as follows. Section 2 introduces the overall design of the new NBDC mechanism, and calculates the theoretical performance of the mechanism through kinematic analysis, static analyses and transient dynamics analysis. Section 3 introduces the experimental platform construction and result analysis of NBDC. Section 4 introduces applications with NBDC embedded in a prosthetic wrist. Section 5 discusses the limitations of this research and possible improvements in the future. The final conclusions can be found in Section 6.

The proposed NBDC based on line-contact self-locking mechanism mainly consists of a fixed support, four wedges, a wedge pedestal, four pins and a pin pedestal. The pin pedestal can be used as the connection to the input end, through which the power system such as the motor could be connected. Four pins are mounted along the circumference of the pin pedestal, the pin drives two sets of wedges to rotate, ultimately generating a self-locking state, an unlocking intermediate state and an unlocking state together with the fixed support (see in Figure 1). Each wedge set is composed of two opposite wedges, connected by a wavy spring in the middle. The shape of each set of wedges is mirror symmetrical. The groove below the wedge connects the pin, and the groove presents a “V” shape. The fixed support is connected to the work platform through bolts, and also connected to the pin pedestal through bearings and pins. Its function is to provide self-locking through the friction between its inner wall and the top arc surface of the wedge in self-locking stage, absorbing the impact from the output end. This clutch is embedded between the wrist rotation motor and the harmonic reducer in practice, with its input end connected to the output shaft of the motor and its output end connected to the harmonic reducer. The specific section view and exploded view of the NBDC mechanism are shown in Figures 2A, B, respectively.

According to the previous analysis, a 3D model was established, and a prototype was assembled. The pin pedestal, wedge pedestal, wedges and fixed support are made of aluminum alloy (7,075 series), wavy springs were customized (stainless steel, 301 series, stiffness is around 0.30 N/mm), the four pins were selected as standard parts (stainless steel, 304 series, Φ 2.5 × 8), the four flange bearings are standard MF63ZZ 3 × 6 × 2.5 (bearing steel, 45#). The prototype is shown in Figures 12B, C, with a diameter of 33 mm and height of 15 mm, weighting 25.5 g.

The NBDC was positioned between two JNNT-S dual keyway torque transducers to test the unlocking torque from the input end and the maximum self-locking torque from the output end, which are shown in Figure 12A. The system configuration is as follows:

(1) The input end and output end were connected to the connecting flange through tightening screws, and then connected to the JNNT-S double keyway torque transducers through an elastic coupling (static torque transducer, movement range of 0°–180°, torque range of 0–20 Nm).

In order to test the bidirectional unlocking idle angle, a 10 cm long rocker was installed at the input end and the output end respectively to facilitate the experiment. The WT901164K angle sensors (sampling frequency is 2000 Hz) were placed at the center of the shafts to capture the angle changes of the two ports simultaneously, as shown in Figure 12D.

By applying torque to the input and output ends respectively, the corresponding response was recorded by the torque sensor. As shown in Figure 13A, when the input end is unlocked, the output torque lags the input torque change and the difference is within 80 Nmm. This value is the unlock torque of the system, which is basically the same as the theoretical value in Figure 5D. From the results of transient dynamics, the self-locking torque of the system during normal operation is about 600 Nmm. When the load applied to the output is 600 Nmm, as shown Figure 13B, there is barely no torque response from the input end (less than 40 Nmm in both directions), which is consistent with the finite element simulation. The reason for the torque fluctuation at the input end is when the diagonal wedge self-locks, the other diagonal wedge rotates a slight angle, and during the rotation, the inner wall of the wedge groove transfers part of the force to the corresponding pin. The force is further transmitted to the torque sensor through the pin pedestal. This small torque will not cause back-driving phenomena at the input end. By rotating the rocker in both directions at the input end, it can be seen that the angular response of the output end is shifted by 14°, as shown in Figure 13C, which is consistent with design of the idle angle.

To better demonstrate how the proposed component could be used in practical applications, a prosthetic wrist with rotation function was built, integrating the proposed NBDC. There are three reasons for the chosen of the application scenario: (1) The rotational degree of freedom of the wrist is mostly used in practice (Seo et al., 2017). (2) The rotation of the wrist is prone to stay unchanged once reach the target angle (Neumann, 2016). (3) The physiological rotational movement of the human wrist comes from the rotation of the radius around the ulna, and the actual rotational movement occurs near the elbow joint. If the amputation was executed near the hand, the amputee would still retain some rotational function of the forearm and does not need a rotationally functional prosthetic wrist. Thus, the prosthetic wrist module with rotational freedom is suitable for amputees with amputations close to the elbow, providing ample space for the implementation of the prosthesis. Figure 14 illustrates the application scenario where the proposed locking component was integrated to a prosthetic wrist. The prosthetic wrist was attached to the amputee through a prosthetic socket, and the constituent components of the prosthesis from the socket to the hand were the driving motor, the self-locking component and the harmonic reducer respectively. The integrating of the proposed locking component would allow the transmission of the rotational motion of the motor to the load transparently, while the time-varying torque generated at the load side would be prevented from transmitting back by this component, which ensures the stability of the prosthetic joint and reduces the power consumption. The component, with a diameter of 33 mm and a length of 15 mm, weighting 25.5 g, could theoretically be integrated in series to any forearm joint except the hand without compromising the total weight and dimension, and thus has the potential to be widely used in prosthetic rotary joints.

Figure 15A illustrates the self-locking performance experiments of NBDC in a prosthetic wrist system, where the self-locking ability of the wrist joint was tested with and without NBDC, respectively, and the results are shown in Figure 15B. Since the harmonic reducer itself has certain self-locking capacity, the upper limit of the self-locking capacity of without the embedded NBDC component is 750 Nmm. By contrast, the self-locking capacity with the NBDC reaches 3560 Nmm in this experiment. It is worth pointing out that 3560 Nmm is not the upper limit of the system with the NBDC, but a safe experimental limit set to protect the harmonic reducer. From the calculation and analysis in Section 3, it can be seen that the theoretical upper limit could reach 600 × 100 = 60,000 Nmm under this condition. However, excessive loads would not occur in real application scenarios, and the improvement from 750 Nmm to 3560 Nmm could adequately demonstrate that the embedding of the NBDC mechanism could bring significant improvement in the self-locking performance of the rotary joint. The specific mechanical requirements and wearability requirements are summarized in Table 1.

This paper designed a new type of NBDC mechanism, theoretically analyzed the self-locking conditions of the model and the influence of different friction coefficients on the self-locking performance, revealed that the friction coefficient μ c f should be at least 0.16, as shown in Eq. 26, which was verified in a transient kinematic finite element simulation shown in Figure 10. The current locking torque of the mechanism is still not ideal, which is mainly constrained by the materials of the two contact bodies. In this paper, 7,075 aluminum alloy is chosen due to the lightness, which is important for prosthetic wrists. If lightness is not the primary consideration, materials with higher yield strengths could be adopted to further increase the maximum locking torque. In the simulation for the performance of different μ c f , as shown in Figure 11, a higher μ c f is preferable to improve the locking torque, and the friction coefficient of the contact surfaces can be further improved by means of surface sandblasting, etc. However, the potential to improve the locking torque in this way is limited, so we chose μ c f = 0.25 as a representative case. In terms of the surface contact form, line contact is currently adopted in this study, which limits the performance to a certain extent, where further improvement could be expected by expanding the contact area. For the number of wedges, it is possible to follow M. Controzzi’s research (Controzzi et al., 2017) by placing more wedges through dimensional optimization, further enhancing the self-locking performance. In terms of the idle angle, it only exists on the motor side, but not on the load side, which is to say, if the motor moves, it has to offset an idle angle before it starts to drive the load. The motion and force on the load side in any direction will not be transmitted to the motor side. In terms of the unlocking torque, the main constraint is the stiffness of the wavy spring. High stiffness will increase the unlocking torque and make it more difficult for the system to work properly. Low stiffness will potentially result in the failure of the spring or the inability to recover the self-locking state in the case of the maximum deformation. Therefore, the type of spring should be optimized in the future to reduce the unlocking torque of the system. During normal operation, driving from the motor requires a 14° idle rotation to trigger the unlocking state of the NBDC, which helps to reduce wear inside the mechanism, but would introduce a position error for the control system. Fortunately, this idle angle can be compensated by an external angle sensor.

In this paper, a novel NBDC is proposed, which can be applied in the forearm rotary motion joints of prosthetic wrists. It may save power to a certain extent under the premise of guaranteeing the safety and stability of manipulations. Detailed kinematic, static and transient dynamic analysis were carried out, and a prototype of the proposed design was assembled and tested to verify its self-locking and unlocking performance. Experimental results showed that the bidirectional self-locking torque of this NBDC for external load is about 600 Nmm, and the unlocking torque at the input end is about 80 Nmm. It is worth pointing out that connecting a reducer in series between the output end and the load can further expand the self-locking performance of the mechanism, thereby expanding its application scenarios.