Introduction

According to a global study, over 35 million individuals worldwide live with lower limb amputations due to traumatic causes1. Individuals with above-knee amputations typically lost knee joints, resulting in more than 80% more energy cost to walk and diminished quality of life relative to non-amputee individuals2,3. Prosthetic knees are the predominant solution for improving ambulatory capability and quality of life of transfemoral amputees, mainly from functionality and comfort aspects3. Despite restoring the basic daily ambulatory functionalities such as walking on level ground, stairs, and ramps, it has been an open challenge to also make the prosthetic knees more comfortable, in terms of lightweight, bionic (polycentric), shock-absorbance, and user-centric. For this purpose, prevailing prosthetic knee design strategies usually utilize multi-bar mechanisms, dampers, and motors4,5,6,7,8,9,10. Unfortunately, the high-density, rigid, metallic mechanics always tend to be large, heavy, complex, and difficult to manufacture, which hinders the further development of rigid prosthetic knees11.

Recent advancements in soft materials are poised to transform the field of robotics, offering innovative solutions and enhanced capabilities12,13. Soft materials, characterized by low density, yield lightweight devices. Their inherent flexibility enables compliance and impact absorption. Furthermore, 3D printability facilitates the customized fabrication of soft wearable robots14,15. These have advanced the development of wearable robotic systems16,17,18,19,20,21,22,23,24,25,26,27,28,29. Soft prostheses such as soft hands27 and soft knees28,29 have been proposed and developed to provide an alternative way of designing light, biomimetic, and cheap prostheses. Notably, the inherent properties of soft materials coincide with the design goals of knee prostheses, making it an alternative way to deal with the open challenge of the prosthetic knee design aspect. Nonetheless, in the context of prosthetic knee applications, achieving controllable polycentric knee flexion during the swing phase while maintaining a high-impedance structure capable of supporting human weight during the stance phase poses a considerable challenge for soft robotics. This difficulty arises from the inevitable ineffective deformation inherent to soft materials that discommode the control as well as the insufficient load-bearing capacity due to compliance, hindering their applications on prosthetic knees. Nor did previous proposals of prosthetic knees28,29 delve into the comprehensive discussion of applications on transfemoral amputees and address the above-mentioned actual problems.

To overcome the challenges, we have employed origami technology, which has experienced remarkable growth within the realm of soft robotics, primarily due to its capacity for substantial deformation during deployment30,31,32,33,34. Emerging research indicates that elastomers reinforced with origami structures exhibit improved performance by reducing ineffective deformation while maintaining a broad range of motion35,36. By constraining facets, it becomes feasible to calculate the intricate deformation of a 3D structure based on a crease pattern designed in a 2D plane, adhering to origami principles. However, despite paper-reinforced elastomers enhancing structural stiffness, identifying an appropriate structure for prosthetic knees remains challenging. Prosthetic knee applications demand both a high loading capacity and lightweight design, necessitating further exploration into innovative solutions.

Plants exhibit numerous structural and functional properties that inspire the development of biomimetic lightweight structures. Horsetails, a commonly seen plant worldwide, are characterized by tubular structures, with some species capable of reaching heights exceeding 5 meters with outer diameters of approximately only 2 centimeters37. Research38,39 has been conducted to reveal the nature of the bending resistance capacity of this kind of plant. It has been proved that they have outstanding stability against fracture during their growth. Upon observation of the segments of their stems, cross-sections of internodes reveal a structure consisting of a thin outer ring of strengthening tissue stabilized by the much thicker inner ring of soft tissue (parenchyma) in the effect of turgor pressure. We have further observed morphological fold structures inside the inner ring formed during the growth of the pith cavity. When subjected to transverse compression, the deformation of the hypodermal sterome (outer strengthening tissue) is less pronounced than that of the parenchyma (inner soft tissue), resulting from further concavity along the folds. This localized concavity leads to increased squeezing on cells in this direction, resulting in elevated turgor pressure. The pressure-induced stability thus protects the stem from fracture, ensuring the continued growth of the horsetail. By leveraging the two key concepts: pressure-induced stability and morphological concave structure, we have achieved the design of lightweight structures exhibiting high loading capacity and structural stability.

In this study, we innovate a soft prosthetic knee for transfemoral amputees, characterized by its lightweight (300 g) and compact design (15 cm in height and 12 cm in width). Utilizing thermoplastic polyurethane (TPU) and 3D printing technology, we have achieved rapid manufacturing of low-cost prosthetic knees, which also streamlined the user-centric design. Drawing upon origami principles, we have devised a specific crease pattern for the knee structure that enables biomimetic polycentric knee rotation within a specific range of motion. By employing origami reinforcement, we have reduced the inefficient deformation of soft material and established an appropriately simplified mathematical model to calculate the kinematic behavior as well as the minimal output torque of the prosthetic knee. Inspired by the horsetail structure, we have introduced pressure-induced stability and morphological concave behavior to the origami design, which enhances the knee’s loading capacity while preserving its mobility and operational capabilities. Preliminary benchtop experimental results demonstrate that the prosthetic knee can emulate the centroids of biological knees, with the mathematical model exhibiting agreement with measurements. The bioinspired structure allows the soft knee to support up to 75 kg—nearly 250 times its weight. The inherent damping property of the elastomer and the pneumatic chamber ensures better shock-absorbing performance against impact from different directions of the soft knee relative to the rigid knee. Clinical trials have illustrated the potential significance of this innovative prosthetic solution for multi-terrain ambulation, indicating a promising direction for further development and refinement.

Results

System overview

The proposed soft prosthesis consists of a soft knee and a carbon fiber foot (Fig. 1a). The knee comprises the thigh linkage, the shank linkage, and a pneumatic chamber with origami reinforcement (Fig. 1b). Based on the folding basics of origami, we have designed a 2D crease pattern of the anterior part of the origami structure (Fig. 1c) to mimic the trajectory of the instantaneous center of rotation (ICR) of a biological knee (the detailed process is shown in the Supplementary methods). By folding the 2D plane according to the designated mountain and valley to a certain degree and subsequently constraining certain edges, we can obtain the 3D origami frame of the structure. Utilizing origami theory, we can calculate the 3D structure based on the design parameters of the crease pattern and the initial state of the 3D configuration. Assuming the facets remain immutable, the 3D structure’s deployment follows the same kinematics as expected. By employing a simplified mathematical model, we can determine the ICR trajectory of the origami structure from the design parameters. Furthermore, by adjusting the crease pattern’s design parameters, we can control the ICR trajectory within a specific range of motion, thereby mimicking the biological ICR trajectory. Here, we mainly focus on the level-ground walking task, since this is the major function amputees acquire in daily life. As the knee joint usually undergoes a bending angle of around 60 degrees during level-ground walking, we only focus on mimicking the ICR in this range. Figure 1d presents the schematics of the soft knee flexing from 0 degrees to 60 degrees.

Fig. 1: Origami-based soft prosthetic knee.
figure 1

a The left is a photo of the soft knee. The right is the schematic of the soft knee. b Schematic of the side view of the soft knee and the origami chamber. c Morphing process of the anterior and the posterior part of the origami structure. d Knee flexion process of the soft knee.

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Biomimetic polycentric origami knee flexion

We targeted to mimic the biological polycentric knee flexion using the origami principle. The biological ICR is determined by the intersection of the instantaneous helical axis on the sagittal plane or its parallel planes according to a biological model40. We aimed to mimic the ICR trajectory during level ground walking, corresponding to a knee flexion range from 0 to 60 degrees. We set the target trajectory as the biological ICR trajectory on a parallel sagittal plane situated 60 mm laterally from the knee’s center (Supplementary Fig. 9). A set of design parameters was identified through an optimization process under certain constraints, detailed in the Supplementary material. By tuning these design parameters, we can change the degree of asymmetry between the upper half part and the lower half part of the structure, further adjusting the ICR trajectory of the soft knee.

Bioinspired weight-bearing mechanism

We have investigated horsetails found in Sichuan, China (Fig. 2a). Figure 2c depicts the cross-sectional observation of the internodes of the horsetail segment corresponding to unloaded and loaded states, respectively (Fig. 2b). As indicated in the detail views in Fig. 2c, when transverse compression is applied to the segments, turgor pressure increases under conspicuous indentations, further stabilizing the structure against buckling. Moreover, morphological folds in the parenchymatous tissue form concavities that compress the cells when subjected to perpendicular force. This results in a localized increase in turgor pressure, preventing local buckling and contributing to the overall structural stability. The fundamental principles are fluidic pressure-induced stability and morphological concavity.

Fig. 2: Horsetail-inspired stabilized soft structure.
figure 2

a A photo of the horsetail. b Unloaded and loaded states of the segment of the horsetail. c Corresponding cross-section of the segment under optical microscope observation reveals that the horsetail’s morphological concave strengthens the structural stability through increased turgor pressure under transverse compression. The deformation of the epicondyle (E) is smaller than that of parenchymatous tissue (PT) shown in the detailed views. The color bar indicates the strain in the parenchymatous tissue, where the warmer the color, the higher the strain the tissue has. The red arrows indicate the direction of pressure inside the horsetail under higher deformation of the parenchyma that strengthens the outer ring. The white arrows show the deformation direction of the shape of the inner ring and the outer ring. The experiment was repeated for 3 different samples. For each sample, the measurement was repeated 10 times. d Schematics of the origami chamber. e The prosthetic knee in the unloaded (left) and loaded (right) states, corresponding to the swing (left) and stance (right) phases during walking, respectively. f Detailed view of the origami chamber in the unloaded (left) and loaded (right) states. The red arrows indicate the direction of pressure inside the chamber that strengthens the knee structure. The black arrows show the deformation direction of the shape of the posterior part and the anterior part.

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As illustrated in Fig. 2d, to integrate the principles into our soft knee unit, we have made the stiffness of the anterior part higher than the posterior part by adjusting the angles between the loading direction and the creases. Thus, the anterior part functionally works similarly to the strengthening tissue in the horsetail. Moreover, we have transposed the pressure-induced stability to our design by integrating a pneumatic chamber that generates a rising internal fluidic pressure in response to compressive forces like the turgor pressure. Further, to achieve morphological concavity, we designed a synchronized movement between the expanding dihedral angle formed by the two front triangles and the drawing closer together of the thigh and shank linkages during knee flexion under weight-bearing. The posterior part assumes a curvature due to the proximity of the thigh and shank while concurrently being stretched towards the anterior part as the dihedral angle expands. This coordinated process engenders the desired concave behavior under compression. The concavity of the posterior part emulates the squeezing action exhibited by the morphological folds in horsetail parenchymatous tissue.

Consequently, when the knee is subjected to weight during stance (Fig. 2e), as the knee flexes under compression, morphological concavity occurs, and there is an increase in pneumatic pressure under indentations, which serves to stabilize the local structure against buckling (Fig. 2f).

Estimation of the output torque

Output torque is paramount in evaluating active prosthetic knees, particularly crucial during the design phase. It gauges the capacity of the prosthesis to restore and mimic the movement abilities of the amputee. However, in soft robotics, predicting the kinetics and kinematics of pliable materials presents a significant challenge, complicating the calculation of output torque during a bending process. In this study, we employ the principle of virtual work on a simplified elastic deformation process to estimate the output torque. Further analytical analysis and experimental trials confirm that this estimation represents a lower boundary for the actual output torque, thus serving as a viable reference point for future prosthetic design considerations.

In compliance with the principle of virtual work, and under the presumption that the Thermoplastic Polyurethane (TPU) material exhibits flexibility without stretchability, the computed output torque \({\tau }_{c}\) is symbolized through a generalized closed-form expression, as denoted by Eq. (1):

$${\tau }_{c}=({P}_{in}-{P}_{atm})\cdot \frac{{{\rm{d}}}V}{{{\rm{d}}}\theta }=P\cdot \frac{{{\rm{d}}}V}{{{\rm{d}}}\theta }$$
(1)

where P is the internal gauge pressure, \({P}_{in}\) is the internal absolute pressure, and \({P}_{atm}\) represents the atmospheric pressure. The virtual knee flexion angle change and the volume change in the equilibrium are represented by dθ and dV, respectively.

Furthermore, upon relaxation of the initial assumption and considering the elasticity of TPU, additional work is necessitated to surpass the energy barrier formulated by this elasticity when the posterior part transforms between convex and concave shapes. When we denote the work derived from elasticity as \({{\rm{\delta }}}{W}_{elast}\), it renders a positive contribution during the knee extension phase, thus correlating directly with the angle variation dθ. As such, the actual output torque, considering TPU elasticity and denoted as \({\tau }_{a}\), can be calculated as:

$${\tau }_{a}=\frac{P\cdot {{\rm{d}}}V+\delta {W}_{elast}}{{{\rm{d}}}\theta }={\tau }_{c}+\frac{\delta {W}_{elast}}{{{\rm{d}}}\theta }\ge {\tau }_{c}$$
(2)

This calculation affirms that the estimated output torque \({\tau }_{c}\) serves as a lower boundary for the actual output torque. Details of the derivation are elaborated in the Supplementary materials.

Benchtop testing

We have performed a series of benchtop experiments to measure the kinematic and kinetic properties of the soft prosthetic knee joint to demonstrate its capabilities.

Knee flexion verification

Figure 3a presents the range of soft knee flexion from 0 degrees to 90 degrees, corresponding to the cavity pressure from 0 KPa to − 85 KPa. The knee closed-loop step position tests showed rise times between 143 and 152 ms, depending on the position step size (Fig. 3a right). Thus, the -3-dB bandwidth of the knee position controller was between 2.3 and 2.5 Hz, which exceeded the position bandwidth of the biological knee41.

Fig. 3: Benchtop experimental results of kinematics and kinetics of the soft knee.
figure 3

a Origami knee flexion angle under contraction (left). Data are shown as mean ± std (n = 10). Each data point represents a technically independent replicate. Step response of the knee closed-loop position controller (right). b Origami deploying ICR trajectory mimicry to the biological ICR in the parallel sagittal plane 60 mm lateral from the knee center regarding the 0 to 60 degrees knee flexion (left). Measured trajectories of points A, B, and D compared to the mathematical modeling results of corresponding points (right). c Shock-absorbing test in three directions on the soft and rigid knee joints, respectively. d The knee unit holds a series of weights with different pre-charged pressures. Data are shown as mean ± std (n = 10). Each data point represents a technically independent replicate. e Measured versus calculated results of the output torque of the knee unit.

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ICR trajectory verification

Through the mathematical model, we have calculated a specific ICR trajectory to fit the target biological ICR trajectory in the range of 0 degrees to 60 degrees (Fig. 3b left) with the RMS value of 0.037065. We have also quantitatively analyzed the goodness of fitting for the measured trajectories with the respective theoretical trajectories of the three points, A, B, and D, which are involved in calculating the mathematical ICR trajectory. The RMS values of points A, B, and D are respectively 0.403412, 0.413472, and 0.007992 (Fig. 3b right).

Shock-absorbing capacity verification

We compared the shock-absorbing capacity of the soft knee unit with the rigid knee under the impact from three different directions. For the impact from distal to proximal (Fig.3c left), we applied 1000 N force on the shank. The impact force through the rigid knee unit decreased to 980 N (98.0% of the applied impact force). Through the soft knee unit, the impact force decreased to 865 N (86.5%). For the impact from anterior to posterior (Fig. 3c middle), we applied 150 N force on the shank. The impact force through the rigid knee unit decreased to 126 N (84.0%). Through the soft knee unit, the impact force decreased to 100 N (66.7%). For the impact from lateral to medial (Fig. 3c right), we applied 150 N force on the shank. The impact force through the rigid knee unit decreased to 144 N (96.0%). Through the soft knee unit, the impact force decreased to 122 N (81.3%). On average, the soft knee absorbed 14.5% more impact force than the rigid knee (the baseline was the applied impact force).

Weight-bearing capacity verification

We measured the weight-bearing capacity of the soft knee unit under different pre-inflated gauge pressures with a maximum strain of 5% (Fig. 3d). The structural loading capacity peaked at 350 N. When an additional pre-charged pressure of 20 kPa was applied, the unit’s maximum loading capacity experienced a significant increase to 580 N. Furthermore, the weight-bearing total exhibited a positive correlation with the level of pre-charge pressure applied. At a pre-charged pressure of 80 kPa, the knee unit could withstand a force of 750 N with a 4.6% compression.

Output torque capacity verification

We measured the output torque capacity of the soft knee unit under different pre-inflated gauge pressures and different positions (Fig. 3e). The obtained measurements are depicted via red points, juxtaposed against the blue surface and corresponding points, which illustrate the estimated torque-angle relationship under varying pressures as per Eq. (2). The results demonstrate that the actual output torque consistently exceeds the calculated values.

Clinical testing

Treadmill walking tasks

Figure 4 shows the experimental results for the participant walking on the treadmill at a pace of 1.0 m/s (Supplementary Movie 1) and 1.25 m/s (Supplementary Movie 2), respectively, wearing the proposed soft knee joint and the daily used rigid knee joint. We have collected data on the affected side and the sound side respectively, in terms of hip angles, knee angles, the muscle activity of the rectus femoris, the ground reaction forces (GRF), and the axial forces and displacements on the shank and thigh. To evaluate the performance of the participant walking with the soft knee and the rigid knee, we extracted a series of characteristic parameters for gait symmetry analysis (Table 1), including the peak hip extension angle (PHEA), the peak hip flexion angle (PHFA), knee flexion at heel strike (HSFA), the peak knee flexion angle (PKFA), peak muscle activity during swing (SW PMA), peak ground reaction force at heel strike (HS PGRF), stance percentage (STP), peak vibration force (PVF), and peak vibration displacement (PVD).

Fig. 4: Treadmill walking experimental results with the soft knee and the daily-used rigid knee.
figure 4

The line graphs display the statistical hip and knee joint angles, muscle activity of rectus femoris, ground reaction force (GRF), and vibration forces on the thigh and the shank during one stride. The histograms next to the line graphs show statistical results of the peak knee flexion angle (PKFA), heel strike flexion angle (HSFA), peak hip flexion angle (PHFA), peak hip extension angle (PHEA), swing phase peak muscle activity (SW PMA), heal strike peak ground reaction force (HS PGRF), peak vibration force (PVF), and peak vibration displacement (PVD) during treadmill walking. Data are shown as mean ± std (n = 3). Each data point represents a biologically independent replicate. The histograms at the bottom show the gait symmetry index. The red color represents the soft prosthetic knee, the blue color represents the rigid prosthetic knee, and the gray color represents the corresponding sound knee. For the vibration forces and displacements, the lighter color represents the force on the shank, while the darker color represents the thigh.

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Table 1 Clinical evaluation of treadmill walking
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Multi-terrain walking tasks

Figure 5 shows the kinematic data at the hip and knee joints recorded for the participant wearing the soft knee joint walking on stairs (Supplementary Movies 3, 4) and ramps (Supplementary Movies 5, 6) and crossing obstacles (Supplementary Movie 7) during treadmill walking. To evaluate the performance of the participant completing complex tasks with the soft knee, we extracted a series of characteristic parameters for gait symmetry analysis (Table 2), including the peak hip swing flexion angle (SW-PHFA), the peak hip stance flexion angle (ST-PHFA), the peak knee swing flexion angle (SW-PKFA), the peak knee stance flexion angle (ST-PKFA), the peak hip extension angle (PHEA), the peak hip flexion angle (PHFA), the peak knee flexion angle (PKFA), and the knee flexion at heel strike (HSFA).

Fig. 5: Different ambulation tasks with the soft prosthetic knee.
figure 5

Representative images of the amputee performing stair ascent, stair descent, ramp ascent, ramp descent, and obstacle crossing. The red color represents the soft prosthetic knee, and the gray color represents the corresponding sound knee. The histograms next to the line graphs show statistical results of the peak hip flexion angle during swing (SW-PHFA) and stance (ST-PHFA), peak knee flexion angle during swing (SW-PKFA) and stance (ST-PKFA), peak hip flexion angle (PHFA), peak hip extension angle (PHEA), heel strike flexion angle (HSFA), and peak knee flexion angle (PKFA). Data are shown as mean ± std (n = 3). Each data point represents a biologically independent replicate.

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Table 2 Clinical evaluation of multi-terrain walking
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All corresponding gait symmetry indices (SI) are calculated with the same method we used previously7.

Outdoor performance

To further test the functionality of the soft prosthetic knee, three participants were asked to perform outdoor fast walking and normal speed ascending and descending stairs and ramps (Supplementary Movies 8, 9, 10).

Discussion

Knee prostheses, as the predominant method for above-knee amputation rehabilitation, should be designed based on the needs and desires of prosthesis users. Functionality, regarding ambulation abilities on different terrains, and comfort, in terms of lightweight, bionic, and shock-absorbing, are the two most important aspects demonstrated by both researchers and users. Besides, considering that the needs and preferences can vary widely across each prosthesis user, a prosthetic knee should be designed user-centrically to satisfy the versatility. Further, above-knee amputees commonly lack the financial means to receive high-end technological prostheses, so it is emerging to provide cheap prosthetic support.

In this study, we have innovated soft prosthetic knee joint for transfemoral amputees. It features a lightweight (300 g) and compact (15 cm in height) wearable component. We have introduced an origami-based structure that can perform biomimetic polycentric knee rotation according to the targeted ICR trajectory. The TPU-based knee joint can be 3D printed and fabricated in two days at a low cost (less than $200). By integrating pressure-induced stability and morphological concave structure inspired by the structure of horsetails, we stabilized the soft structure to achieve the capability of supporting body weight (~ 75 kg) and actively providing a certain degree of torque (~25 Nm). The inherent damping property of the elastomer and pneumatic chamber can absorb impact forces from different directions. The amputee wearing our soft prosthetic knee can perform multi-terrain ambulation. This innovative design has provided an alternative way to build a lightweight, bionic, shock-absorbing, user-centric, and cheap soft prosthetic knee joint for transfemoral amputees to use.

Benchtop experiments have demonstrated that, with facet reinforcement, the prosthetic knee adheres to the predictions of the model grounded in origami principles. The soft prosthetic knee has a sufficient range of motion to support amputees’ daily ambulation requirements on stairs. Although the elasticity and the small pump employed have decreased the bandwidth of the soft knee position controller, it seems just enough to satisfy the walking requirements. In addition, the shock-absorbing experiments verified that the soft knee showed better shock-absorbing capacity than the rigid knee. Furthermore, the weight-bearing verification experimentally indicates that the proposed pre-charged biomimetic structure elicits a significant increase in structural stiffness, mirroring the horsetail structure’s stabilization against buckling via turgor pressure. The knee unit’s maximum loading capacity can be tuned through adjustments in the pre-charged pressure. Specifically, the proposed knee unit, with proper pre-charging, has the capability to sustain the weight of a human. Through the output torque verification, the results emphatically demonstrate that the actual output torque consistently exceeds the estimated values. The maximum 25 Nm output torque can be further increased by increasing the elasticity, the thickness of the chamber, and the inner pressure. However, the preliminary design can still satisfy the requirements of assisting an 85 kg amputee in ascending or descending stairs, just like the semi-active prosthetic knees7,42 do.

Clinical experimental results from ambulation trials demonstrated that the soft prosthetic knee could support the amputee in walking at normal speed, with comparable performance in gait symmetry compared to the passive prosthesis. However, kinematic data of knee flexion at the heel strike (HSFA) shown in Fig. 4 and Table 1 implies that the soft knee shows a better approximation to the sound side than that of the rigid knee. In addition, the gait symmetry index also implies that the participant shows better gait symmetry in the peak knee flexion angle (PKFA) during treadmill walking. The elasticity of the pneumatic chamber allows the soft knee to perform slight knee flexion passively when receiving increased compressive forces at the heel strike. Further deformation at the heel strike would increase the inner pressure of the chamber which in turn stabilizes the knee from further flexion. Thus, the soft knee can keep its robustness while performing small deformation to absorb impacts from varied loads. On the contrary, as for the rigid knee, though the hydraulic cylinder can absorb impacts from knee flexion, the rigid frame and the linkages are non-deformable and cannot absorb impacts from other directions. This is also proved by impact absorbance experimental results shown in the benchtop experiments and the axial force and displacement measurements (PVF and PVD) shown in Fig. 4 and Table 1. The axial impact forces through the soft knee are considerably reduced relative to those through the rigid knee, which implies that the impacts conducted to the residual thigh through the soft knee are smaller than those through the rigid knee. This result indicates the potential advantage of the soft knee in comfort relative to the rigid knee. Furthermore, given that the soft prosthetic knee is lighter than the rigid one, the electromyography (EMG) signal on the residual rectus femoris shows that the amputee exerts less effort on hip flexion during walking with the soft knee than wearing the rigid knee. Improved gait symmetry on the stance percentage of the affected side also indicated that the participants could walk better without swinging their residual leg in advance. Consequently, despite the fact that the amputees are relatively unfamiliar with the soft prosthetic knee compared to their regularly used prosthetic knee, they were still able to walk with comparable gait symmetry and enhanced comfort when wearing the soft prosthetic knee. Furthermore, the preliminary validation of multi-terrain ambulation indicates that the soft knee can support the amputee to ascend and descend stairs and ramps step over step at self-selected speed and cross obstacles during treadmill walking. As the soft knee is unfamiliar to the public, it takes time for the participant to get used to the knee. Thus, the amputee is very careful when performing heel strikes on stairs and ramps, which affects the gait symmetry in the stance phase.

The development of the soft prosthetic knee offers an alternative design approach for lower limb prostheses. Unhindered by traditional mechanical constraints, prosthetic knees can be designed in alternative ways. Designers can realize various functions of a prosthesis simply by adjusting the shape of a specific soft structure, negating the need to differentiate functional modules. Functional modifications such as damping, centers of rotation, and range of motion might be achieved by altering parameters like the length of an edge, the scale of an angle, or other structural characteristics. To actuate the soft knee, designers have more flexibility to select methods without the constraints of mechanical connections and transmissions. Leveraging 3D printing technology simplifies the process of adjusting design parameters and manufacturing the device, thereby meeting the requirements for customization and research with relatively low economic and time costs. We believe that the development and validation of this soft prosthetic knee has inaugurated an interdisciplinary research field.

While the proposed soft prosthetic knee represents an initial stage in design development, it carries certain restrictions within its current structure. The origami-inspired configuration, though innovative, can only replicate a portion of the instantaneous center of rotation (ICR) trajectories inherent to organic knee movement. Nonetheless, it paves the way towards achieving biomimetic polycentric knee rotation utilizing origami-based architectures. At present, the maximum velocity achieved by an amputee while using this soft knee is approximately 1.25 m/s. This speed is relatively slower compared to the fast walking speed of 1.5 m/s. This could potentially be attributed to the user’s lack of familiarity with the soft knee mechanism.

Methods

This paper has presented an innovative soft prosthetic knee. To validate the designed soft prosthetic knee, we first set up a mathematical model to calculate the relationship between the 2D crease pattern design with the 3D origami structure. We further calculate the spatial geometric deployment of the 3D structure to obtain the maximum knee flexion angle and the trajectory of ICR. Based on the biological ICR model and the design restrictions of the origami structure, we found a series of design parameters that meet the design objective (Supplementary Table 1). According to the virtual work principle, combined with the mathematical model, we have calculated the minimum output torque surface of the knee. Finally, we 3D printed the knee architecture and embedded the electric system with a finite-state-based control strategy.

Benchtop testing

For the knee flexion and the ICR trajectory verifications, the soft knee was placed in a motion analysis system (Motion Analysis, USA) with the shank pylon secured on the platform. Four markers were affixed to positions corresponding to the set points A, B, C, and D in the mathematical model, as described in the Supplementary materials. By measuring the coordinates of these four points, we could calculate the knee flexion angle. The chamber pressure was measured by an air pressure sensor (XGZP6847A040KPG33). Since we used points A, B, and D to calculate the ICR trajectory within the model (detailed in the Supplementary material), we assessed the model’s validity by comparing the measured trajectories of these points.

For the shock-absorbing capacity verifications, the thigh pylon of the soft knee was fixed on a frame. A servo electric cylinder (NFT60-T16-300-P10, China) was set in three different directions to hit the shank of the soft knee with pre-set forces. The force for impact on the distal-proximal direction was set to 1000 N. For impact on the anterior-posterior and lateral-medial directions, the forces were set to 150 N. The cylinder approached the prosthesis with a speed of 500 mm/s to mimic the impact from heel strike and kicking on obstacles. When the impact force increased to the set maximum force, the cylinder stopped, and the six-axis force sensor (SRI M3717C, China) recorded the forces on the thigh.

For the weight-bearing capacity verification, the shank pylon of the soft knee was fixed on a computerized electronic universal testing machine (UTM4503X, Suns Tech, China) and subjected to compression from proximal to distal, thus simulating the weight-bearing process. The gauge pressure of the knee unit was successively adjusted to 0, 20, 40, 60, and 80 kPa in the series of compression experiments.

For the output torque capacity verifications, the thigh and the shank pylons of the soft knee were fixed on a specifically designed frame equipped with an angle sensor (Angtron-RE-25) and a torque sensor (CJJN-1) to measure the static torque corresponding to specific angles and pressures. The measured angles were set incrementally at 0°, 10°, 20°, 30°, 40°, 50°, 60°, 70°, and 80°. Concurrently, the pressures were regulated from 10 KPa to 80 KPa in 10 KPa intervals.

Ethics

All participants provided written informed consent, and the study was approved by the Ethics Committee of Peking University.

Clinical testing

We recruited three participants with transfemoral amputation (36 ± 4.6 years old, 1.74 ± 0.13 m height, 71 ± 15 kg body mass; Supplementary Fig. 15 and Supplementary Table 3) for this study. To perform kinematic alignment for the prosthetic knee, we relied on accumulated professional experience and subjective feedback from the participants, all under medical supervision.

The participant was directed to complete a specific locomotion circuit whilst wearing the prosthetic knee. The treadmill walking tasks involved ten trials on a treadmill at both his self-determined comfortable speed (1.0 m/s) and a set speed (1.25 m/s), each lasting three minutes. Identically, the participant was asked to repeat the same locomotion circuit using his regularly employed prosthesis. Stair and ramp ambulation tasks involved ten trials for each task with self-selected speed wearing the soft prosthetic knee joint. For the obstacle-crossing task, the participant was asked to walk on the treadmill at his comfortable speed and cross the obstacles set in the anterior simultaneously.

Data collection entailed gathering kinematic information through a motion capture system (Vicon Valkyrie 16, Oxford Metrics Limited, UK). In addition, muscle activity from the rectus femoris on the affected side was captured via wireless EMG sensors (Delsys Trigno, DELSYS, USA), while ground reaction forces were recorded via the force plate on the treadmill (Bertec FIT 5, Bertec, USA). Data is collected and analyzed using Nexus (Nexus 2.16.0, Oxford Metrics Limited, UK). Through this data, gait symmetry was calculated. The gait symmetry index (SI) was computed based on the same method used in our previous work7. Further, we have also recorded the axial displacements (WT-VB01-485, China) and forces (M3713C, SRI Instrument, China) from vibration during walking on the prosthetic shank and thigh to verify the shock-absorbing capacity of the soft knee joint.

Origami structure design

The origami design of the knee should address biomimetic polycentric rotation and the weight-bearing strategy inspired by the horsetail simultaneously. Although the soft knee unit is 3D printed in one piece, the proposed origami structure functionally comprises two parts: the anterior part, and the posterior part. The anterior part is designed as the main part to achieve a polycentric rotation and to achieve the concave behavior on the posterior part.

For the 2D crease pattern design for the anterior part of the deployable structure, the solid lines are defined as mountains while the dashed ones as valleys (Supplementary Fig. 10a). A1A2D2D1 is defined as a rectangle. A12 and D12 are the midpoints of lines A1A2 and D1D2, respectively. The pattern is symmetric with respect to lines A12D12. Connecting E1 and E2 as a subline intersecting with line A12D12 at point E12. So, E12 is the midpoint of line E1E2. Based on this crease pattern, we have extracted 4 design parameters for the mathematical model setup. We defined the length of A1E1 as L1, the length of D1E1 as L2, the angle \(\angle {{\rm{A}}}1{{\rm{BA}}}12\) as \(\alpha 1\), and the angle \(\angle {{\rm{D}}}1{{\rm{CD}}}12\) as \(\alpha 2\). Then We could always fold the 2D plane according to the crease pattern and coincide A1A12 with A2A12 and D1D12 with D2D12 to form the 3D structure (Supplementary Fig. 11c). The dynamic state of the spatial structure is determined by the dihedral angle of plane BCE2 and plane BCE1. Then we defined half of the dihedral angle as \(\beta\). During knee flexion, the origami structure would fold, where \(\beta\) would increase as the dihedral angle would expand. From equations (35) – (38) in the Supplementary materials, we could know that the angles \(\angle {{\rm{A}}}1{{\rm{BE}}}12\) and \(\angle {{\rm{DCE}}}12\) are inversely proportional to \(\beta\). Supplementary Fig. 3a shows the decrease of angles \(\angle {{\rm{A}}}1{{\rm{BE}}}12\) and \(\angle {{\rm{DCE}}}12\) during the deployment. The increase of \(\alpha 1\) would make the curve steeper (Supplementary Fig. 3b). Similarly, the increase of \(\alpha 2\) would make the curve steeper (Supplementary Fig. 3c). The change of parameters \(\alpha 1\) and \(\alpha 2\) would change the degree of asymmetry between the upper half part and the lower half part. This asymmetry change would result in a change in the ICR trajectory of the polycentric rotation.

The posterior part is mainly designed to follow the motion of the anterior part and form a chamber together with the anterior part. Supplementary Fig. 10b shows the posterior part crease pattern design. We defined a diamond-shaped 2D crease pattern AbE1bDbE2b. Connecting AbDb and E1bE2b. The two lines intersect at point E12b. Defining that points E12p and E12d are the trisection points of AbE12b and DbE12b, respectively. Connecting E1bE12p, E1bE12d, E2bE12p, and E2bE12d. The triangles bounded by the dashed lines are the area to strengthen, so the posterior part could provide strength against the human body weight while still following the deployment of the anterior part. Conventionally, the posterior part cannot fold according to the origami rules. However, considering the stretchable property of the material, the posterior part shows a morphing behavior as a stretchable origami unit. By constraining lines AbE1b, AbE2b, DbE1b, and DbE2b, to lines AE1, AE2, DE1, and DE2, respectively, we could integrate the posterior part and the anterior part together and form the knee unit with the posterior part is convex (Supplementary Fig. 10c). During the knee flexion, as the dihedral angle \(\angle {{\rm{E}}}1{{\rm{E}}}12{{\rm{E}}}2\) expands, the posterior part is compressed due to the decreasing of angles \(\angle {{\rm{A}}}1{{\rm{BE}}}12\) and \(\angle {{\rm{DCE}}}12\). Meanwhile, the posterior part is also stretched to approach the anterior part because of the expansion of the dihedral angle. As a result, points E12 and E12b move towards each other, and the posterior part transfers from convex to concave.

Control architecture

For all amputee experiments, we have implemented a hierarchical control system with three nested layers to enable different ambulation modes (Supplementary Fig. 11).

The high-level controller selects the desired ambulation mode. Here, we manually select the ambulation mode. All finite-state machines in this controller contain four states: Front Stance (FST), Back Stance (BST), Front Swing (FSW), and Back Stance (BSW). The transition between these states is based on the orientation of the thigh (whether the thigh is in front of the body or behind the body) and the ground reaction force (whether the foot is in cadence or on the ground).

The mid-level controller generates the desired inner pressure based on the desired ambulation mode. For the four states in the high-level controller, different control strategies are used. For FST, the valve is set to inflate, and the chamber should be pre-inflated to a certain pressure, and the inner pressure changes according to the ground reaction force. For BST, the valve is set to inflate, and the chamber should be pre-inflated to a certain pressure, and the inner pressure changes according to the thigh position. For FSW, if the ambulation state is stair ascent, the valve is set to deflate, and the inner pressure changes according to the thigh position; or else, the valve is set to inflate, and the inner pressure changes according to the thigh position. For BSW, the valve is set to deflate, and the chamber should be pre-deflated to a certain pressure, and the inner pressure changes according to the thigh swing speed.

The low-level controller is a closed-loop pressure controller. The desired pressure and the current pressure are input to the controller.

Embedded system

As shown in Supplementary Fig. 12, the microcontroller (STM32f407VET6) of the embedded system is connected to sensors, including an inertial measurement unit (LPMS-ME1), a ground reaction force sensor (BFH1K-3EB-Q30), and an air pressure sensor (XGZP6847A040KPG33). The microcontroller controls three electric relays (BMZ-02K1-E) that are connected to two solenoid valves (0802SW) and a vacuum pump (KMDP-C60). The whole embedded system is powered by a Li-ion battery (24 V 1200 mAh). While the average energy consumption power during 1 m/s level-ground walking is 20 W, the battery can support about 86 min of operation. Owing to the pneumatic actuation and modular design of the soft knee prosthesis, the pumps, valves, electronic boards, and battery for the knee can be contained in a backpack (total weight of 1200 g) as shown in Supplementary Fig. 14 that can be carried by the amputee subject (Supplementary Table 2). A bench-top experiment was conducted to show joint articulation powered by the pneumatic actuation system (Supplementary Movie 11).

Materials and fabrication

As shown in Supplementary Fig. 13, the knee unit design was carried out using SolidWorks CAD software. The material was commercial thermoplastic polyurethane (TPU) powder with a shore hardness of 90 A. The corresponding.STL file was imported into a Selective Laser Sintering 3D printer (SLS 500, Wuhan 3dpzz, China) to print the prototype with the TPU powder with a wall thickness of 1.5 mm. After cleaning the remaining powder inside the chamber, the prototype was soaked into N, N-Dimethylformamide (DMF) as a post-process for further polyreaction to increase air tightness. To keep the anterior facets relatively immutable, we further 3D printed two frontal facets by MultiJet Fusing (MJF) 3D printer (HP Jet Fusion 4200, HP, USA) with their commercial nylon powder (HP3DHR-PA12) with a thickness of 1 mm. The nylon facets were bonded on the TPU prototype by Ergo 5600 (Ergo, Switzerland). The height of the knee unit is 150 mm, and the weight is 300 g.

Statistic

For important quantitative metrics related to amputee participant testing, we calculated mean values (± std). Within amputee testing data, we subsample represents one stride (segmented from heel strike to heel strike) from a given ambulation mode. MATLAB R2022b is used in this paper for data analysis.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.