Rehabilitation of the ankle joint is a critical component in restoring mobility for patients suffering from injuries, post-stroke conditions, or degenerative diseases. Conventional rehabilitation methods heavily rely on physiotherapists, leading to high costs, inconsistent results, and scalability issues. While numerous robotic devices have been developed to address this, many existing designs face significant challenges. A primary issue is the misalignment between the mechanical rotation center of the robotic device and the patient’s actual anatomical joint center, which can cause unnatural movement, discomfort, and even secondary injuries. Furthermore, many devices treat the ankle as an isolated joint, neglecting the synergistic movement patterns of the lower limb, particularly the coupling with the knee joint. This oversight limits the effectiveness of stretching the surrounding musculotendinous structures. This paper presents the design and comprehensive analysis of a novel bionic robot for knee-ankle rehabilitation, specifically engineered to overcome these limitations by mimicking natural human lower-limb kinematics.
The proposed bionic robot is fundamentally inspired by the observation of seated human movement. In a natural seated posture, stretching the ankle joint (dorsiflexion/plantarflexion) is often achieved not by an isolated ankle movement but by a coordinated motion where the lower leg swings about the knee while the foot maintains contact with the ground or a surface. This action ensures a proper stretch of the muscles crossing both the knee and ankle. To translate this biological principle into a mechanical design, the Theory of Inventive Problem Solving (TRIZ) was employed, specifically addressing the physical contradiction: the ankle needs to be fixed to align rotation centers, yet it needs to be mobile to allow natural coupled motion. The solution was found using the “separation in space” principle. The design separates the space of ankle rotation from the space of lower-leg swing, integrating the patient’s own limb as a part of the kinematic chain.
The overall architecture of the bionic robot is a hybrid serial-parallel mechanism, combining the advantages of both. It consists of two main subsystems connected in series: a knee joint swinging mechanism and an ankle joint rehabilitation mechanism. The knee mechanism is a serial chain providing one vertical translational degree of freedom (for initial posture adjustment and vertical compensation) and one rotational degree of freedom (for swinging the lower leg). The ankle mechanism is a parallel platform with three rotational degrees of freedom, directly acting on the footplate to provide inversion/eversion and abduction/adduction. Crucially, the entire ankle mechanism is mounted on a mobile sliding platform. During coupled rehabilitation, the patient’s foot is secured to the ankle platform, whose center is aligned with the anatomical ankle center. The knee mechanism then swings the patient’s lower leg, which pushes the entire ankle assembly along the slide, thereby producing a dorsiflexion/plantarflexion motion through traction. This ingenious bionic robot design ensures the anatomical joint center remains coincident with the mechanism’s functional center throughout the exercise.
The mobility of the combined human-robot system is analyzed using the Kutzbach–Grübler formula for spatial mechanisms:
$$ F = 6(n – g – 1) + \sum_{i=1}^{g} f_i $$
where \( n \) is the number of links (including the base and moving platforms, and considering the human limb segments as links), \( g \) is the number of joints, and \( f_i \) is the number of degrees of freedom of the \( i \)-th joint. Considering the mechanical structure and modeling the human knee as a revolute joint and the ankle as a spherical joint, the total number of links \( n = 7 \). The mechanism has \( g = 6 \) joints with a total of \( \sum f_i = 5 \) degrees of freedom (considering constraints from the parallel ankle mechanism). Substituting into the formula:
$$ F = 6 \times (7 – 6 – 1) + 5 = 5 $$
This confirms the hybrid bionic robot possesses 5 degrees of freedom, matching the required mobility for knee flexion/extension and the three rotational degrees of the ankle.
To establish precise control, a kinematic model is developed. A base coordinate frame \( O-X_oY_oZ_o \) is fixed to the robot’s base. The knee swinging angle is denoted by \( \delta \). For the ankle’s isolated motions, let \( \alpha \), \( \beta \), and \( \gamma \) represent the dorsiflexion/plantarflexion, abduction/adduction, and inversion/eversion angles, respectively. However, in the coupled mode, the dorsiflexion/plantarflexion \( \alpha \) is directly driven by the knee swing \( \delta \), with the relationship \( \alpha = \delta \). The homogeneous transformation for the ankle’s orientation, considering rotations in the order Z-Y-X (yaw-pitch-roll corresponding to \( \gamma, \beta, \alpha \)), is given by the rotation matrix \( \mathbf{R} \):
$$ \mathbf{R} = \mathbf{R}_z(\gamma) \mathbf{R}_y(\beta) \mathbf{R}_x(\alpha) = \begin{bmatrix} c\beta c\gamma & c\gamma s\beta s\alpha – s\gamma c\alpha & c\gamma s\beta c\alpha + s\gamma s\alpha \\ s\gamma c\beta & s\beta s\alpha s\gamma + c\gamma c\alpha & s\beta s\gamma c\alpha – c\gamma s\alpha \\ -s\beta & c\beta s\alpha & c\alpha c\beta \end{bmatrix} $$
where \( c\theta = \cos(\theta) \) and \( s\theta = \sin(\theta) \). In the coupled motion, the swing occurs primarily in the sagittal plane, simplifying the interaction. The position of the ankle center \( \mathbf{p}_c \) in the base frame can be derived from vector loop closure. If \( \mathbf{p}_b \) is the position of the knee center and \( \mathbf{l}_{bc} \) is the constant vector from knee to ankle in the leg frame, then:
$$ \mathbf{p}_c = \mathbf{p}_b + \mathbf{R} \cdot \mathbf{l}_{bc} $$
Given the knee swing angle \( \delta \) and the leg length \( L \), the vertical and horizontal displacement components of the ankle due to the swing are \( \Delta z = L(1 – \cos \delta) \) and \( \Delta y = L \sin \delta \), respectively. This mapping allows the trajectory of the ankle center to be computed directly from the knee actuator input. For the parallel ankle mechanism, inverse kinematics is solved to find the required actuator inputs (e.g., lengths of prismatic actuators or angles of driving links) to achieve desired \( \beta \) and \( \gamma \) orientations of the footplate.
A critical performance metric for any rehabilitation bionic robot is its workspace, which must encompass the physiological range of motion of the human ankle. Literature data on healthy ankle motion ranges were aggregated. The proposed robot’s workspace was then simulated and compared against these physiological limits using boundary search methods in MATLAB. The results, summarized in the table below, demonstrate that the robot’s achievable range exceeds the required physiological range in all rotational axes, ensuring comprehensive coverage for rehabilitation exercises.
| Motion Type | Physiological Range (°) | Robot’s Range (°) |
|---|---|---|
| Dorsiflexion / Plantarflexion (α) | -22.5 to 36.5 | -23.6 to 37.2 |
| Inversion / Eversion (γ) | -26.2 to 25.4 | -27.3 to 26.7 |
| Abduction / Adduction (β) | -15.9 to 15.9 | -16.2 to 15.9 |
Visualization of the robot’s 3D orientation workspace shows a high degree of coincidence with the physiological motion space, validating the design’s capability to replicate natural ankle movements. This close match is a direct result of the bionic robot‘s design philosophy, which seeks to emulate, rather than constrain, natural anatomy.
Dynamic performance and control stability are paramount for safe human-robot interaction. A dynamic simulation was conducted using both MATLAB for numerical analysis and ADAMS for multi-body dynamics verification. A composite rehabilitation trajectory involving all three ankle rotations over a 9-second period was commanded. The angular outputs from both simulation environments were compared. The time-history curves for \( \alpha \), \( \beta \), and \( \gamma \) showed smooth, continuous motion without discontinuities or sharp jerks, indicating stable kinematic performance. The error between the MATLAB theoretical model and the ADAMS physical model was computed. The maximum absolute errors for each motion type throughout the simulation cycle were found to be within a very small tolerance, as shown in the following table:
| Motion Type | Max. Absolute Error |e| (°) |
|---|---|
| Dorsiflexion / Plantarflexion | 0.204 |
| Inversion / Eversion | 0.146 |
| Abduction / Adduction | 0.099 |
These negligible error values (all below 0.5°) confirm the accuracy of the kinematic model and the inherent stability of the mechanical structure. Based on the simulation results and to prioritize patient safety, the operational limits of the bionic robot can be conservatively set within the following safe ranges to absolutely prevent any risk of over-extension or secondary injury:
| Motion Type | Operational Safe Range (°) |
|---|---|
| Dorsiflexion / Plantarflexion (α) | -20 to 30 |
| Inversion / Eversion (γ) | -15 to 15 |
| Abduction / Adduction (β) | -30 to 30 |
In conclusion, this work presents the successful design and analysis of a novel knee-ankle rehabilitation bionic robot. The key innovation lies in its hybrid, biologically inspired architecture that solves the fundamental problem of center misalignment by integrating the patient’s limb into a coupled kinematic chain. The bionic robot effectively separates the spaces of leg swing and ankle rotation, enabling naturalistic dorsiflexion/plantarflexion through traction rather than forced rotation. Kinematic and workspace analyses prove that the device can cover the full physiological range of ankle motion. Dynamic simulations validate the stability and accuracy of its movements. This bionic robot offers a promising pathway for more effective, natural, and safe rehabilitation by fundamentally aligning robotic assistance with human biomechanics.