As a researcher in robotics, I have always been fascinated by the potential of bionic robots to navigate complex terrains. Unlike wheeled or tracked robots, legged bionic robots offer discrete foot placement, adaptability to uneven surfaces, and enhanced stability through posture adjustment. However, many existing multi-legged bionic robots suffer from complex control systems and high manufacturing costs due to multiple actuators per leg. To address this, I focused on single-degree-of-freedom (DOF) linkage mechanisms, which reduce control complexity and improve energy efficiency. Among these, the Jansen linkage mechanism stands out for its efficient walking performance. In this work, I present a novel rotary multi-legged bionic robot based on the Jansen linkage, featuring a unique turntable transmission system. This bionic robot aims to combine simplicity, robustness, and adaptability for applications in rescue operations and rough-terrain transportation.
The core of my bionic robot is a single-DOF bionic mechanical leg inspired by the Jansen mechanism. This leg consists of two triangular trusses connected by seven revolute joints and six links, with a crank driving the motion. The foot traces a trajectory that mimics biological walking, including phases for ground contact, stride, lift, and swing. To verify the mobility, I applied screw theory to analyze the DOF. The motion screws for the joints are represented as $\$1 = (0, 0, 1; 0, 0, 0)$, $\$2 = (0, 0, 1; a_2, b_2, 0)$, and so on up to $\$10$. The constraint screws are derived as $\$^r_1 = (0, 0, 1; 0, 0, 0)$, $\$^r_2 = (0, 0, 0; 1, 0, 0)$, and $\$^r_3 = (0, 0, 0; 0, 1, 0)$, indicating three common constraints. Using the DOF formula for mechanisms with redundant constraints and local freedoms considered zero, the mobility M is calculated as:
$$ M = d(n – g – 1) + \sum_{i=1}^{g} f_i + v – \zeta = 3(8 – 10 – 1) + 10 = 1 $$
where d=3 is the order, n=8 is the number of links, g=10 is the number of joints, f_i=1 for each revolute joint, v=0 is the redundant constraint, and ζ=0 is the local DOF. This confirms the single-DOF nature of the bionic mechanical leg, ensuring simple actuation for the bionic robot.
For kinematic analysis, I employed the complex vector method to model the foot trajectory. The leg mechanism is decomposed into planar linkages, as shown in the杆组拆分 diagram. Defining link lengths from the crank O₁A (L₁) to the foot point F, the position vectors are expressed in complex form. For instance, the vector from O₁ to F is:
$$ \mathbf{r}_{O_1F} = L_1 e^{i\beta} + L_2 e^{i\beta_1} + L_3 e^{i\beta_4} + L_4 e^{i\beta_{11}} + L_5 e^{i\beta_{13}} $$
where β is the crank angle, and β₁, β₄, β₁₁, β₁₃ are angles of other links derived from geometric constraints. The foot coordinates (X_F, Y_F) are:
$$ X_F = L_1 \cos \beta + L_2 \cos \beta_1 + L_3 \cos \beta_4 + L_4 \cos \beta_{11} + L_5 \cos \beta_{13} $$
$$ Y_F = L_1 \sin \beta + L_2 \sin \beta_1 + L_3 \sin \beta_4 + L_4 \sin \beta_{11} + L_5 \sin \beta_{13} $$
These equations allow simulation of the foot path. I set initial link lengths based on structural considerations, as summarized in Table 1.
| Link | Length (mm) | Link | Length (mm) |
|---|---|---|---|
| O₁A (L₁) | 20 | DA (L₇) | 82.5 |
| AB (L₂) | 66.7 | DE (L₈) | 48.9 |
| BC (L₃) | 74.4 | DO₂ (L₉) | 52.4 |
| CE (L₄) | 52.5 | O₂B (L₁₀) | 55.3 |
| EF (L₅) | 87.6 | O₂C (L₁₁) | 53.5 |
| FD (L₆) | 65.3 | O₁O₂ (L₁₂) | 51.8 |
Using ADAMS software, I simulated the foot trajectory and compared it with MATLAB results from the kinematic equations. The trajectories matched closely, validating the model. The foot path shows a stride length L_s and stride height L_h, critical for walking performance. To optimize the bionic robot’s gait, I analyzed how L_s and L_h vary with crank length L₁ and frame inclination angle α₁. For L₁, the stride length increases linearly, approximated by:
$$ L_s = 4.5L_1 – 0.5 $$
while L_h changes non-linearly. For α₁, both L_s and L_h decrease as α₁ increases, with L_h being more sensitive. This allows tuning for specific applications: larger L₁ or smaller α₁ enhances obstacle clearance for the bionic robot, whereas smaller L₁ or larger α₁ favors stability on flat terrain.
Based on this, I designed the rotary multi-legged bionic robot to meet technical requirements, such as a mass under 2 kg, speed over 1 km/h, and obstacle clearance above 30 mm. The key innovation is the turntable transmission mechanism, akin to a needle bearing, which reduces friction and enables multiple leg pairs to be driven by a single motor. Eccentric shafts on the turntable connect to legs at phase differences of 120°, 90°, or 60°, allowing configurations with 3, 4, or 6 leg pairs for adaptability. This bionic robot features a compact size of 334 mm × 220 mm × 188 mm.
For the leg joints, I incorporated thrust ball bearings to minimize friction and withstand lateral forces. The foot uses an adaptive design with a curved bottom to conform to ground contours, improving stability. The overall bionic robot assembly integrates six leg pairs (three per side) for balanced support. Gait timing was analyzed using SolidWorks. Defining support phase from 60° to 300° crank angle and swing phase from 0° to 60° and 300° to 360°, the stride period T ensures that four feet are often grounded, forming a quadrilateral support area for robustness. The phase relationships for legs A, B, and C are derived from the 120° shaft offsets, resulting in a stable walking pattern for this bionic robot.
Functionally, the bionic robot’s straight-line speed v relates to crank angular velocity ω by v = 0.75ω mm/s, given a 90 mm stride per leg cycle. Turning is achieved by differential motor control, enabling zero-radius rotation. For slope climbing, the maximum incline α is limited by the support length L and center-of-mass height Z_n:
$$ Z_n \tan \alpha \leq \frac{L}{2} $$
yielding α ≤ 15° under ideal conditions. Obstacle negotiation depends on foot clearance: the bionic robot can surmount steps up to 30 mm high and trenches up to 90 mm wide, based on the optimized stride height and length.
I built a prototype to test real-world performance. Experiments on flat ground confirmed smooth forward, backward, and turning motions. On slopes and uneven surfaces like grass or gravel, the bionic robot demonstrated adequate mobility, though minor leg interference occurred due to fabrication tolerances. Key metrics are summarized in Table 2.
| Parameter | Value |
|---|---|
| Mass | 1.5 kg |
| Dimensions | 334 mm × 220 mm × 188 mm |
| Average Speed | 1.73 km/h |
| Max Slope Angle | 15° |
| Max Obstacle Height | 30 mm |
| Max Trench Width | 90 mm |
| Motor Voltage | 12 V |
| Control Voltage | 5 V |
| Ultrasonic Range | 2–450 cm |
| Communication Range | 10 m |
In conclusion, this work presents a rotary multi-legged bionic robot that leverages the Jansen linkage for efficient, single-DOF leg motion. Through kinematic modeling and optimization, I tailored the foot trajectory for enhanced stride and clearance. The turntable transmission simplifies actuation, while adaptive feet and bearing-based joints improve durability. Experimental validation shows promising performance across varied terrains, highlighting the bionic robot’s potential for practical deployment. Future efforts will focus on refining leg geometry for higher obstacles and integrating sensors for autonomous navigation, further advancing the capabilities of bionic robots in challenging environments.