The pursuit of creating legged machines that can operate with the agility, efficiency, and adaptability of animals has been a central focus in robotics for decades. Among these, the quadruped bionic robot stands out due to its inherent static and dynamic stability, making it a prime candidate for navigating complex, unstructured terrains where wheeled or tracked vehicles fail. Our research is dedicated to advancing the mechanical design of such bionic robots, specifically targeting the critical challenge of achieving high payload capacity without sacrificing speed, mobility, or energy efficiency. The leg mechanism is the cornerstone of a walking machine’s performance, and most existing quadruped robots employ serial chain leg architectures. While simple to model and control, these serial legs often place actuators distally, increasing the inertial load on proximal joints and limiting structural stiffness, which in turn restricts payload-to-weight ratios and endurance.
To overcome these fundamental limitations, we have turned our attention to hybrid leg mechanisms. The core philosophy is to synergistically combine the advantageous properties of parallel and serial architectures. Parallel mechanisms are renowned for their high stiffness, excellent load-bearing capacity, and favorable force distribution among actuators, as the moving platform is supported by multiple kinematic chains. However, they typically suffer from a limited workspace. Serial mechanisms, in contrast, offer a large, dexterous workspace but are inherently less rigid. Our hybrid leg design strategically integrates a parallel mechanism to handle the primary weight-bearing and propulsive forces within the leg’s sagittal plane, while a serial component provides the necessary lateral mobility for balance and steering. This paper presents a detailed investigation into this design paradigm, proposing, analyzing, and comparing three distinct 3-degree-of-freedom (3-DOF) hybrid leg configurations for a quadruped bionic robot.
The fundamental design principle for our bionic robot leg is derived from biological observation and functional decomposition. For effective walking, trotting, and balance recovery, a minimum of three degrees of freedom per leg is required. The primary locomotion—forward/backward motion and body lifting/lowering—occurs predominantly in the sagittal plane. When an animal carries a heavy load or runs swiftly, the major ground reaction forces are also aligned within this plane. The lateral swinging motion at the hip, however, is primarily used for balancing during stance, making turning maneuvers, and reacting swiftly to lateral disturbances to maintain dynamic stability.
Therefore, our hybrid leg topology employs a 2-DOF planar parallel mechanism serially connected to a 1-DOF four-bar linkage. The 2-DOF parallel subsystem is responsible for generating the foot trajectory in the sagittal plane (protraction/retraction and lifting/lowering). Its parallel nature ensures that the actuators can be mounted proximally on the main body, drastically reducing the leg’s moving mass and inertia. This configuration inherently provides high structural stiffness, allowing the bionic robot to sustain significant payloads. The 1-DOF four-bar linkage acts as a hip yaw mechanism, providing lateral swinging motion. This decouples the sagittal plane motion from the lateral steering motion, simplifying control and enabling fast, independent responses to lateral imbalances. The overall bionic robot model is established with a body-fixed coordinate system and four leg-fixed coordinate systems, utilizing symmetry to simplify kinematic and dynamic analyses. The velocity relationship for the whole machine is given by a block-diagonal Jacobian matrix:
$$
\begin{bmatrix}
\dot{\mathbf{x}}_1 \\
\dot{\mathbf{x}}_2 \\
\dot{\mathbf{x}}_3 \\
\dot{\mathbf{x}}_4
\end{bmatrix}
=
\begin{bmatrix}
\mathbf{J}_1 & \mathbf{0} & \mathbf{0} & \mathbf{0} \\
\mathbf{0} & \mathbf{J}_2 & \mathbf{0} & \mathbf{0} \\
\mathbf{0} & \mathbf{0} & \mathbf{J}_3 & \mathbf{0} \\
\mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{J}_4
\end{bmatrix}
\begin{bmatrix}
\dot{\boldsymbol{\theta}}_1 \\
\dot{\boldsymbol{\theta}}_2 \\
\dot{\boldsymbol{\theta}}_3 \\
\dot{\boldsymbol{\theta}}_4
\end{bmatrix}
$$
Three Hybrid Leg Architectures for the Bionic Robot
Configuration A: Closed-Loop Trajectory Design
This design features two servo motors and one motor-driven ball screw actuator. Its defining characteristic is that the two servo motors driving the parallel part of the sagittal plane mechanism are capable of generating a closed-loop foot trajectory by themselves. This property can theoretically simplify the control for cyclical gaits like a trot. However, a significant drawback is the location of the ball screw actuator relatively low on the leg structure. This placement increases the moving mass and inertia of the distal leg segment, which can negatively impact dynamic stability and increase energy consumption during high-speed motion.
Configuration B: Fully Proximal Actuation
This architecture employs three motor-driven ball screws, all mounted on the robot’s main body. The primary advantage is the complete reduction of distal leg mass, as all actuators are fixed to the torso. This centralization of mass improves the dynamic characteristics of the leg swing and reduces the torque requirements on the actuators themselves. The leg becomes a purely kinematic chain driven remotely, which is beneficial for high-speed, low-inertia motion. The trade-off often involves a more complex transmission system (e.g., push-pull rods or cables) to convey motion from the body to the leg joints.
Configuration C: Symmetric Motion Amplification
This configuration utilizes linear actuators (envisioned as hydraulic cylinders or linear electric motors) and incorporates a symmetric motion amplification linkage within its sagittal plane parallel mechanism. This design allows a relatively short actuator stroke to produce a large foot displacement, effectively increasing the workspace. A critical benefit is that the moment of inertia of the leg’s sagittal plane structure remains nearly constant throughout its extension/retraction cycle. This constant inertia property eliminates varying inertial coupling effects, simplifying dynamic control and contributing to more stable and predictable high-frequency movements, which is a key goal for an agile bionic robot.
Comparative Analysis: Workspace and Mobility
The effective workspace of a leg is a primary determinant of a bionic robot’s mobility, dictating its maximum stride length, obstacle clearance height, and crouching depth. We constructed the reachable workspace for each of the three hybrid leg configurations under the same torso height constraint. A quantitative comparison is presented in the table below.
| Configuration | Max Crouch Height (mm) | Max Stride Length (mm) | Max Obstacle Height (mm) |
|---|---|---|---|
| A | 230 | 300 | 100 |
| B | 250 | 400 | 150 |
| C | 300 | 600 | 200 |
Configuration C offers the largest and most symmetric workspace. The symmetry in forward and backward reach is particularly important for the bionic robot’s omnidirectional mobility and for maintaining consistent gait parameters regardless of direction. The significantly larger stride length of Configuration C directly enables higher potential locomotion speeds for the bionic robot.
Comparative Analysis: Load-Bearing Capacity
Payload capacity is a paramount metric for a utility-focused bionic robot. We analyze this through the concept of force manipulability or the force ellipsoid. The mapping from actuator force/torque space to the Cartesian force space at the foot is given by the transpose of the inverse Jacobian:
$$
\mathbf{F} = \mathbf{J}^{-T} \boldsymbol{\tau}
$$
Assuming the actuators can each deliver a unit force/torque ($||\boldsymbol{\tau}|| \leq 1$), the set of achievable foot forces $\mathbf{F}$ forms an ellipsoid in Cartesian space. The size and shape of this ellipsoid at a given leg posture represent its load-bearing capability in different directions. We evaluated this capability at several key points (1-10) along a standard trotting trajectory with a stride length of 300 mm. The analysis revealed that Configuration C not only provides the largest force ellipsoid volume (indicating greater overall force output) but also maintains a remarkably consistent size and shape throughout the stance phase. In contrast, Configurations A and B show significant variation in their force capacity depending on the leg posture, with their maximum capability occurring only near the middle of the stance phase. The consistent, high load capacity of Configuration C makes the bionic robot more robust and predictable when carrying heavy loads over varying terrain.
Comparative Analysis: Kinematic Isotropy
Kinematic isotropy measures the uniformity of motion (or force) transmission capability in different Cartesian directions. For a bionic robot, good isotropy in the forward/backward (X) and lateral (Y) directions during stance is crucial for effective impulse generation and balance recovery. The isotropic index $\mu$ is defined as the ratio of the minimum to the maximum singular value of the leg’s Jacobian matrix $\mathbf{J}$ at the foot:
$$
\mu = \frac{\sigma_{\text{min}}(\mathbf{J})}{\sigma_{\text{max}}(\mathbf{J})}
$$
A value of $\mu$ close to 1 indicates that the leg can move or exert force equally well in all directions at that configuration (isotropic). A value close to 0 indicates a directionally degenerate, or ill-conditioned, configuration. We plotted the evolution of $\mu$ for the X and Y directions separately over the same trotting trajectory points.
| Configuration | Isotropy Trend (X vs. Y) | Key Observation |
|---|---|---|
| A | Varies significantly, often low. | Motion/force capability is highly direction-dependent and asymmetric. |
| B | Shows large variation, generally poor. | Worse directional uniformity than A, indicating less balanced design. |
| C | Consistently higher and more stable. | Approaches isotropy ($\mu \approx 1$) at several points, indicating well-balanced force/motion transmission in X and Y. |
The superior and more stable isotropy of Configuration C means this bionic robot leg design can generate balanced propulsion and lateral correction forces across a wider portion of its stride, enhancing locomotion stability and control authority.
Torque Requirement: Hybrid vs. Classic Serial Leg
To further justify the hybrid approach, we compare the actuator torque requirement of Configuration C’s sagittal plane parallel mechanism with that of a classic 2-DOF serial leg (hip pitch and knee pitch). Assuming massless links and focusing on static force transformation, let $F_r$ and $F_t$ be the radial and tangential components of the ground reaction force at the foot. For the hybrid leg (Configuration C), with two proximal torques $T_{h\_l}$ and $T_{h\_r}$, and for the serial leg with hip torque $T_{hip}$ and knee torque $T_{knee}$, the mappings are derived from their respective Jacobians. The maximum required torque magnitudes for supporting pure radial or pure tangential forces are summarized below:
| Load Type | Hybrid Leg (Config C) Max |T| | Serial Leg Max |T| |
|---|---|---|
| Pure Radial Force $F_r$ | $F_r L |\sin \alpha|$ | $F_r L |\sin \alpha|$ |
| Pure Tangential Force $F_t$ | $F_t L |\cos \alpha|$ | $2 F_t L |\cos \alpha|$ |
Where $L$ is a characteristic link length and $\alpha$ is a leg angle. This simple analysis reveals a critical advantage: for handling tangential forces (which are dominant during propulsion and braking), the hybrid bionic robot leg requires only half the maximum actuator torque compared to the serial leg. This translates directly into smaller, lighter actuators, lower energy consumption, and reduced heat generation—all vital factors for an autonomous, high-performance bionic robot.
Experimental Prototype and Validation
Based on the comprehensive comparative analysis—which favored Configuration C for its large symmetric workspace, high and consistent load capacity, excellent kinematic isotropy, and lower torque requirements—we selected this architecture for our physical bionic robot prototype. The prototype is constructed from high-strength aluminum alloy, with dimensions of approximately 1200 mm (length) x 500 mm (width) x 1000 mm (height). It incorporates an on-board power supply and a hybrid motor-hydraulic drive system for the linear actuators. The total weight of the bionic robot, including all power and drive systems, is under 130 kg.
The key performance test involved loaded locomotion. The bionic robot successfully demonstrated stable trotting gait while carrying a payload of 100 kg. This experiment validated the theoretical advantages of the hybrid leg design, confirming its superior payload-to-weight ratio and stable dynamic performance. The bionic robot exhibited smooth and powerful strides, demonstrating the practical viability of the hybrid parallel-serial leg mechanism for creating robust, load-carrying quadruped platforms.
Conclusion
In this work, we have systematically addressed the design of high-capacity legs for quadruped bionic robots. We proposed and analyzed three novel 3-DOF hybrid leg configurations that ingeniously merge a 2-DOF planar parallel mechanism with a 1-DOF serial four-bar linkage. This synthesis harnesses the parallel structure’s stiffness and force efficiency for sagittal plane propulsion and load-bearing, while the serial linkage provides essential lateral mobility for steering and balance.
A rigorous comparison based on workspace, load-bearing capacity (force ellipsoid), and kinematic isotropy clearly identified Configuration C—featuring symmetric motion amplification and nearly constant leg inertia—as the optimal design. This configuration was further shown to require significantly lower actuator torques for generating tangential ground forces compared to a traditional serial leg, highlighting a fundamental efficiency gain.
The successful development and testing of a full-scale prototype bionic robot based on Configuration C, capable of carrying a 100 kg payload, provide concrete validation of our design methodology and theoretical analyses. This research establishes a solid foundation for the development of a new generation of quadruped bionic robots that do not force a trade-off between agility and strength, paving the way for their deployment in demanding real-world applications such as logistics, disaster response, and exploration.