In recent years, the rapid advancement of robot technology has paved the way for innovative solutions in assistive devices, particularly for aging populations and individuals with disabilities. As a researcher in the field of robot technology, I have focused on developing life support robots that can operate effectively in unstructured home environments. One critical challenge in this domain is the design of a compact and efficient waist mechanism that enables human-like bending motions while maintaining stability. Traditional waist structures in humanoid robots often suffer from complexity, bulkiness, and limited operational space, which restrict their practicality. In this paper, we propose a novel bionic waist mechanism based on a series-parallel multi-link configuration, driven by a single power source, to address these limitations. Our approach leverages robot technology principles to simulate human spinal movements, enhancing the robot’s reachable workspace and field of vision. Through kinematic modeling and simulation, we demonstrate the mechanism’s performance in achieving forward and backward bending postures, underscoring its potential in life support applications.
The design of life support robots requires a balance between mobility, stability, and functionality. Wheeled mobile robots are commonly used due to their maneuverability, but their small chassis size can lead to instability during dynamic movements. To mitigate this, we have developed a bionic waist mechanism that minimizes重心偏移 while providing a large bending range. This mechanism incorporates a Watt-I type six-bar linkage, combining serial and parallel elements to achieve high stiffness and simplified control. The core of our robot technology innovation lies in the use of a single input to drive multiple output links, enabling complex motions without the need for multiple actuators. The mechanism consists of two quadrilateral loops: $A_1B_1O_1C_1$ and $A_2B_2C_2O_2$, with rigid connections between specific links to form a closed kinematic chain. The degrees of freedom (DOF) are calculated using the Grübler formula:
$$ F = 3(n – 1) – 2p_L $$
where $n = 5$ is the number of moving links and $p_L = 7$ is the number of lower pairs. This results in $F = 1$, indicating that the mechanism can be controlled with a single actuator, a key advantage in robot technology for reducing complexity and cost.
To analyze the kinematic behavior, we established a coordinate system with origin at $C_1$ and derived the vector loop equations based on the closed chains. The position of the output point $O_2$ is critical for determining the robot’s operational space. The vector equations are as follows:
$$ \begin{cases}
\vec{C_1O_1} + \vec{O_1B_1} = \vec{C_1A_1} + \vec{A_1B_1} \\
\vec{O_1A_2} + \vec{A_2C_2} = \vec{O_1B_2} + \vec{B_2C_2} \\
\vec{C_1O_2} = \vec{C_1O_1} + \vec{O_1B_1} + \vec{B_1O_2}
\end{cases} $$
Projecting these vectors onto the X and Y axes yields the following equations for displacement analysis:
$$ \begin{aligned}
X\text{-axis:} & \quad l_2 \cos \beta + l_3 \cos \gamma = l_1 \cos \alpha \\
& \quad l_5 \cos(\gamma – \theta_2) + l_6 \cos \epsilon = l_7 \cos(\beta + \theta_4) + l_8 \cos \eta \\
Y\text{-axis:} & \quad l_2 \sin \beta + l_3 \sin \gamma = l_1 \sin \alpha – l_4 \\
& \quad l_5 \sin(\gamma – \theta_2) + l_6 \sin \epsilon = l_7 \sin(\beta + \theta_4) + l_8 \sin \eta
\end{aligned} $$
Here, $l_i$ represents the lengths of the links, and $\alpha$, $\beta$, $\gamma$, $\epsilon$, $\eta$ are the angles of the respective links with respect to the X-axis. The output point $O_2$ coordinates are given by:
$$ \begin{aligned}
X_{O_2} &= l_3 \cos \gamma + l_7 \cos(\beta + \theta_4) + l_9 \cos(\eta + \theta_5) \\
Y_{O_2} &= l_3 \sin \gamma + l_7 \sin(\beta + \theta_4) + l_9 \sin(\eta + \theta_5)
\end{aligned} $$
By solving these equations, we can determine the angular displacements of the driven links as functions of the input angle $\gamma$. The solutions are derived using trigonometric identities, resulting in expressions for $\alpha$, $\beta$, $\epsilon$, and $\eta$. For instance, $\beta$ is computed as:
$$ \beta = \arcsin\left( \frac{l_2^2 + l_3^2 – N_1^2 – N_2^2}{2l_2 \sqrt{N_1^2 + N_2^2}} \right) – \arctan\left( \frac{N_2}{N_1} \right) $$
where $N_1$ and $N_2$ are intermediate variables defined based on the geometry. This kinematic model forms the foundation for our simulation studies in robot technology.
To evaluate the mechanism’s performance, we conducted numerical simulations using MATLAB and virtual simulations with Adams software. The link parameters were set as follows: $l_1 = 254.9\text{mm}$, $l_2 = 89.3\text{mm}$, $l_3 = 135\text{mm}$, $l_4 = 41\text{mm}$, $l_5 = 58.8\text{mm}$, $l_6 = 261.4\text{mm}$, $l_7 = 140\text{mm}$, $l_8 = 77.7\text{mm}$, $l_9 = 140\text{mm}$, $l_{10} = 81\text{mm}$, with fixed angles $\theta_4 = 34^\circ$ and $\theta_5 = 45^\circ$. The input link $C_1O_1$ was driven through a range of $\gamma$ from $49^\circ$ to $-41^\circ$, using an “acceleration-constant-deceleration” profile to ensure smooth motion. This approach is common in robot technology to minimize jerks and stresses on the mechanism.
The angular displacements and velocities of the driven links were analyzed over time. The results, summarized in Table 1, show the variations in $\alpha$, $\beta$, $\epsilon$, and $\eta$ as functions of the input angle $\gamma$. The output link $B_2C_2$ exhibits a significant range of motion, with $\eta$ decreasing from $77.5^\circ$ to $45.2^\circ$ during forward bending and increasing during backward bending. This demonstrates the mechanism’s ability to achieve human-like postures, a key aspect of robot technology for life support applications.
| Input Angle $\gamma$ (°) | $\alpha$ (°) | $\beta$ (°) | $\epsilon$ (°) | $\eta$ (°) |
|---|---|---|---|---|
| 49 | 120.5 | 80.2 | 65.3 | 77.5 |
| 30 | 115.8 | 75.6 | 60.1 | 70.2 |
| 10 | 110.3 | 70.1 | 55.4 | 62.8 |
| -10 | 105.6 | 65.3 | 50.7 | 55.1 |
| -30 | 100.9 | 60.8 | 45.9 | 48.3 |
| -41 | 98.2 | 58.1 | 43.2 | 45.2 |
The angular velocities were derived by differentiating the displacement equations with respect to time. For example, the angular velocity of link $B_2C_2$, denoted as $\omega_\eta$, is given by:
$$ \omega_\eta = -\omega_\gamma \cdot \frac{l_5 \cos(\gamma – \theta_2 – \epsilon) + l_6 \cos(\epsilon – \eta)}{l_8 \sin(\eta – \epsilon)} $$
Simulation results indicate that $\omega_\eta$ reaches a maximum magnitude of $18.04^\circ/\text{s}$ at $t = 4.625\text{s}$, during the transition between bending postures. This peak velocity occurs near the limit positions and is opposite in direction to the input velocity, highlighting the dynamic characteristics of the mechanism. Such insights are crucial in robot technology for designing control strategies that ensure stability and precision.
The position of the output point $O_2$ was tracked throughout the motion cycle. As shown in Table 2, forward bending results in a displacement of $109\text{mm}$ forward and $111\text{mm}$ downward, while backward bending yields $124\text{mm}$ backward and $34\text{mm}$ downward. This asymmetry in workspace is advantageous for tasks requiring extended reach in front of the robot, such as picking up objects from the floor. The larger forward bending range aligns with common human activities, making this mechanism well-suited for life support robot technology.
| Bending Posture | Forward Displacement (mm) | Downward Displacement (mm) |
|---|---|---|
| Forward | 109 | 111 |
| Backward | 124 | 34 |
Virtual simulations in Adams confirmed the mechanism’s kinematic performance. The model was integrated into a life support robot prototype, and the bending motions were visualized at different time instances. The robot successfully achieved both forward and backward bending postures, validating the design’s feasibility. The single-input drive system simplified control, while the multi-link structure provided the necessary stiffness and range of motion. These results underscore the effectiveness of our approach in advancing robot technology for assistive applications.
In conclusion, we have designed and analyzed a bionic waist mechanism that enhances the capabilities of life support robots. The series-parallel multi-link configuration offers a compact and efficient solution for achieving human-like bending motions with a single actuator. Kinematic analysis and simulations demonstrate significant improvements in operational space and dynamic performance. Future work will focus on structural optimization, dynamic control, and experimental validation to further refine the mechanism. This innovation in robot technology holds promise for addressing the growing demands of elderly care and disability support, contributing to the development of more adaptable and user-friendly robots.