Theoretical Validation of Multi-Motor Mechanism for Lightweight Robot Joint

Shan Zexin, Endo Mitsuru, Nakamura Hiroshi, Tanaka Shimpei

第42回日本ロボット学会学術講演会 RSJ2024

1G3-01

背景 – Background

Lightweight robots are increasingly sought after in human-robot collaboration (HRC) applications to improve safety and flexibility. Weight reduction enhances back-drivability and minimizes contact force, both of which are crucial for performance in HRC. However, traditional robot joints rely on a single motor with a high-ratio gearbox (e.g., strain wave, RV, planetary), which, while achieving high torque density, also leads to high joint weight, increased reflected inertia, and mechanical inefficiencies that hinder back-drivability. Limited customization of these gearboxes further constrains optimization for weight reduction.

This study explores a novel multi-motor (MM) joint mechanism with a dual-stage gear train to address these challenges. The MM mechanism utilizes multiple small motors instead of a single high-power motor, potentially reducing gearbox size and weight while improving back-drivability. Unlike prior MM applications focused on power enhancement or energy optimization, this approach prioritizes weight reduction for high-torque robotic joints. The study aims to validate the feasibility of this design by comparing its weight advantages to conventional single-motor assemblies.

手法 – Method

Dual-Stage Multi-Motor Design

The proposed dual-stage multi-motor (MM) mechanism consists of two gear train stages, as illustrated in Figure 1. The first stage includes multiple small motors, each connected to a spur gear in parallel. The second stage features a ring gear driven by multiple spur gears, serving as the joint output. This design aims to achieve weight reduction while maintaining high torque output.

Dual-stage

Figure 1: Conceptual figure of multi-motor mechanism.

2.1 Weight Formulation

The total weight MtotalMtotal of the mechanism is given by:

$M_{total}=n_m M_{m-i}+M_{s1}+M_{s2}$

where $n_m$ is the number of motors, $M_{m-i}$ is the weight of an individual motor and $M_{s1}$ and $M_{s2}$ are the weights of the first and second-stage gears, respectively. The overall reduction ratio $N_{dual}$ is determined by the gear diameters in both stages or the required joint torque output:

\[N_{dual}= N_{s1}N_{s2} =\frac{d_{s1-dn}}{d_{s1-p}} \cdot \frac{d_{s2-dg}}{d_{s2-r}} = \frac{\tau_{J}}{n_{m}\:\tau_{m-i}}\]

where $N_{s1}$ and $N_{s2}$ are the reduction ratios of the first and second stages, respectively, and $\tau_{J}$ is the required joint torque. The weight of the gears is determined by their material properties and dimensions, leading to the total weight formulation:

\[M_{total}= \:n_{m}M_{m-i} + \frac{\rho\pi F}{4}(n_{m}d_{s1-p}^2 +n_{m}\frac{N_{dual}^2}{N_{s1}^2}d_{s1-p}+n_{m}d_{s2-dg}^2 +4N_{s1}d_{s2-dg}S_R+4S_R^2)\]

where $\rho$ is the material density and $S_R$ is the rim thickness of the ring gear.

2.2 Space Limitation Considerations

As shown in Figure 2, the joint design is subject to a maximum diameter constraint of 200 mm. The ring gear is set to this maximum diameter, but the second-stage driving gear must be carefully designed to avoid exceeding the space limit. This constraint is expressed as:

\[d_{s2-r}-d_{s2-dg}+d_{s1-dn} \leq 200\,\mathrm{mm}\]

This ensures that the gear arrangement remains within the allowable space while achieving the required reduction ratio.

SpaceLimit

Figure 2: Space limitation.

2.3 Optimization of Design Parameters

To achieve weight reduction, the key variables to optimize are the number of motors $n_m$, the first-stage reduction ratio $N_{s1}$, and the overall reduction ratio $N_{dual}$. The study minimizes total weight while maintaining target torque (140 Nm), speed (25 RPM), and a maximum allowable weight (4.2 kg). The gears are made from Aluminum 6061-T6 (density: 2700 kg/m³), and commercially available motors with varying power levels are considered for evaluating different values of $N_{dual}$.

検証結果 – Result

3.1 Optimal Configuration

The total weight of the dual-stage MM mechanism was analyzed for different configurations, varying the number of motors $n_m$ and the first-stage reduction ratio $N_{s1}$. The optimal configuration was found to be $n_m = 2, N_{s1} = 5, N_{dual} = 55$ using Motor 5, achieving a total weight of 2.39 kg, which is 43% lighter than the target joint. The CAD model confirmed a similar weight (2.41 kg).

A preliminary gear strength analysis identified excessive stress in the second-stage driving gear, requiring a material change from Aluminum 6061-T6 to stainless steel 440C, with a negligible weight increase of 0.008 kg.

3.2 Feasibility and Limitations

The proposed mechanism achieves significant weight reduction and improved back-drivability compared to conventional single-motor designs, making it well-suited for human-robot collaboration (HRC). However, further studies are needed to:

Explore more motor options for better optimization.
Investigate full robot integration, as this study focuses on a single joint.
Analyze mechanical characteristics (e.g., backlash, stiffness, friction).
Build a prototype for real-world validation.

3.3 Potential and Future Work

The dual-stage MM mechanism allows for greater customization, enabling advanced output control (torque ripple, efficiency) and energy optimization via multi-motor coordination. Its modular and flexible design provides a promising foundation for lightweight industrial robots. Future work will focus on refining mechanical characteristics and validating performance through experiments.

結論 – Conclusion

This study proposed a preliminary dual-stage multi-motor (MM) mechanism and conducted a theoretical validation for weight reduction. The results confirmed that the mechanism achieves 43% weight reduction compared to a conventional robot joint, demonstrating its feasibility for lightweight industrial robot applications. Future work will optimize motor selection, analyze mechanical characteristics, develop control strategies, and build a prototype to validate real-world performance.

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