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I designed a compact planetary-geared actuator optimized for torque-dense, backdrivable motion in quadrupeds, modeled after the MIT Mini Cheetah's.
Core Skills
CAD prototyping | DFM | Actuator mechanical design
Project Motivation
To understand actuator architecture, which is essential to the morphology and mechanical design of humanoid robots, I developed an improved version of the original MIT Mini Cheetah actuator. My goal was to optimize key performance criteria such as torque density and control bandwidth while keeping costs as low as possible.
Context
The MIT Mini Cheetah is a quadruped robot with 12 identical low-cost actuators — 3 per leg (hip, abductor, knee).
Key Design Criteria
Parameter | Mini cheetah 1 Value | How it was Measured | Why It Matters |
Peak Torque | > 17 Nm | Dynamometer measurement with gradually increasing torque until failure | Peak ground reaction forces during running can reach ~3x the mini cheetah’s bodyweight, requiring joints to handle ~17 Nm to avoid gear failure |
Torque Density | > 38.6Nm/kg | Calculated by dividing peak torque by total actuator mass | High torque density is critical for lightweight, high-performance robots that need agile, explosive movements |
Continuous torque | > 6 Nm | At thermal equilibrium after running actuator at constant load for 30+ minutes, find the max torque | Important for steady movement |
Force Control Bandwidth | > 100 Hz | Apply step change in force, then measure actual response time to find the bandwidth. Run such sinusoidal force commands at increasing frequencies | The quadruped’s contact times can be as short as 85 ms; the system needs >100Hz bandwidth for it to respond without delays |
Joint Inertia | ~ 0.0012 kg·m² | Mount actuator, time its oscillation period then calculate inertia | Lower joint inertia reduces impact forces and increases responsiveness |
Operating Temperature | <50°C, > -10°C | Thermal Imaging | Prevents plastic softening |
Alternative Gearbox Reduction Systems
Architecture | Torque Transmission Mechanism | Applications | Pros vs. Cons |
Direct Drive | [via direct mechanical link]
Motor shaft is connected directly to the joint; torque is transferred 1:1 to the output. | Unitree B1, ANYmal | Pros
• 0 backlash
• Highly backdrivable - torque comes straight from the motor shaft
Cons
• Requires a lot of torque to turn which demands large/heavy motors that decrease torque density. |
Series Elastic | [via spring trasmission]
A spring is inserted between the motor and the joint. The motor compresses/streteches the spring which moves the limb controls torque | Boston Dynamics Atlas | Pros
• Spring naturally absorbs shock on gears
• Functions as an inexpensive yet reasonably accurate force sensor
Cons
• Resonance caused by spring reduces bandwidth which delays responsiveness |
Harmonic Drive | [via interlocking gears]
A flexible metal ring (flexspline) is forced into contact with a fixed outer ring (circular spline) by a rotating wave generator. The deformation between teeth transmits torque with high precision | Boston Dynamics Spot | Pros
• 0 backlash - teeth are always engaged
• High gear ratio (50~360 : 1), excellent torque amplification
Cons
• Expensive due to precision parts
• Very low backdrivability because of high gear ratio |
Cycloidal Drive | [via interlocking gears]
A rotating cam moves a disc against a set of pins, which create curved paths that drive the output shaft. | HyQ | Pros
• High gear ratio (100:1), effectively amplifies torque
• Strong shock resistance since load is distributed across many contact points
Cons
• Expensive as it requires precise pin placement |
Planetary Gear | [via interlocking gears]
Motor turns a small central gear (the sun gear), which spins multiple planet gears that rotate a carrier and amplify the torque output | MIT mini cheetah | Pros
• Moderate backdrivability due to low gear ratio
• Low internal friction, good for efficient torque transmission
Cons
• Torque transmission is less efficient
|
Belt-Driven | [via friction, like a bike chain]
The motor turns a pulley which spins a belt that wraps around another pulley connected to the joint. | MIT mini cheetah knee joint | Pros
• High backdrivability - belts can slip and allow reverse motion
• Good impact absorption from belt elasticity
Cons
• Limited torque capacity - it’s depends on belt tension
• Belt teeth are subject to slipping |
Worm Gear | [via interlocking gears]
Sliding helical contact. | Forklifts | Pros
• High gear ratio is great for holding loads without power
Cons
• Not backdrivable due to self-locking mechanism
• Torque transmission efficiency is low due to significant sliding friction |
I will start off with a planetary gear actuator since it offers a good balance of performance and cost. The high torque density and backdrivability as well as it being relatively affordable makes it a solid choice for a lightweight quadruped like the mini cheetah.
Final Design
My modified actuator features a Brushless DC motor and a single stage planetary gear reduction system.
Key Feature #1: Planetary Gear System
- Sun gear teeth: 8
- Planetary gear teeth: 16
- Ring gear teeth: 40
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Main design decisions and modifications
1. Sizing sun gear’s shaft to withstand torsional stress form planet gears (with FoS = 2)
2. Redesigned sun gear to reduce teeth count from 15 to 8, made each thicker; 6:1 gear ratio
3. Out-runner instead of In-runner motor
4. Wider, 1/3 fewer magnets → cuts magnets cost by 13%
5. 3D print all components in PC plastic except front & back housing, rotor, and stator → cuts cost by ~50% and weight ~20%, but may cause overheating; requires experimental validation.
Design Validation & Performance Prediction
Design comparison
*Assumed value based on MIT’s original calculations as it could not be derived from theoretical prediction
Parameter | My value | Mini cheetah value | Passed required value? | How to improve |
Peak Torque | 17.47Nm | 17 Nm | ✔️ | • N45H → N48H magnets (⬆️ magnetic flux density)
• Reduce air gap between rotor magnets and stator teeth (⬆️ magnetic flux)
• increase stator length (enables more copper wire turns) |
Torque Density | 49.9Nm/kg | 38.6Nm/kg | ✔️ | • Hollowing the motor shaft (⬇️ mass but could introduce more stress)
• Thinning actuator housing walls based on FEA stress distribution |
Continuous torque | requires testing | 6 Nm | * | • Thicker copper wire to reduce heating (enables sustained higher currents for ⬆️ continuous torque) |
Force Control Bandwidth | 101.3Hz | 101 Hz | ✔️ | • Thicker metal for planet carrier (stiffer material enables actuator to respond to torque changes w/out delay) |
Joint Inertia | requires testing | 0.0012 kg·m² | * | • Optimize for smaller diameter and more compact motor (reflected inertia is proportional to radius^2) |
Operating Temperature | requires testing | <50°C, > -10°C | * | • Apply thermal paste on the stator’s copper windings (⬆️ thermal conductivity and heat dissipation), potentially add forced convection |
Next steps
Buy AWG16 Copper wire and try Delta-Wye winding with ESC connected, then test if the motor is pulling current; if yes, then winding should be functional. I will then purchase a board from an open source controller project called Dagor Brushless Controller which uses 3 phase FOC based control to provide torque control at peak current 40A.
I’m currently 3D printing and assembling my actuator prototype for testing at the University of Sydney (studying abroad and surfing!!)
If I had more time…
- Refine air gap design
- Explore outrunner vs. inrunner motor for torque density vs. backdrivability & cooling tradeoff
- FEA on housing to strategically reduce mass
- Testing for magnetic saturation in the laminated stator core and potential thermal management issues
Primary Sources
Bledt, Gerardo, et al. “MIT Cheetah 3: Design and Control of a Robust, Dynamic Quadruped Robot.” 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Oct. 2018, doi:10.1109/iros.2018.8593885.
Katz, Benjamin, et al. “Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control.” 2019 International Conference on Robotics and Automation (ICRA), May 2019, doi:10.1109/icra.2019.8793865.
Liu, Yan, et al. “Soft Actuators Built from Cellulose Paper: A Review on Actuation, Material, Fabrication, and Applications.” Journal of Science: Advanced Materials and Devices, vol. 6, no. 3, Sept. 2021, pp. 321–337, doi:10.1016/j.jsamd.2021.06.004.
Wensing, Patrick M., et al. “Proprioceptive Actuator Design in the MIT Cheetah: Impact Mitigation and High-Bandwidth Physical Interaction for Dynamic Legged Robots.” IEEE Transactions on Robotics, vol. 33, no. 3, June 2017, pp. 509–522, doi:10.1109/tro.2016.2640183.
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