Task performance↑ Maximize
Jump height
m
Predicted vertical slider rise, capturing how the actuator and joint control perform together.
AN INTERACTIVE RESEARCH COMPANION
Task-Oriented Co-Design and Optimization of Geared Actuators for Robotic Applications
More torque.
Higher jump?
A stronger actuator doesn’t always make a better robot.
Build the hardware. Shape the control.
Discover what happens when you design them together.
01
The jump lab
Educational model / Equations & sources ⓘ
An independent teaching model; results do not reproduce the paper’s actuator predictions or experiments. Inspect these formulas ↗
A
Build your actuator
IDEALIZED MOTOR + GEARBOX
Diameter ranges reserve room for slots and the stator yoke.
- Peak torque
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- No-load speed
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- Mass / actuator
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- Nominal torque density
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- Reflected rotor inertia
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One design, used at both joints.
48 V equivalent supply · 5.5 kg payload.
Ideal gearbox · no transmission loss.
VERTICAL-GUIDE LEGREADY TO JUMP
Predicted body rise—mAdjust a slider. Test your intuition.
Your designPrevious attempt
0.00 s
PUSH-OFF → FLIGHT
Foot sliding—
Motion details
Air time—
Friction loss—
Will the foot hold?
STICKING- Normal force N
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- Tangential force T
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- Grip used |T| / μN
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The force vector must stay inside |T| ≤ μN.
B
Shape the control
How should the joints share the push?
Drag either curve’s points to edit its effort.
Hip · solidKnee · dashed
Available torque used
Knee extension progress
The hip and knee can move independently when the foot slides. A poorly coordinated push can kick the foot out instead of lifting the body.
Torque meets speed
KNEE JOINTAvailableUsed during push-off
HARDWARE × CONTROL
What if they were designed together?
Compare your starting design with control optimization, hardware optimization, and co-design.
EXPLORING DESIGNSEvaluating designs…
4 STRATEGIESChoose a result to load its hardware, curves, and jump.
Selected design details
A bounded numerical search, not a guarantee of a global optimum.
Model assumptions & limitations
This is an educational model for exploring trade-offs. Its numerical results are not predictions for the fabricated actuator or a reproduction of the paper’s validated simulation.
Hardware
Slot area and air-gap geometry set nominal torque under fixed electromagnetic loading assumptions. A DC-equivalent circuit applies separate current and voltage limits. Iron and copper volumes contribute to mass; the gearbox is ideal. Reference constants are illustrative and uncalibrated.
Read every equation, assumption and source ↗Motion & control
The 0.25 m thigh and shank have independent joint motion while the foot slides. Hip motion stays on a vertical guide. Static friction may hold the foot; at its limit the model switches to sliding and keeps integrating both joint coordinates. Six Bézier coefficients per joint set effort over knee extension.
Sliding: T = −μN sign(vfoot)Scope
Sliding dissipates energy but is not an automatic failure or score penalty. The site reports actual body rise and foot travel. Upward takeoff uses COM velocity and a frozen-pose flight approximation. Ground collision, joint travel limits, or unloading without upward COM velocity end an unsuccessful attempt; flight joint dynamics and impacts are not integrated.
Inspect the contact model ↗02
RESEARCH DESIGN & EXPERIMENTSFrom the model to the machine
TASK-ORIENTED ACTUATOR CO-DESIGN
Design for the jump.
Build for the real world.
The research couples motor electromagnetic design, planetary gearbox sizing, actuator mass and inertia, and task dynamics. Surrogate models make the hardware search tractable; joint torque policies are optimized for each candidate.
0.729kgMeasured prototype mass
35.7N·m/kgNominal rated torque / measured mass
Fabricated actuatorINSIDE THE PAPER
A coupled design space.
From electromagnetic geometry to gears and task feasibility, each candidate must work as a complete actuator.
Motor–gearbox co-design
20+ coupled hardware & control variablesMotor
Electromagnetics & windingSlot–pole layout
DiscreteSlot / pole combinations18S / 16P · 18S / 20P · 18S / 22P
24S / 22P · 24S / 26P · 24S / 28P
27S / 30P
24S / 22P · 24S / 26P · 24S / 28P
27S / 30P
Feasibility checks
Fundamental winding factor kw,1 > 0.9.
Radial geometry
ContinuousStator outer diameter60–96 mm
Stator bore diameter36.1–75 mm
Tooth width2–5 mm
Slot depth1–19.15 mm
Feasibility checks
Valid stator and slot geometry.
Slot & magnet geometry
ContinuousTooth-tip height0.5–2 mm
Slot-opening width0.5–2 mm
Magnet thickness1–3 mm
Magnet arc120–180° electrical
Feasibility checks
Positive clearances and manufacturable geometry.
Axial geometry & winding
MixedMotor stack length1–30 mm
Wire diameterStandard wire index
Parallel branchesSymmetry divisors
Winding turnsDerived from slot area & wire size
Feasibility checks
Realizable winding and current / voltage limits.
Planetary reducer
Transmission & strengthTopology & target ratio
DiscretePlanetary topologyNGW · NW · 3K
Target reduction ratio1–50 · step 0.5
Feasibility checks
Assembly and ratio feasibility.
Gear geometry
MixedTooth numbers
SunPlanet 1Ring 1Planet 2Ring 2
One integer tooth count per member · 3K exampleProfile-shift coefficients
SunPlanet 1Ring 1Planet 2Ring 2
One profile-shift coefficient per member · 3K exampleWorking center distanceOne shared center distance across meshes
Gear modules
Mesh aMesh bMesh c
3K: meshes a and b share a module; mesh c has its own.Feasibility checks
Gear geometry and tooth-root strength constraints. Member-level boxes illustrate 3K; NGW and NW use different member sets. Repeated physical planets share the same member design. These counts are parameter entries, not unconstrained degrees of freedom.
Joint torque control
12 coefficients · optimized for each hardware candidateHip Bézier curve · 6 coefficients
Point 1Point 2Point 3Point 4Point 5Point 6
Knee Bézier curve · 6 coefficients
Point 1Point 2Point 3Point 4Point 5Point 6
Each coefficient ranges from 0 to 1. Separate curves determine how the two joints share the push.
Candidate evaluation
Derived quantities and constraints
Actuator package
Derived · constrainedAssembled diameter≤ 98 mm
Assembled length≤ 50 mm
Task contact
Derived · constrainedNormal forceFn ≥ 0
Tangential force|Ft| ≤ μFn
OPTIMIZATION TARGETS
Two objectives, optimized together.
Actuator performance↑ Maximize
Rated output torque density
N·m/kg
Rated output torque per unit actuator mass, evaluated at a common conductor current density of 6 A/mm².
NSGA-II searches for Pareto-optimal trade-offs between these two objectives.
PAPER RESULTS
The Pareto fronts.
Higher torque density does not always mean a higher jump.
Select a group to highlight it. Hover or tap a point to inspect its objectives.
All slot–pole combinations
A real-world comparison
The fabricated actuator alongside the DM8009 reference.
Measured slider rise
+12.0%48 V · 5.5 kg bench load · twice-rated torque: 40 N·m / 52 N·m. Rise includes extension from the initial crouch.
Nominal rated torque density
+60%Nominal rated output torque divided by actuator mass. Prototype: 26 N·m / 0.729 kg.
Actuator mass
−18.6%Measured prototype mass compared with the DM8009 reference mass.
The fabricated prototype was selected from an earlier design search. It is not a newly fabricated point from the updated dual-joint Bézier co-design Pareto set.