01 · Question
What changes at joint 2 when only joint 1 is driven?
Can a two-link arm be understood as two isolated pendulums, or does the motion of the full mechanism matter?
02 · Prediction
A passive elbow should wave loosely.
With the shoulder driven, the initial expectation was a janky arm with an elbow that trailed or moved without an explicit elbow command. With gravity off, the staged motion should look cleaner because the motors would not be opposing gravitational load.
03 · Experiment · explorable evidence
Scrub the recorded MuJoCo trajectories.
These are precomputed samples from the canonical two-link MuJoCo experiment, rendered in-browser from exported state—not browser-simulated physics. Switch a condition or scrub time to compare the mechanism, command, and acceleration.
Manual scrubbing remains available when reduced motion is preferred.
- qpos
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- qvel
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- ctrl
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- qacc
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Data: headless export from the canonical MuJoCo experiment ↗, sampled at 60 fps. The renderer only draws the recorded state.
04 · What happened
The passive elbow moved with zero elbow command.
In the passive, elbow-down run with normal gravity, joint 2 visibly moved while only joint 1 was commanded. Scrub the passive condition: ctrl[1] stays at 0.0 even as joint 2’s position, velocity, and acceleration change.
05 · Model update
The independent-joint model is insufficient.
Behavior depends on the state and motion of the full mechanism, not only on each joint’s local command. The held condition changes the motion; gravity-off makes the staged coordination cleaner. A target cross-feed can create controller-imposed coordination, but that is not evidence for the passive physical coupling shown here.
06 · Stop boundary
Do not optimize the waveform past the question.
Exact wave tuning was abandoned once it stopped testing the multi-DOF mental model. The gravity-off staged coordination is included as a comparison, not as proof of physical coupling.
Source