pull_thumb goes negative (−19.5 N, flexion 0.69); every other motor pushes open.Hinges versus a saddle #
- Index to pinky are chains of hinge joints. A fist rolls them into a tight spiral, each knuckle approaching 90°.
- The thumb hangs from the carpometacarpal (CMC) saddle joint at the wrist. It sweeps across the palm — opposition — instead of simply curling. Much of “closing the thumb” is rotation of the whole thumb, not bending at its knuckles.
What MediaPipe measures because of it #
Interior angles come from 3D landmark positions, so the sweep only partly shows up as knuckle bend:
| Open | Fully closed | Travel | |
|---|---|---|---|
| Finger — mean of MCP/PIP/DIP | ≈ 3.10 rad | ≈ 1.60 rad | 1.50 rad |
| Thumb — mean of CMC/MCP/IP | ≈ 2.90 rad | ≈ 2.30 rad | 0.60 rad |
A fully closed thumb stops near 2.30 rad (~132°). Even its open angle sits below a finger’s — a relaxed thumb is never in line with the wrist.
The failure the separate window fixes #
With the finger window, a thumb squeezed as far as it goes gives:
$$\text{flexion} = \frac{3.10 - 2.30}{1.50} = 0.53 \quad\Rightarrow\quad F = 50 - 100 \times 0.53 \approx -3\ \text{N}$$Fully closed thumb, half-closed command. With its own window:
$$\text{flexion} = \frac{2.90 - 2.30}{0.60} = 1.0 \quad\Rightarrow\quad F = -50\ \text{N}$$if finger_name == "thumb":
straight_limit = THUMB_STRAIGHT_ANGLE # 2.90
curled_limit = THUMB_CURLED_ANGLE # 2.30
else:
straight_limit = RAW_STRAIGHT_ANGLE # 3.10
curled_limit = RAW_CURLED_ANGLE # 1.60The trade-off: a narrow window is a twitchy window #
The thumb covers 0 → 1 in 0.60 rad, so it is 2.5× more sensitive than the fingers (\(1.50 / 0.60\)). Landmark jitter that barely moves a finger visibly moves the thumb. If the thumb flickers:
- widen its window slightly (e.g. 2.95 → 2.25), or
- add temporal filtering — a One-Euro filter is on the production roadmap.
The robot thumb closes differently too #
On the simulation side, the thumb doesn’t close like a finger either. At the full −50 N pull its CMC joint reaches ~92° but its MP and IP joints stop around 54° and 46°, while every index joint reaches ~94°.
The likely cause is the thumb tendon’s routing geometry — once the CMC hits its stop, the path leaves little moment arm to curl the distal joints further — but it hasn’t been isolated yet. The vision thresholds and the robot’s joint distribution are independent problems; Part 11 covers the physics.
