From camera coordinates to mechanical radians

contact@mulhamfetna.com (Mulham Fetna) — Tue, 08 Sep 2026 00:00:00 +0000

Twenty-one points in a camera’s coordinate system on one side. A CAD assembly with hard mechanical stops on the other. This is the arithmetic that makes them agree — and the one row where it currently does not.

The vision layer gives you 21 points floating in a normalized coordinate space that has no physical units and a faked depth axis. The mechanical layer gives you fifteen revolute joints, each with a lower and upper bound in radians that came out of a CAD mate.

Nothing connects them. Building that connection is the actual work of this project, and it happens in about forty lines of Python.

flowchart LR
    A["21 landmarks
(x, y, z) normalized"] --> B["Triplet selection
15 × (p₁, p₂, p₃)"]
    B --> C["Two vectors per joint
v₁ = p₁ − p₂ · v₂ = p₃ − p₂"]
    C --> D["Dot product → arccos
θ in radians"]
    D --> E["Normalize
flexion ∈ [0, 1]"]
    E --> F["Lerp onto URDF limits
θ_urdf"]
    F --> G["JointState
names + positions"]

Step 1 — pick three points
#

To measure a joint you need the joint itself and the two bones meeting at it. In landmark terms: the vertex, plus its two neighbours.

Mathematics on Mulham Fetna

From camera coordinates to mechanical radians

Step 1 — pick three points #

Step 1 — pick three points
#