Kinematic configuration

Degrees of freedom, their arrangement, reach and segment lengths

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Snapshot of this document in the GEMs repository. The repository itself is the current version. Bản chụp tài liệu này trong repo GEMs. Bản đang chạy nằm ở chính repo.

The specification declares envelopes; this declares a point on them. Joint count and reach are not capability ranges — a body has the joints it has — so they are fixed here rather than in spec/.

Everything below is a declared configuration, not a derived constraint. A different configuration satisfying the same envelopes is a different body, not a wrong one.

1. Degrees of freedom

1.1 Why seven-DOF arms

Six DOF positions and orients an end effector. The seventh makes the arm redundant: the same hand pose is reachable through a range of elbow positions, so the arm can work around an obstacle, or around a person, without giving up the pose it is holding.

That redundancy is not a convenience here. Group 4 of spec 01 puts safe human contact at the core, and a non-redundant arm in contact with a person has exactly one way to hold a pose — if that way is blocked, it must break contact or force through.

Reference point: a real 1.2 m humanoid ships 5-DOF arms and 25 DOF total, with no hands. This configuration is a step up in exactly the places the application frame asks for.

1.2 Hands, and why they are counted apart

A human hand carries roughly 21 DOF. Two of them would nearly double the whole body's joint count, so hands are declared as their own tier with a range:

Which one is fitted is ⟦CTRL⟧. The hands are the single largest lever on total joint count, and a specification that folded them into one number would hide that.

1.3 The working figure

Budgets elsewhere in this repository use 41 DOF. That is this configuration's core 31 plus minimum hands (2 × 5) — the low end, chosen so that budgets derived from it are not flattered.

Even the largest configuration is 0.06% of the 8 Gbps link. Joint count is not a bandwidth problem; it is a mass and reliability problem.

1.4 The trunk is a spine, not a waist

In a human the trunk does not turn at one joint. Rotation is spread over many vertebrae, most of it through the thoracic spine; the lumbar spine barely turns at all, its facet joints set against it (Anatomy Standard). A single yaw joint at the waist turns the body exactly where a human does not, and at large angles reads as a figure twisted at one seam.

Decision D-9, 2026-09-26: a coupled multi-segment spine. The trunk is three segments — lumbar, lower thoracic, and the upper thorax that carries the shoulders, the neck and the battery pack. Each of three axes — yaw, pitch and lateral bend — has one actuator, and a coupling mechanism (gearing, cable or an elastic continuum element; ⟦IMPL⟧) spreads its motion over the three segments. The motion is distributed like a spine's; the actuator count is that of a three-axis waist.

Rejected: one actuator per segment per axis, the approach of musculoskeletal humanoids such as Kotaro and Kenshiro. It is the most flexible, but those designs report poor controllability and low load capacity, and nine trunk actuators would break the actuator mass budget (f_act).

An implemented precedent for the coupling. The Flexinoid spine (Ali and Abdullah, Scientific Reports 2025; electrical/sources/) is a five-vertebra tensegrity column — rigid struts, TPU cables, a spherical joint at each level — with pitch and roll driven by two actuators in the lumbar region through tendons and series elastic elements, the tensegrity transmitting the motion up the column. Per vertebra 25° flexion and ±10° lateral bend, ±30° lateral bend in total; unpowered it carries 15 kg passively. Two differences from this body: its yaw is a separate revolute joint at the shoulder mount, where here yaw is the third coupled axis; and its lateral range is a third of the 90° targeted here. It shows the mechanism class works at human scale, not that these figures do.

A caution on cable coupling, from the same literature. The 3-DOF tendon-driven waist of Wang et al. (Advanced Robotics 2023; specification restated in Mech. Mach. Theory 216:106220, 2025) couples three actuators through wires and pulleys. Under a 10 kg torso surrogate at 80°/s, wire slack put the path 63 mm off the unloaded reference, and the authors added a spring gravity-compensation module to recover accuracy. For the coupling mechanism here — still ⟦IMPL⟧ — that is evidence against plain cable coupling at this body's trunk mass, and for either geared coupling or cable coupling with pretension and gravity compensation. Spring compensation of trunk pitch and roll also serves the energy measure of spec 03.2 (series elastic elements storing what gravity would otherwise cost).

The coupling ratio between segments is ⟦IMPL⟧. The simulation model spreads each axis equally; the human distribution — most rotation thoracic, little lumbar — is the reference the mechanical design should move toward. The battery pack sits on the top segment, rigid with the shoulders, so the spine turns beneath it.

Lateral bend is new with this decision. It is sized, with the other two trunk axes, from measured human trunk strength per kilogram (electrical/): 0.95 Nm/kg, 91 Nm at the 96 kg reference point.

1.5 Range of motion: mechanism, not biology

The body's joint limits are set by what the mechanism allows, not by human range of motion. Wider travel gives the real-time code more ways to turn the body before impact — the way animals twist to protect what is vulnerable — and fewer moments of being pinned at a limit exactly when a reaction is needed. Human range stays available as a profile, not as the mechanism.

Design targets for mechanical travel, total range — decided 2026-09-26, to be revised by simulation and, if it happens, by assembly:

Where flexion is already bounded by segments meeting — a forearm against an upper arm near 150° — the added travel is on the other side of straight.

Locks are separate from limits. A lock that holds a joint for standing (spec 03.2, measure 4) engages at a chosen angle — the knee at 0° — and is independent of the mechanical travel beyond it. Two conditions follow from separating them: a lock whose release would let the joint pass straight must be engaged without power (spring-applied), since a knee that can pass 0° collapses if the lock opens on power loss; and it must carry the full static load path.

1.6 Not counted as joints

Facial micro-actuators and pupil actuation (spec 05.3) are not structural joints: they carry no load, need no torque sensing, and are not logged per-joint. They are declared with the sensing channels they serve.

2. Reach and segment lengths

For a ~1.65 m body (D-8, 2026-09-26; 1.75 m before), taken from ordinary human proportion and scaled by height:

The 0.66 m figure is full reach. The arm-torque sizing of spec 02.6 uses the 0.61 m grip-centre lever, since 2026-09-26; before that it used the fingertip, which overstated the shoulder lever by a tenth.

3. What this configuration commits elsewhere

Joint count does not fix f_act. More joints means more actuators, but a joint's actuator is sized by the torque it carries, and an ankle carries nothing like a wrist. The actuator mass fraction stays ⟦IMPL⟧ until parts are chosen; what this document fixes is how many there are, not what they weigh.

4. Open