This is a 2D re-derivation of the same arm, not a flattened screenshot of the 3D scene. The arm only ever bends in one vertical plane — a yaw joint at the base picks which plane, and inside it three nested joints (shoulder, elbow, wrist) place the tool tip exactly as in the 3D model:
u,v plane (before yaw):
p0 = (0, H0)
p1 = p0 + (−L1 sinθs, L1 cosθs)
p2 = p1 + (−L2 sin(θs+θe), L2 cos(θs+θe))
p3 = p2 + (−L3 sin(θs+θe+θw), L3 cos(θs+θe+θw))
world (after yaw): X = u·cos(yaw), Z = −u·sin(yaw)
The side-elevation panel draws that (u, v) plane directly — literally the cross-section a real safety engineer would draw. The plan view draws the same chain projected into world (X, Z) as the yaw sweeps, so you can see the base rotate toward the source rack and then toward the reactor. Fixed props (rack, reactor, leak) are real 3D points; the elevation view fades them out when the current cutting plane passes more than ~0.6 m to the side of them, and shrinks the reactor's drawn radius by √(R²−w²) exactly like slicing a cylinder with a plane at perpendicular offset w.
Between waypoints all four joints follow a minimum-jerk profile (zero velocity and acceleration at both ends):
τ = t / T
s(τ) = 10τ³ − 15τ⁴ + 6τ⁵
The gas sensor is a first-order mass balance — leak generation minus ventilation removal — relaxing exponentially toward a distance-attenuated steady state, shown live in the trend strip along with the threshold line:
C_eq = leak_on ? Q0 / (1 + (d/L)²) : 0
dC/dt = (C_eq − C) / τ_relax
Cell interlock: the instant C crosses the threshold, whatever move is in progress is abandoned for a fast retract-to-home — independent of the cycle-speed slider, exactly like a safety-rated PLC interlock overriding a motion controller. It clears (with hysteresis, at 80% of threshold) only once ventilation brings the reading back down, then the arm resumes a fresh cycle from home.