First pallet · receiving bay

Longitudinal motion

m·a = Fdrive − mg sin(θ) − Froll − Fdrag − Fbrake. Motor force is limited by a simple torque curve and the available power. The tyre force is capped by Coulomb friction, then reduced by the friction-circle share used by cornering.

Tyre grip and braking

Fmax = μN and dstop = v² / (2μg cos θ) for the level-ground ideal overlay. The chart is analytical and assumes constant grip, flat ground, and no reaction delay.

Stability

φtip = atan((track / 2 − |Δcg|) / hcg). Dynamic body tilt is approximated as atan(ay/g). The warning compares the live lateral demand with the current effective threshold, which increases as the load is lifted.

Suspension and hydraulics

T = 2π√(m/k) is the undamped single-mass spring period. A damped quarter-car proxy creates visible travel. Mast lift and tilt are rate-limited kinematic hydraulic actuators.

Visible rig hierarchy

• chassis · 3,200 kg rigid body, counterweight and overhead guard
• chassis → wheel_fl / wheel_fr · powered revolute axle joints
• chassis → wheel_rl / wheel_rr · rear steering revolute joints
• chassis → mast_outer · tilt revolute joint, −0.11 to +0.16 rad
• mast_outer → mast_inner → carriage · nested prismatic lift stages
• carriage → fork_l / fork_r → load_pallet · fixed fork and payload assemblies

Assumptions / simplifications

• Planar chassis motion; no full 6-DOF rigid-body solver or collision impulses.
• Single surface friction coefficient; rain changes μ from 0.72 to 0.43.
• Electric motor, brakes, suspension, hydraulic pressure and load flex are simplified educational models.
• Tip-over indicator is a simplified warning, not an operating load chart or safety certification.

Run window.__selfTest() in the browser console for three closed-form checks. Exact formula checks also run in test_physics.mjs under Node.