Articulated Platform Dynamics

Multi-unit configurations require mechanical articulation. Three coupling arrangements dominate field applications:

Coupling Type	Articulation Range	Load Transfer	Terrain Suitability
Fixed-hitch	0° (rigid)	Direct vertical & shear transfer	Paved, packed surfaces; limited off-road
Pivot-hitch	±12–15° lateral, ±8° vertical	Vertical load bearing; lateral damping via articulation	Mixed terrain; gravel, light wash crossings
Ball-and-socket	±20° full-axis freedom	Distributed load; full compliance in three axes	Rough terrain, high breakover; steep approach/departure

Fixed-hitch configurations eliminate articulation entirely, transmitting all loads directly. Useful for stable terrain where breakover geometry permits. Pivot-hitch arrangements allow lateral flex under load and vertical compliance at the coupling point. Ball-and-socket couplings permit full three-axis movement, essential for rough terrain where towed unit attitude independent of primary platform.

Tongue weight—the vertical load imposed at the coupling point—governs system behavior across all coupling types. Optimal range: 10–15% of towed unit mass.

Nominal Case: 12% Tongue Weight

A towed unit of 1000 units mass exerts 120 units vertical load at coupling. Primary platform experiences 120 units downward force. Rear axle loading increases; front axle relief is slight but measurable. Load distribution is stable across speed ranges and surface types.

Insufficient Tongue Weight (<8%)

Coupling point becomes loosely loaded. Lateral oscillation begins at moderate speeds. Towed unit yaws independently under gusts or surface irregularities, inducing fishtailing. Oscillation amplitude increases with speed until critical velocity—typically 35–45 km/h on gravel—where resonant swinging develops. Control recovery requires speed reduction below oscillation onset threshold.

Excessive Tongue Weight (>18%)

Rear axle of primary platform becomes overloaded. Front axle relief reduces steering authority and traction. Breakover angle at coupling point degrades—geometry tightens and clearance reduces. Wear on coupling components accelerates. Lateral stability improves but turning radius increases. Effective ground clearance at the coupling diminishes 15–20% for each additional 3% above optimal.

Field Measurements

Configurations in service show:

• Optimal range (10–15%): lateral oscillation frequency <0.3 Hz under normal operating conditions
• Insufficient (<8%): oscillation onset 30–50 km/h; critical instability 45–55 km/h
• Excessive (>18%): coupling wear rate increases 40%; ground clearance loss of 5–8 cm per coupling cycle

Articulated systems present unique breakover constraints. A primary platform alone exhibits a simple breakover angle. A towed unit alone has its own breakover angle. Combined, the system breakover is always less than either unit independently.

Geometry Model

Visualize the sequence: primary unit front wheels ascend an obstacle. Chassis pitches upward. At the peak of primary unit travel—maximum nose elevation—the coupling point is at ground level. The towed unit begins its ascent. Maximum coupling height occurs when both units balance on their respective contact points. As the towed unit front wheels clear the obstacle, the coupling point descends, and total system pitch angle increases.

The critical constraint: when primary unit rear wheels leave ground and coupling point remains the sole contact, the towed unit front wheels have not yet engaged the obstacle. This gap—the articulation gap—determines the limiting breakover angle.

Typical Configuration

• Primary unit breakover angle: 22° (measured nose-to-rear contact point)
• Towed unit breakover angle: 18° (measured coupling-to-towed-rear contact)
• Coupling height above primary rear axle: 0.4 m
• System breakover angle (combined): 14°

The system limit—14°—is 36% lower than the primary unit's capability alone. This is the operative constraint for multi-unit passage. Neither unit achieves its theoretical maximum because the articulation point—the coupling—becomes the limiting element. The towed unit cannot engage the obstacle until the primary unit has fully crested it, creating a kinematic dependency.

Articulated configurations exhibit gradient limits that vary by surface type. These thresholds define maximum safe slope angles for sustained travel without oscillation onset or lateral rollover risk.

Surface Type	Max Safe Gradient	Primary Failure Mode	Notes
Compacted gravel	10%	Lateral oscillation; slip-skid	Oscillation onset 40–50 km/h; skid risk increases above 8%
Soil (firm, dry)	8%	Lateral slip; traction loss	Towed unit lateral force amplifies on 6%+ grades
Sand	6%	Sinkage; loss of coupling integrity	Coupling forces increase with embedded platform; extraction force increases
Wet clay / saturated soil	4%	Lateral slip; adhesion loss	Friction coefficient <0.4; lateral force easily exceeds traction envelope

Camber Effects

Articulated configurations amplify lateral forces on cross-slope terrain. A towed unit on a 5° camber surface experiences lateral loading equivalent to a 7–8° grade. The rigid coupling point cannot independently adjust; both units lean together. Lateral oscillation risk increases significantly above 3° camber when gradient approaches limits.

Oscillation Onset

When articulated systems approach gradient or camber limits, lateral oscillation develops. Onset speed depends on:

• Coupling stiffness (fixed < pivot < ball-and-socket damping effect)
• Gradient and camber combination
• Towed unit mass relative to primary platform
• Tire pressure and sidewall compliance

Observable behavior: lateral yaw amplitude grows with time. For a system at 6% gradient on soil, oscillation onset occurs around 35 km/h. Beyond onset, amplitude increases 2–3 cm per second of travel. At 15 cm yaw amplitude, directional control becomes marginal. Further speed increase triggers uncontrolled high-amplitude oscillation (30–40 cm swings) which precedes lateral rollover.

Overland routes present variable constraints on multi-unit passage. Steep grades, tight turns, and rough terrain limit towed unit capability. Feasibility assessment is route-specific.

Route Segment	Primary Constraint	Feasibility	Notes
Mojave Sand Basin	Sand breakover; coupling depth	Single-unit only	Maximum gradient 4%; sand depth variable 0.3–1.2 m; towed coupling sinks rapidly
Divide Transit (north)	Switchback radius; articulation angle	Limited (specific segments)	Radius minimum 18 m; requires 25–30° articulation; feasible with tight coupling control
Basin and Range (central)	Gradient and breakover	No	Segments exceed 12% grade; breakover angles 18–20°; multi-unit physically impossible
Plateau Traverse (west)	Gradient only; terrain stable	Yes	Maximum gradient 8%; packed surface; no articulation complications
Desert Wash Crossing	Coupling clearance; soft ground	Yes, with caution	Wash depth variable; coupling point becomes critical; advance survey required

Practical routing with towed units: select segments with grades <8%, breakover <16°, and minimum turn radius 20 m. Mojave Sand Basin and Basin and Range Transit are not feasible. Plateau Traverse west and selected Divide Transit segments permit passage with standard pivot-hitch configurations.

Articulated configurations require special procedure for reverse travel and tight approaches.

Articulation Angle Limits

During reversal, the coupling angle between primary and towed units increases as turning radius tightens. Maximum safe articulation angles:

• Pivot-hitch: ±15° lateral (mechanical stop)
• Ball-and-socket: ±25° effective (hose & cable routing limits)

Beyond these limits, coupling point stresses increase. Hoses and control cables may kink or pinch. Structural loads at coupling eyes exceed nominal design. In field conditions, loss of articulation range signals imminent coupling failure.

Minimum Turning Radius (Reverse)

Reverse minimum turning radius depends on:

• Primary platform wheelbase: L₁
• Coupling length (pivot-point to towed unit front): L₂
• Towed unit wheelbase: L₃
• Maximum articulation angle: θ_max

Simplified field formula (pivot-hitch, 15° limit):
R_min ≈ L₁ + L₂·sin(15°) ≈ L₁ + 0.26·L₂

For a typical configuration (L₁ = 3.0 m, L₂ = 2.0 m): R_min ≈ 3.5 m. In practice, reversing articulated systems in confined spaces (switchbacks, narrow segments) requires multiple back-and-forward movements to achieve 180° turns.

Constrained Approach Procedure

1. Approach narrow segment in forward direction at minimal speed (<5 km/h)
2. At constraint point, deploy precision reverse: incremental backing with full articulation angle
3. Forward micro-movement to reset angle. Repeat.
4. Total passage may require 3–5 articulation cycles
5. Towed unit rear wheels are the final limiting constraint; ensure clear line before committing final movement

Backup spotting is essential. Towed unit behavior is non-intuitive; rear tracking becomes more acute as articulation angle increases. A narrow wash or rock face easily catches towed unit trailing edge during reversal.

Dynamics measured on articulated configurations in service. Stability thresholds determined by controlled testing on representative surfaces.