One original symmetric open bevel differential with two side gears and four spider pinions. Dimensions, materials and car body are illustrative, not a manufacturer-specific CAD model.
The final drive uses an intersecting bevel pair, not a hypoid offset. Pitch cones, tooth counts and phase constraints are explicit; tapered tooth forms are approximate and do not certify conjugate contact, backlash, strength or manufacturing geometry.
The external housing stays fixed in the housing frame. Exploded inspection is a static layout, not a repair procedure or a physically demonstrated disassembly order.
Road mode assumes equal 0.30 m tire radii, no longitudinal or lateral slip, a rigid 1.6 m rear track, 2.6 m wheelbase and ideal low-speed steering geometry. It does not model forces needed to follow the curve.
The 12-second progress reveal is retimed independently from physical travel time. Bench rotation is slowed eight times. Input values and reported rates retain their stated physical units.
Ideal torque/power calculations omit losses, gear and wheel inertia, dynamic transients, differential friction and tire force versus slip.
The grip view is a static capacity comparison. Exceeding the displayed no-slip bound does not calculate wheel-spin rpm, traction recovery or whether a car will move.
The paper activity tests path geometry, not torque division or a working gear mechanism. It has not yet been classroom-trialed.
The rolling geometry: Use rear-midpoint turn radius R, rear track t, wheel radius r and midpoint speed v. Inner and outer rear radii are R − t/2 and R + t/2. Their ground speeds are v(1 − t/(2R)) and v(1 + t/(2R)); divide by r for angular speeds. A quarter-circle path length is πR/2. Straight motion is the zero-curvature limit.
Why the front wheels point differently: In ideal low-speed Ackermann geometry, all wheel axes meet the same instantaneous turning center. With wheelbase L, the inner and outer steering angles satisfy tan δ = L/(R ∓ t/2). Front-wheel paths are longer than the matching rear paths. This is a no-slip geometric construction, not a high-speed tire-handling model.
The differential constraint: With forward rolling positive on both outputs, ωL + ωR = 2ωC. The same relation holds for accumulated angles with consistent initial phases. Our 40-tooth side gears and 20-tooth spider pinions require the spider’s own-axis rotation to be twice the output departure from the case, in the corresponding opposite rolling sense. Opposite camera viewpoints can reverse apparent clockwise directions without changing the scalar convention.
Torque and power must agree: Ignoring friction and internal inertia, TL = TR = TC/2. The 4:1 final drive gives TC = 4Tin and ωin = 4ωC. Power conservation then gives Tinωin = TLωL + TRωR. At our default 100 N·m input torque and 3 m/s midpoint speed, the ideal case has 400 N·m, the outputs 200 N·m each, and the two output powers sum to 4000 W.
What the weak side limits: Let each supplied capacity be the maximum tire/road reaction torque that can be sustained in this simplified steady, no-slip condition. The ideal equal output torque cannot exceed the smaller capacity. The maximum sustainable case torque is twice that smaller value. This does not specify wheel spin-up, vehicle acceleration or whether available traction overcomes all resistance.
One checked corner: Our authored example has a 1.6 m track, 2.6 m wheelbase, 0.30 m tires and a 6 m rear-midpoint radius. In a left quarter-turn, the rear paths are about 8.168 m and 10.681 m: 4⅓ and 5⅔ wheel turns. Their mean is exactly 5 case turns. The inner front wheel steers about 26.565° and the outer about 20.925°.
What has been checked
Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.
Each source supports the associated claim. Sources do not certify this implementation or its visuals.
About the cover illustration
The cover is an offline rendering of the lesson’s original tapered gear geometry. The housing is removed and selected parts are separated slightly for inspection. It is an educational construction, not manufacturer CAD; its tooth surfaces do not certify manufacturing contact.