In an ideal symmetric bevel differential with equal side gears, the carrier speed is the arithmetic average of the two signed side-gear speeds. Reversing one side changes an additive average into a subtractive average.
Two-speed Transmission with Differential Motion Interactive Calculator
Enter two positive normalized side-gear speed indices. The tool reports the carrier index when the side gears turn in the same direction and when side B is reversed; it is not a general epicyclic or belt-drive design model.
Equation Used
- The two side gears have equal effective tooth counts and the carrier is the output.
- Inputs a and b are positive normalized side-gear speed indices relative to the same reference, not reduction ratios.
- Same-direction mode uses signed inputs +a and +b; opposed-direction mode uses +a and -b.
- Only speed kinematics are represented; torque sharing and power flow are not inferred.
- Tooth counts, tooth geometry, shafts, bearings, backlash, efficiency, loads, stress, lubrication, shift dynamics, control hardware and suitability are omitted.
Symmetric Differential Speed Averaging
For an ideal bevel differential with equal side gears, the carrier angular speed is the arithmetic average of the two signed side-gear speeds. With both entered magnitudes turning in the same direction, the carrier index is (a+b)/2. Reversing side B gives an opposed-direction magnitude |a-b|/2.
What This Calculator Represents
The animation shows two equal side gears and a carrier in a specialized symmetric differential. It alternates between same-direction and opposed-direction side inputs so the two carrier results can be compared.
The entered values are normalized speed indices. They are not pulley ratios, motor speeds or a complete transmission specification.
Equal-Side-Gear Ideal Kinematics
opposed-direction carrier index = |a-b|/2
spread = same-direction / opposed-direction, when opposed-direction is nonzero
opposed/same percentage = 100 × opposed-direction / same-direction
The one-half factor is essential: the carrier averages the two signed side speeds; it does not rotate at their raw sum or difference.
Worked Ideal Example
For entered side-speed indices a=3 and b=2, same-direction operation gives a carrier index of 2.5. Reversing side B gives an opposed-direction carrier magnitude of 0.5, a 5.00 spread and an opposed/same percentage of 20.0%.
Model Boundary
- Calculated: the equal-side-gear carrier average for two signed input combinations.
- Illustrated: a symmetric bevel-differential schematic with the carrier as output.
- Not calculated: a belt layout, generic epicyclic tooth-count relations, motor speed, torque split, power circulation, efficiency, forces, bearing loads, tooth stress, backlash, lubrication, shift behavior, controls or suitability.
Frequently Asked Questions
Why divide the sum or difference by two?
An equal-side-gear differential carrier rotates at the average of the two signed side-gear speeds.
Are a and b gear reduction ratios?
No. They are normalized side-gear speed indices.
What happens when a equals b in opposed mode?
The ideal carrier index is zero, so the same/opposed spread is undefined.
Does this apply to unequal side gears?
No.
Does it predict torque sharing or efficiency?
No.
Can it design a differential transmission?
No.
References
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