= Split-torque transmission
A \b[split-torque transmission] divides transmitted load among two or more mechanical paths and subsequently combines their contributions. Its purpose is to let several meshes carry a total load that would otherwise pass through one path. The <gear torque-path load fraction> depends on compatibility, <stiffness>, gaps and mounting; a symmetric layout alone does not prove equal sharing.
For an original idealization, refer both branch torques to the same shaft coordinate and let their common elastic twist be $\theta$. With torsional stiffnesses $K_1,K_2$ and no initial gaps,
$$
\tau_1=K_1\theta,\quad \tau_2=K_2\theta,\quad
\tau=\tau_1+\tau_2,\quad
\frac{\tau_1}{\tau}=\frac{K_1}{K_1+K_2}.
$$
Values $K_1=40000$ and $K_2=60000\,\mathrm{N\,m/rad}$ under total <torque> $1000\,\mathrm{N\,m}$ give $\theta=0.01\,\mathrm{rad}$ and branch torques $400$ and $600\,\mathrm{N\,m}$. If each branch were limited to $600\,\mathrm{N\,m}$, this sharing would limit total load to $1000\,\mathrm{N\,m}$; equal sharing would permit $1200\,\mathrm{N\,m}$ within the same simplified capacity assumptions.
Parallel-path <gear efficiency> also differs from the product rule for serial stages. If input <power> fractions are $a_j$ with $\sum_j a_j=1$, and each branch delivers fraction $\eta_j$ of its input power to the common output boundary, then
$$
\eta_{\rm total}=\sum_j a_j\eta_j.
$$
For fractions $0.4,0.6$ and efficiencies $0.96,0.94$, the result is $0.948$. Multiplying the two branch efficiencies would describe a different arrangement of power boundaries.
The primary face-gear program reported input-pinion torque division about $48\%/52\%$, while its two idlers shared about $57\%/43\%$. These were measured results with stated calibration limitations, not exact consequences of the layout.<Development of Face Gear Technology for Industrial and Aerospace Power Transmission by Gregory F. Heath and others>[Summary, printed p. iii; Conclusions, printed p. 84, torque splits and strain/load calibration limits]{ref}
A meaningful load-sharing test measures both paths over relevant load and position ranges. <Strain gauges> need an appropriate <measurement calibration> because different tooth load distributions can produce different strain responses for the same transmitted load. <Floating pinions> provide one mechanism for reducing imbalance, but the complete assembly and its constraints still determine the operating split.
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