Dual-Array Variable Mechanical Advantage Transmissions with Guide-Load Balancing for Mechanical Launchers

Abstract

Variable mechanical advantage transmissions can drive a downstream fixed-ratio stage from dual arrays of engagement members on opposite sides of a central guide. Anchoring each array’s tension member independently partitions the stage’s 𝑘 falls between two separate lines. This removes ⌊𝑘/2⌋ elements from the busiest rope path, reducing friction and bending losses while enabling larger stage ratios that slow the stage blocks and reduce required member counts.

However, mirror-symmetric dual arrays cannot balance guide reactions at odd stage ratios 𝑘: because the partitioned falls differ by one (|𝑛₁ − 𝑛₂| = 1), symmetry imposes a permanent, uncorrectable lateral load of |𝑛₁ − 𝑛₂|/𝑘 (e.g., 20% at 𝑘 = 5). Dynamic guide balance is restored by configuring deliberately unequal, semi-symmetric arrays according to the generalized condition 𝐺1 ∶ 𝐺2 = 𝑛₂𝑇₂ ∶ 𝑛₁𝑇₁, wherein the array actuating more falls or suffering lower path losses is assigned a smaller displacement ratio. The independent geometry doubles design degrees of freedom, improving ratio profile tracking threefold. Furthermore, initiating engagement with the array serving fewer falls (𝑛₁ = ⌊𝑘/2⌋) suppresses inter-engagement force drift, cutting residual lateral loads by 39% to 57% at 𝑘 = 5 and dominating the alternative lead assignment across almost the whole accuracy-balance trade at 𝑘 = 7 and 𝑘 = 9.

In simulated 1,000:1 mass-ratio launches, semi-symmetric designs at 𝑘 = 7 (7 members/array) and 𝑘 = 9 (5 members/array) reduce peak-to-mean compliant payload forces from 1.40 to 1.12 and 2.19 to 1.48, respectively, compared to matched single or mirror symmetric baselines, while cutting line contacts. Against the mirror-symmetric machine the peak lateral guide load falls from 14.3% to 8.1% of the carriage reaction at 𝑘 = 7 and from 11.1% to 7.0% at 𝑘 = 9, reductions of 43% and 37%, or 14.6 kN and 9.3 kN on a peak reaction of about 230 kN.