The dual-array RopeComb: a guide-balanced transmission with synthesisable rising mechanical advantage for impedance-matched launch
Efficiently transferring kinetic energy from a slow, high-force driver to a light payload, with a near-uniform output force, requires a transmission whose mechanical advantage rises along a steeply convex profile. Continuous-contour mechanisms (variable-radius drums, cams) become prohibitive at scale through diameter span, inertia and rim burst. The RopeComb bypasses these limits by synthesising profiles ($G = 0 \to 100+$) from discrete constant-radius sheaves deflecting tension members into staggered spans. Each fold's ratio vanishes at first contact, enabling snatch-free engagement at 10 m/s without clutches or dampers. Because the array ratio is closed-form, bounded least squares matches uniform-force targets to within 0.6-1.5% across mass ratios of 100:1 to 10,000:1 using 8-13 members. To carry large carriage reactions without the overturning moment a single array imposes, two independent arrays flank a central guide and drive a partitioned fixed-ratio stage ($n_1 + n_2 = k$). Sizing array ratios and member counts in the fall-count ratio $n_2 : n_1$ cancels 97.7% of the single-array reaction and 95% of its overturning moment in simulated 1,000:1 launches at $k=7$, reducing compliant peak-to-mean payload force from 1.40 to 1.13. All results are numerical.