Abstract
<jats:p>Transferring kinetic energy from a slow, high-force source, such as a descending mass, a ram or a spring, to a fast, light payload requires a transmission whose mechanical advantage rises continuously through the stroke. We introduce the RopeComb: a passive, configurable rope-and-pulley transmission in which a translating carriage progressively deflects a tension member into successive fixed spans. Two independent geometric freedoms per member (span width and engagement offset) make essentially any monotonically rising profile reachable, and because the resulting displacement ratio has a closed form, matching a target is a smooth least-squares fit rather than a search. By specifying a source deceleration rather than a payload force, and solving for the force that produces it, the geometry can be optimised for uniform payload force. Across mass ratios of 100:1, 1,000:1 and 10,000:1, arrays of eight to thirteen members track that target to within 1.5% and reach its exit velocity in arrays 1.9-2.8 m wide. Measured against the work needed to raise the source again, through the braking distance as well as the height that sets its entry speed, the transmission delivers 86.3% of the input to the payload; that figure is fixed by the entry and final speeds and the braking distance alone, and does not depend on mass ratio. The three simulated designs realise it to within 0.4%. It precedes a correction for the rotational inertia of sheaves in the fast path, which is first-order, scale-invariant, and costs a further 9 to 12% of exit velocity, leaving the payload 66 to 72% of cycle input rather than 86.3%. The stroke is terminated by a traction-loss instability, and the specified deceleration is the hardest that leaves the tension member continuously loaded throughout, with release occurring before the terminal transient. Pairing the RopeComb with a compliant, pre-tensioned output member absorbs the transients of discrete engagement, holding peak-to-mean payload force to 1.09-1.19x, where the rigid mechanism gives 2.0-2.1x. That places its force uniformity at or beyond the nominal 1.25x of a steam catapult and approaching the 1.05x of an electromagnetic launcher, achieved with passive mechanics and no electrical storage, power conditioning or steam plant. The RopeComb figures reported here are simulated; the steam and electromagnetic figures they are compared against are measured on fielded hardware.</jats:p>