PMC

Conventional 3-leg inverter driving a permanent-magnet synchronous motor (PMSM) (a) and dual-fed open-ended winding PMSM (b).

Autonomous leg exoskeleton. (A) The autonomous exoskeleton applies torque about the human ankle joint during walking, adding positive mechanical power to the wearer during the push-off portion of stance phase. During the swing phase, the device applies negligible forces on the wearer by allowing small amounts of slack into the cord. The mechanism consists of a winch actuator and fiberglass struts that directly apply a resultant torque about the ankle. (B) The winch actuator provides a torque on the ankle by winding the cord around the spool. As the cord is tightened, a force is applied to the struts on either side of the leg. The winch actuator’s brushless motor applies the torque to the ankle joint through a transmission that consists of the belt transmission stage in series with the geometric transmission stage comprising spool, idler roller and strut.

Elastic coupling mechanism of the F₁-ATPase power stroke. (A) Catalytic dwell (0°) after ATP hydrolysis at β_D. Tightly wound γ−coiled-coil and (αβ)₃-ring are tethered (). Power stroke starts by β_E-Pi release to allow coiled-coil unwinding. (B) Phase 1 rotation (0°–60°): γ−coiled-coil torsion spring unwinds to equilibrium γ-foot domain position of 34°. β_E binds ATP at any phase 1 rotational position, 34° is optimal. β_D dissociates ADP optimally at 34° but can slow phase 2 if delayed. (C) Phase 1 → phase 2 switch at 60° when the γ−coiled-coil reaches the winding limit. Electrostatic interactions between Mg-ATP and groups on the β_E lever and catalytic domains force conformational changes to break γ−coiled-coil tether and push β_E lever against subunit γ to rotate foot and coiled-coil. A different tether () may cause a second spring (80°–100°). (D) Catalytic dwell begins when γ-foot reaches 120°, and β-subunit conformations change (β_E → β_T and β_D → β_E). ATP hydrolysis rewinds torsion spring.

a, Solid line, schematic internal energy landscape for a simplified two-minima motor. Dashed and dotted lines, energetic contribution of external AC field applied along the 0°–180° axis. Insets, energy functions in polar coordinates. b, Solid lines, snapshots of the sum of internal motor energy plus field contribution. Dashed lines, expected trajectory of the rotor arm on field direction inversion. Initial position per field half-cycle is indicated by a dot. c, Energy landscapes for the hypothetical two-minima motor from a and b plotted as 2D space-time surfaces and computed for three exemplary orientations of motor relative to field axis (see insets). Field axis is along the 0°–180° direction. Yellow dots, exemplary single-particle trajectories as simulated by Langevin dynamics. d, Distribution of cumulative angular displacements after two, four and six AC field cycles aggregated from a simulated Langevin dynamics trajectory. The prominent peaks at 180° intervals are due to the twofold symmetry in the simulated energy landscape. e, Irreversibility analysis for simulated motors. Shown is an ensemble average over 20 simulated motors evaluated at different displacement values and for time intervals of two, four and six AC cycles, as indicated by colour. The motors contain a twofold symmetry as illustrated in panel a, in which in the blue scheme motor orientations with 45° relative to the field were used and in the red scheme symmetric orientations (0°) were used. Solid lines, guides to the eye to emphasize the trend or the lack thereof. f, Irreversibility analysis of experimentally observed motor particles. Colouring of the distribution indicates the time interval as in panel d. To account for variations in rotation speed, the linear trend in each rotor was renormalized to a slope of unity before computing the distributions shown. A line with unit slope was added to guide the eye. See Extended Data Fig. for the irreversibility analysis of experimentally observed particles. g, Left, schematics of a motor variant that includes a ssDNA torsional spring at the pivot point. Right, exemplary experimentally observed cumulative angular displacement of single motor particles. First phase: AC field off, spring relaxed. Second phase: AC field on, spring is wound up. Third phase: AC field off, spring is unwinding and driving the motion. See also Supplementary Videos  and .