Torsional artificial muscles generating fast, large-angle rotation have been recently demonstrated, which exploit the helical configuration of twist-spun carbon nanotube yarns. These wax-infiltrated, electrothermally powered artificial muscles are torsionally underdamped, thereby experiencing dynamic oscillations that complicate positional control. Here, using the strategy spiders deploy to eliminate uncontrolled spinning at the end of dragline silk, we have developed ultrafast hybrid carbon nanotube yarn muscles that generated a 9,800 r.p.m. rotation without noticeable oscillation. A high-loss viscoelastic material, comprising paraffin wax and polystyrene-poly(ethylene-butylene)-polystyrene copolymer, was used as yarn guest to give an overdamped dynamic response. Using more than 10-fold decrease in mechanical stabilization time, compared with previous nanotube yarn torsional muscles, dynamic mirror positioning that is both fast and accurate is demonstrated. Scalability to provide constant volumetric torsional work capacity is demonstrated over a 10-fold change in yarn cross-sectional area, which is important for upscaled applications.