A Sit-to-Stand Assist Sized by Knee-Torque Physics: Who Fails from a Standard Chair, and the Cheapest Combination That Brings Them Under Their Torque Ceiling

Rising from a chair is the transfer that often decides whether an older or weak user needs another person present. This paper computes, from a stated two-segment biomechanical model evaluated at seat-off, the peak knee-extensor torque demanded by sit-to-stand as a function of seat height, user mass, and foot position, and compares that demand with published knee-strength ranges for older adults used as fixed inputs (5th percentile 48.0 N·m per leg, median 78.0 N·m per leg). From a standard 45 cm chair with neutral feet, demand rises from 40.6 N·m per leg at 50 kg to 73.1 N·m per leg at 90 kg, so a user at 5th-percentile older knee strength fails at every mass from 60 kg upward (48.7–73.1 N·m per leg, 101.5–152.3% of capacity). Three low-cost interventions are evaluated on the same model: raising the seat, placing the feet back combined with an armrest push (a 120 N total arm push removes 10.5 N·m per leg), and a spring assist (150 N removes 15.0 N·m per leg; 250 N removes 25.0 N·m per leg). Requiring a safety factor of 1.25 — demand at or below a 38.4 N·m per leg ceiling for the 5th-percentile class — the cheapest combination costs $0 in parts for users of 50–70 kg (foot placement and arm push, plus technique only), $14 for users of 80–90 kg (adding a 5 cm seat raiser), and at most $72 for a 90 kg user who cannot push with the arms (5 cm raiser plus a 150 N spring). The assist does not solve standing balance, does not help a user without trunk control, and fails in the combined case of bilateral weakness, a low seat, compressible seating, and forward feet, where computed demand reaches 123.1 N·m per leg. All results are simulated, not measured; nothing in this paper was built, sat on, or tested on people.