A Stance-Stability Bound for Passive Prosthetic Knees and a Low-Cost Single-Axis Design That Satisfies It

A passive prosthetic knee has no motor to hold it straight. During stance it stays extended only if the ground reaction force passes behind the knee axis, producing a restoring extension moment, assisted by joint friction. This paper derives that condition from statics, computes the alignment-offset window that satisfies it under a simple stated gait model, and specifies a low-cost single-axis knee whose adjustment range covers the window. For a 70 kg user walking at 1.0 m/s, the alignment offset must lie between 20.5 mm and 86.6 mm, a window 66.0 mm wide. Across user masses of 50 to 110 kg and speeds of 0.6 to 1.4 m/s, the lower bound ranges only from 19.1 mm to 21.9 mm and the upper bound from 81.6 mm to 91.1 mm. A sliding alignment plate providing 0 to 50 mm of offset therefore covers every computed lower bound, with a nominal setting of 25 mm giving a restoring moment of 6.52 N m at the critical loading-response instant and 23.69 N m at mid-stance. The failure boundaries are narrow and are stated at full size: the nominal setting loses its stability margin on a downhill slope of only 0.54 degrees (2.33 degrees at a 40 mm setting), a toe-catch stumble produces 82.4 to 219.7 N m of flexion moment against a maximum friction moment of 22.4 N m, and raising friction to 22 N m costs 38.5 percent of walking power in swing. Total parts cost for the specified design is 51.00 USD. No device is described as built, worn, or tested on people. SIMULATED, NOT MEASURED.