A Tip-Over Bound for Rollators and Walkers, and a Geometry Change That Widens It

A rollator is needed most at the moment it is least stable: when its user leans hard on the handles, crosses a door threshold, stops on a slope, or catches themselves during a stumble. This paper computes three rigid-body stability bounds for a standard rollator geometry carrying an 80 kg reference user. First, static tip angles: with the user leaning on the handles with 20% of body weight, the forward tip angle is 10.59 degrees and the sideways tip angle is 14.44 degrees; at a 30% lean the forward tip angle falls to 8.80 degrees. Second, the threshold event: if a front wheel is arrested by a door threshold while the user continues forward, the energy bound gives a critical speed of 0.563 m/s, below a slow walking speed of 0.8 m/s, and the horizontal force needed to push a loaded 100 mm front wheel over a 15 mm threshold is 186.2 N. Third, brake holding: with the brakes locked on the rear wheels, the friction limit holds the device to 18.26 degrees on a dry floor (a 33.0% grade) but only 10.90 degrees on a wet floor (a 19.2% grade). A single geometry change — extending the support polygon forward and rearward, widening the track, fitting a larger front wheel, and moving the handles 20 mm rearward — raises the forward tip angle at a 20% lean to 17.74 degrees, raises the threshold critical speed to 0.948 m/s, and lowers the 15 mm threshold force to 140.3 N, at a cost of 2.0 kg of added device mass, 0.08 m of added width, and 0.16 m of added length. One limit no geometry change removes: a full body-weight stumble-catch at 1.5 m/s carries 90.0 J of kinetic energy against a 40.2 J pivot barrier even for the enlarged base — 2.24 times more energy than the base can absorb — and would need a forward stability margin of 0.473 m. All results are computed, not measured. SIMULATED, NOT MEASURED.