A guideline for the design of a four-wheeled walker.pdf

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where a is the acceleration of the wheel. All variables
are known except this acceleration. Isolating
for the acceleration,
a = A y - WAz/w/2g. (8)
For uniform acceleration (a = const.) over a small
interval of time t,
For the case ofthe wheel not contacting the ground
(Fz = 0),
Converging on a Design Parameter
(9)
where d, is an incremental distance slid over a
small interval of time. Assuming V o = 0 over this
short time span with constant acceleration,
r, = w/ zg 'a
a = Fylw/2g'
(10)
(11)
(12)
Once acceleration is determined, the distance can
be calculated. The distance that the mass moves
between each data point can then be summed for
the total slide distance. Dangerous sliding can occur
at either of the braked wheels at two points
during the trial, sitting down and then standing
up. The maximum of these four sliding distances
was set to 5 em. This distance is large enough not
to demand extreme walker designs, yet small
enough not to cause stress to the user while sitting.
The above calculations can be used to find the
relationship between any two variables ifthe other
five are known. For example, if the effect of the
seat position on the required walker mass must be
determined, all other variables are held constant,
and an iterative procedure can be performed for
each walker mass to isolate the seat position that
will allow for the desired maximum sliding distance.
Any seat position behind this value will be
a safe design with respect to sliding, while positions
further to the front will cause excessive sliding.
The bisection method was used to converge on
desired values to within 5%.
Tipping
Ifat any time the applied force vector and walker
weight combine for a resultant force outside of
the wheelbase, the wheels will begin to rise offthe
ground. The only opposing force that will help to
maintain the stability of the walker is the walker
weight. As long as the resultant of the combined
walker weight Wand applied force F are contained
within the wheelbase, tipping will be avoided. Five
ofthe design variables affect tipping: seat position,
wheelbase, walker mass, center of gravity, and
configuration. For example, a larger wheel base reduces
the tipping moment caused by the forces applied
outside of the wheelbase by shortening the
distances that they are acting from the wheels. The
position of the center of gravity of the walker will
control how great a stabilizing moment the walker
weight will cause about the wheels. Moment calculations
were performed to estimate design variables
that would allow for a 2-cm rise of either the
braked wheels or the casters.
Brake Failure
Brake failure can occur only when there is
enough normal force acting through the braked
wheels to avoid sliding. If the shear (horizontal)
force applied to either ofthe braked wheels creates
enough of a shear stress at the brake pad to exceed
the grip of the brake on the tire, the wheels will
roll. As in sliding, small movements of the walker
will go unnoticed by the user. Figure B6 shows the
shear force applied by the user through one braked
wheel over an entire trial. The horizontal line represents
the shear that the brake can withstand
without allowing rolling. The portion of the curve
above this line indicates rolling. The maximum
shear force that allows less than 5 em (2 in.) of rolling
must be found to avoid significant brake failure.
Design variables that will affect brake failure
are the seat-handle configuration and the walker
mass. As the walker mass increases, there is a
greater load to accelerate, resulting in less movement.
Calculations similar to the sliding analysis
were then performed to estimate design variables
that would allow for a 5-cm roll of either of the
braked wheels.
GUIDELINE FOR WALKER DESIGN 129