Since last year, Steve has been confined to a wheelchair. He gets in and out of it with help from a device called a Hoyer Lift:
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| Hillrom |
The straps at the head and legs have several different notches to adjust the length from the hoist attachments. Along with those adjustments, Steve can also lie higher or lower in the sling, and adjust the angle between his legs and torso. Given these options then, Sally asks: How do we adjust things to get Steve to be more/less upright?
This turns out to be a surprisingly complicated geometry problem. I started off by diagramming it this way:
a and b are the lengths of the two straps, L is Steve's height, h is how far down the pad he's positioned, and θ is the leg-torso angle. We can use the Law of Cosines to first find the width of the two triangles, w, and then the angle between the lift straps:
What we need to figure out from here is the coordinates of that lowest point, where the sling bends. To do that, I rotated the setup so that a lay on the x-axis, and worked out the geometry from there. If the point we want is at (x,y) in these coordinates, then we can write
Solving these 4 equations together produces pages of messy equations, so instead I decided to do it numerically. Since my goal was to make an interactive tool my parents could use, I'm working in JavaScript, so I had to make my own equation solver. I decided to use the bisection method, in which we find the point where a function crosses zero by bracketing it more and more finely. For some combinations of parameters the algorithm fails to find a solution, and the angles don't always look right, but I think it can give a feel for how these different choices factor into the final angle that the lift rests. You can see the code here, or just play with it below!
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