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MATH.md

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Thoughts

Information found

Different Wheel Chair Types

Different calculation coniderations for these chairs

  • Mid wheel drive chairs
  • Rear wheel drive chair with full differential steering
  • Manual Wheel Chair

Making a Radius Calculation

  • These chairs pivot on a centered axis which gives the chairs a negligible increase to turn radius outside of the phycial size of the chair.

Turn Radius Equation(s)

Method 1 -- RADIUS - of Outside Front Wheel -- Gives occasional negative number

Information found

variables

  • a = width between front two wheels
  • b = width between front and back wheels
  • c = width between back two wheels
  • tau = angle of wheel (estimated between 30 and 45 deg)

Formula

  • Radius = b/sin($\psi$) + (a-c)/2

Method 2 -- RADIUS - of Front Wheel -- Simplified version but feels erroneous

Information Found

Variables

  • w = Distance between front and back axis
  • alpha = Degree of turn for front wheel
  • R = Radius of front wheel

Formula

  • R = W / $\sin$($\alpha$)

Method 3 -- DIAMETER - for wheel chair turning -- Complicated but thorough

Information found

Variables

  • y = Width between chair center and back wheel
  • h = Width between chair center and front wheel
  • g = Width between front and back wheel
  • alpha = Angle of front wheel
  • x = Width between front most part of chair to center back wheel

Formula

TD = 2 * $\sqrt{y + h + (g/sin(\alpha))^2 + x^2}$

Additional information

Detailed math -- Where the different wheel chair types image was pulled from

  • This gives information to check if a hallway is wide enough for a wheel chair to do a 180deg turn

Assumptions

  • Output will be the same units as the input. This will be predefined to be cm
  • Wheel chair starts turn in center of door way
  • Ideal turn angle is instantly achieved
  • Wheel chair will be able to make a single turn into hallway without having to backup

STANDARD MANUAL WHEELCHAIR

  • Total width: 64 cm
  • Folded wheelchair width: 24 cm
  • Seat width: 46 cm
  • Rear wheel diameter: 58 cm
  • Front wheel diameter: 20 cm
  • Seat height: 49 cm
  • Total wheelchair height: 87 cm
  • Total length: 106 cm
  • Seat depth: 40 cm
  • Seat height: 45 cm