Mechanical Principles of Wheelchair Design Fperson CG F1 F2 F3 Amos Winter Graduate Student Department of Mechanical Engineering Massachusetts Institute of Technology Ralf Hotchkiss Chief Engineer Whirlwind Wheelchair International This manual is free to anyone Please photocopy and distribute Forces Where useful Seat Forange Forange 2 N Frame Wheels Footrests Add forces Description A force is the amount one object tries to push or pull another object The earth exerts a force on every object pulling it towards the ground This is known as the force due to gravity When you measure the weight of a person you are measuring the force of gravity pulling on him When an object is stationary all the forces acting on it are balanced When the forces are not balanced the object will move Forces are measured in Newtons or pounds To convert kilograms to Newtons multiply the number of kilograms by 9 81 One kilogram is equal to 2 2 lbs 0 Fhand Forange Fhand 0 Fhand 2 N Fhand 2 N Example Holding an orange When you hold an orange you feel the force of gravity trying to pull it to the ground Your hand has to push up on the orange to keep it from falling The force the orange exerts on your hand is equal in amount and opposite in direction to the force your hand is exerting on the orange see the equation When you put the orange on a table now the table is pushing on it with an equal and opposite force When you drop the orange the forces on it are unbalanced The orange falls because the force of gravity pulls it to the ground This manual is free to anyone Please photocopy and distribute 1 Center of gravity Where useful Fwrench Fwrench 10 N CG Seat Frame Ffinger Wheels Lhandle Footrests Lhead Lhandle Lhead Add forces Description The center of gravity CG of an object is the point where it can be balanced If you wanted to think of gravity pulling on an object at a single point the CG is that location Understanding CG location is important in wheelchair design You can approximate the force a person exerts on a wheelchair as his total weight applied at the CG of his body which is a point around his hips 0 F finger Fwrench F finger 10 N Example Find the CG of a wrench The CG of the wrench is the point where the wrench can be balanced More mass is concentrated at the head which makes the CG closer to the head and not at the center of the handle This manual is free to anyone Please photocopy and distribute 2 Free body diagram Where useful Seat Frame Wheels Fperson 500 N Add forces Fperson 0 2 Fcaster 2 Fwheel Fperson Fwheel CG Fcaster Footrests Fcaster Description A free body diagram FBD is a visual representation of the forces acting on an object You have already seen FBDs in the previous examples As in the case of stationary objects like the orange and wrench example there are forces acting on them to balance the force of gravity pulling them to the ground Fwheel Example Sitting in a wheelchair The figure shows the FBD of a person in a wheelchair If you know the weight of the person you know the force her body exerts on the wheelchair Because the wheelchair is not moving the forces the ground exerts on the wheels and casters must add up to be equal and opposite to the force from the person s weight note the Add forces equation is for 2 wheels and 2 casters In the next sections you will learn how to calculate the forces exerted by the ground on the wheels and casters This manual is free to anyone Please photocopy and distribute 3 Moments Fwrench 10N Where useful Frame Wheels A CG Fhandle Lhandle 12cm Add forces Description A moment is like a force but instead of trying to push an object it tries to twist it A moment is a force applied to a lever arm When you tighten a bolt you apply a moment to the bolt with a wrench You produce the force with your body and the lever arm is the handle of the wrench The moment is calculated by multiplying the force times the perpendicular at a 90o angle distance from the pivot point In every FBD if the object is stationary both the forces and moments need to add up to zero Lhead 8cm Fhead 0 Fhandle Fhead Fwrench Fhandle Fhead 10 N Add moments 0 Fwrench Lhandle Fhead Lhandle Lhead L 10 N 12cm F F wrench handle 6N F 4N head Lhandle Lhead 12cm 8cm handle Example Find forces with moments Support a wrench on two fingers as shown in the figure above Since the object is not moving we know the moments at each point must add up to zero Calculating moments from point A the moment from the weight of the wrench which acts at the CG tries to make the wrench spin clockwise The moment from our finger under the head tries to make the wrench spin anticlockwise negative direction Knowing the moments add to zero we can calculate the force at the head Use the addition of vertical forces to find the force at the handle This manual is free to anyone Please photocopy and distribute 4 Add forces Tipping angle 0 2 Fcasters 2 Fwheels Fperson tan tip Fperson 0 2 Fcasters 2 Fwheels 500 N Add moments 0 Fperson Lcaster 2 Fwheel Lcaster Lwheel Fwheel A A tip arctan B B Can also calculate tip from height wheels lift off ground h A tip arcsin tip 2 A CG 500 N 40 6cm 200 N 40 6cm 10 2cm Fcaster 50 N CG Tipping angle and height for different chairs geometries L F person caster Lcaster Lwheel Fwheel Fperson Fcaster Lcaster Fwheel Lwheel A B tip htip 0 3 17o 11cm 0 4 21o 18cm tip 0 5 27o 28cm Fwheel ground B htip Example Forces on a wheelchair Example Wheelchair tipping angle Find the forces acting on the wheels of the wheelchair in the above figure If you know the weight of the person in the chair the location of her CG and the distance between the wheels you can calculate the forces on the wheels by using moments The calculations in the example above add the moments about the front caster A wheelchair will tip over when the forces and moments acting on the chair become unbalanced When the wheelchair tips to a point where the CG of the user is vertically aligned with the point where the wheel contacts the ground the chair is unstable The angle the wheelchair makes with the ground at this point is called the tipping angle tip as shown in the figure above If the wheelchair tips further it will fall over because there is no moment to counteract the moment generated by the CG This manual is free to anyone Please photocopy and distribute 5 Internal forces Mnut Cut Fhand Where useful Frame Wheels L 2 Fnut L Fhand Mcut …