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## Wheelchair Simulation

```% Author: JONAH KADOKO
% Tufts University
% Numerical Methods (ES 55) FINAL PROJECT (Nov 2 2011)
%

% The purpose of this program is to simulate the dynamics of a wheelchair at
% given parameters: namely, Mass of rider, road profile, force of
% propulsion, bearing frictional torque, and wheelchair dimensions.

% The main figure of the program will plot a wheelchair moving along a
% user-defined road. The user can choose to plot energy, distance, speed
% and jerk graphs by clicking buttons on the main figure to the left.

% The following are the required files:
%   wheelchair1.m - function that carries the differential equation
%           governing dynamics of wheelchair. Essential.
%   PlotOther.m - script that plots results of energy,distance, velocity,
%           acceleration andjerk. Essential
%   road.m - function that calculates the (x,y) coordinates of road profile
%           as well as the curved distance along the road. Essential.
%   wCcalculations.m - function that calculates energy, distance etc from
%           the output of ODE23. Essential.
%   endEvent.m - function for ending ODE23 solver. Essential.
%   wC.mat - (x,y) coordinates of wheelchair drawing. Important if the user
%           desires a visually appealing animation. Less Essential.
%   [importing_jpg_for_xy_points.m] - script for importing jpeg picture to
%           (x,y) coordinates. This file is not needed unless the user
%           wants to modify the wheelchairpicture
%   [animaition.avi] - animation vedio, this is optional. Uncomment
%           VideoWriter() line and mov() lines
clear;close all;

% Parameters of the wheelchair/rider
Mw=5; % Mass of back wheel (kg)
theta=[-180 20]; % initial position of and speed of wheelchair [rad rad/s]
Rp=0.4; % radius of the push ring (m)
Rbw=0.5; % radius of the back wheel (m)
Mr=100; % Mass of rider in kg
F=100; % force input +by the rider (N)
k=1; % frictional coefficient of bearings (greater than 1 is fine)
dt=0.1; % size of time steps (s)
tMax=300; % the time to simulate (s)
T=5; % time it takes for the rider to put more force (s)

xMax=500; % the maximum amount of distance to be travelled by the rider
% (x.^3)*(-0.010)+x.^2*0.5 - Potential candidate for road profile (m)
%
rdFunc=@(x) exp(-.001*x).*sin(0.01*x); % road profile function (m)
[nxRd,nyRd,ns]=road(rdFunc,-xMax); % calculating behind the starting point
s=[ns s];xRd=[nxRd xRd];yRd=[nyRd yRd];

% Differential equation governing the dynamics of the wheelchair
tspan=0:dt:tMax;
options=odeset('events',@endEvent); % set the end conditions
[t,Ang]=ode23(@wheelchair1,tspan,theta,options,xRd,yRd,s,F,Rp,Rbw,Mw,Mr,k,T);
yMax=max(yRd);yMin=min(yRd);

% Calculations  of Energy, Displacement, Speed,
[kE,pE,tE,dispXY,dispX,dispY,dist,v,Acc,Jerk]=wCcalculations(t,Ang,F,Rbw,Mr,Mw,s,xRd,yRd,dt);

load wC % load the coordinates of the picture of wheelchair. I drew this
% picture using CAD software and then extracted the (x,y) coordinates using
% MATLAB. Feel free to replace wC with custom picture.

% Define the limits of the graphs
screenSize=get(0,'ScreenSize');plotW=0;
GUI=figure('Position',screenSize,'Name','WheelChair Simulation Window','NumberTitle','off');
% animation variables
% This feature is not present in some versions of MATLAB
% mov=VideoWriter('animationES55.avi');mov.FrameRate=10;open(mov);
% Define the limits of the graphs
d=1e-2; % this is the duration of one frame
fSize=16; % Font size
wchair=wC;Rw_anim=1; nChair=length(wchair);% wheel chair figure
dispMax=max(dispXY);dispMin=min(dispXY);
vMin=min(v); vMax=max(v);
tMax=max(t); % maximum time
if yMax <5,yMax=5; end
if yMin>-5, yMin=-5; end
% WheelChair Parameters
Lmin=min(wC(:,1));Lmax=max(wC(:,1));%Length limits of the wheelchair
Hmin=min(wC(:,2));Hmax=max(wC(:,2));%Height limits of wheelchair
sX=0.1*xMax/(Lmax-Lmin); % calculating the scale factor in X
sY=0.2*(yMax-yMin)/(Hmax-Hmin); % calculating the scale factor in Y
wC=[sX*wC(:,1) sY*wC(:,2)]; % scale wheel chair  and ...
%   Translate the wheel chair to start at origin
% the frontWheel min is at row = 3882
% The backWheel min is at row = 2323
bkWheelMin=[wC(2323,1),wC(2323,2)];frWheelMin=[wC(3882,1),wC(3882,2)];
Lmin=min(wC(:,1));Lmax=max(wC(:,1));L=abs(bkWheelMin(1)-frWheelMin(1));
wC=wC+repmat([-bkWheelMin(1) -bkWheelMin(2)],nChair,1);
bkWheelMin=[wC(2323,1),wC(2323,2)];frWheelMin=[wC(3882,1),wC(3882,2)];
rot=eye(2); % this is the rotation matrix for the wheelchair (not using it)

% SET GUI controls
runButton=uicontrol('style','pushbutton','string','RUN',...
plotEnergy=uicontrol('style','pushbutton','string','Plot pE,kE & dist',...
'position',[25 500 90 50],'callback','PlotOther;plotW=1;');
plotVel=uicontrol('style','pushbutton','string','Plot v, & Acc',...
'position',[25 400 90 50],'callback','PlotOther;plotW=2;');
plotJerk=uicontrol('style','pushbutton','string','Plot Jerk;',...
'position',[25 300 90 50],'callback','PlotOther;plotW=3;');

% Loop through every frame

for frame=1:length(Ang)

% calculate the intersection of the wheel chair front wheels with road
%    My idea was to rotate the orientation of wheel chair with the slope of
%    the road. It worked fine except that the sloped wheelchair is not
%    visually appealing. I will work on that in future versions.
%     theta=intersection(rdFunc,bkWheelY,bkWheelX,L);
%     rot=[cos(theta) sin(theta);
%     -sin(theta) cos(theta)];

%     move and rotate the wheel chair
wchair=repmat([dispX(frame) dispY(frame)],nChair,1)+wC*rot;

%   plot the wheelchair
plot(wchair(:,1),wchair(:,2),'o','MarkerSize',Rw_anim);hold on;

plot(xRd,yRd,'m','LineWidth',3);
title('Animation of Wheel Chair','FontSize',fSize,'FontWeight','bold');
xlabel('x (m)','FontSize',fSize,'FontWeight','bold');
ylabel('z (m)','FontSize',fSize,'FontWeight','bold');hold off;
axis([-1.3*xMax xMax yMin 0.4*(yMax-yMin)+yMax]);
%     axis([dispMin*Rbw dispMax*Rbw 0 10]);
% Write the video file. This feature is not available in some MATLAB
% versions.
%     frame=getframe(GUI,screenSize);
%     writeVideo(mov,frame);
pause(d);
end
% close(mov);
```

### Results

I verified my math with the math in this paper and I found it to be realistic.

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