Ski boot walking attachment appendix
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Code
Logarithmic Decrement
readenct.m
Reads in the text file generated by the MSE Rectilinear apparatus.
function [t,f,val]=readenct(filename,vd,encnum)
a=textread(filename,'','headerlines',23);
if strcmp(vd,'d')
val=-a(:,encnum+1);
end
if strcmp(vd,'v')
val=-a(:,encnum+5);
end
t=a(:,1);
f=a(:,2);
num4.m
Using the data returned by readenct, allows determination of physical constants using logarithmic decrament analysis.
[time,force,displacement]=readenct('medium_natural.txt','d',1);
figure(1)
plot(time,displacement+0.1198);
axis([10.6 11.4 -4 4.2])
a=ginput
c=max(a)
figure(2)
plot(time,displacement+0.1198);
axis([10.6 11.4 -4 4.2])
b=ginput
d=max(b)
prompt={'Number of Peaks in between','X Coordinate First MAX.','X Coordinate Second MAX.'}
name='Get User Input';
numlines=1;
defaultanswer={'0','0','0'};
answer=inputdlg(prompt,name,numlines,defaultanswer);
n=str2double(answer{1});
x1=str2double(answer{2});
x2=str2double(answer{3});
T=(x2-x1)/(n);
dampingRatio=((1/(n-1))*(log(c(1,2)/d(1,2))))/sqrt((4*pi^2)+((1/(n-1))*(log(c(1,2)/d(1,2))))^2)
naturalFrequency=((1/(n-1))*log(c(1,2)/d(1,2)))/(dampingRatio*T)
dampedNaturalFrequency=naturalFrequency*sqrt(1-dampingRatio^2)
m=0.79;
k=naturalFrequency^2*m
CoefficientOfDamping=dampingRatio*2*sqrt(k*m)
MATLAB model
gmodel
The core code; calls for construction of a physical model, which is then iterated through the time of a step.
function gmodel
clear all
close all
%layerconfigs(:,1) = [1 1 1 5 1 4 5 1 4 5 1 4 1 5 1 1 5 1 4 1 5 1 5 4 1 1 1 1 4 1 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1];
layerconfigs(:,1) = [1 1 1 5 1 4 5 1 4 5 1 4 1 5 1 1 5 1 1 4 1 1 5 1 4 1 1 1 4 1 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1 1 4 1];
%heel is zero
xlen = .3;
xres = .0075;
zlen = .075;
ddstep = [0 0];
compression_modifier = [0 0];
xpos = 0:xres:xlen;
y0 = spline([0 4 6 10 12],[.8,1.3,1.6,1.3,.8],xpos); %initial height
%convert to meters
y0 = .0254*y0;
body_mass = 70; %kg
for j = 1:1
dd = zeros(size(y0)); %deflection
rubber_layers = makelayers(layerconfigs(:,j));
%begin step!
%step takes time, gets cblocked by gait... so:
%start each step, add other elems as they contact, but cblock as foot
%rolls?
%[foot_theta foot_length ankle_x ankle_y hip_x hip_y lint] = flexdata_cd_dat;
[foot_theta foot_length ankle_x ankle_y hip_x hip_y_nod lint all_y] = flexdata_cd_dat;
%Convert inches to metric
ankle_x = .0254*ankle_x;
ankle_y = .0254*ankle_y;
hip_x = .0254*hip_x;
hip_y_nod = .0254*hip_y_nod;
all_y = .0254*all_y;
hip_y = all_y(:,1)-mean(all_y(:,1));
step_time = .50;
theta = linspace(-pi/6,pi/6,round(length(lint)*step_time));
time = linspace(0,step_time,length(theta));
%make subsets of everything (we care about foot contact only here)
foot_theta = foot_theta(1:length(theta));
ankle_x = ankle_x(1:length(theta));
ankle_y = ankle_y(1:length(theta));
hip_x = hip_x(1:length(theta));
hip_y_nod = hip_y_nod(1:length(theta))-mean(hip_y_nod(1:length(theta)));
hip_y = hip_y(1:length(theta));
theta = foot_theta; %LOL
hip_y = smooth(hip_y,100,'sgolay',3);
hip_y_adj = hip_y;
for i = 3:length(theta)
stepsecs = time(i)-time(i-1);
clearfornext = 0;
%while clearfornext < 1
%find lengths
theta(i)
lens = -((xpos-mean(xpos))*sin(theta(i)))+abs(y0*cos(theta(i)))-abs(dd*cos(theta(i)));
[lens_sort lens_sort_ix] = sort(lens);
incontact = sum(lens>=lens_sort(end)-ddstep(i-1)*compression_modifier(i-1))
contact_indexes = lens_sort_ix(end-incontact+1:end)
lens
numcontact(i) = incontact;
ddstep(i) = lens_sort(end) - lens_sort(end-incontact);
hip_dely_dumb = hip_y(i) - hip_y(i-1);
hip_dy_dumb(i) = hip_dely_dumb/stepsecs; %dumb calc of hip y velocity
hip_dy2_dumb(i) = (hip_dy_dumb(i) - ((hip_y(i-1) - hip_y(i-2))/stepsecs))/stepsecs;
%force applied
k = rubber_layers(1,contact_indexes);
c = rubber_layers(2,contact_indexes);
f_expected = hip_dy2_dumb(i) * body_mass;
fex(i) = f_expected;
w0 = (sum(k)/body_mass)^.5;
gamma = sum(c)/(2*(sum(k)*body_mass)^.5);
wd = w0*(1-gamma^2)^.5;
wdi(i) = wd;
compression_modifier(i) = stepsecs/wd*8200;
dd(contact_indexes) = dd(contact_indexes) + ddstep(i)*compression_modifier(i);
dd(dd>y0*.5) = y0(dd>y0*.5)*.5;
f_app_k = sum(k ./ body_mass .* dd(contact_indexes));
f_app_c = f_expected - f_app_k;
hip_dy_adj(i) = -f_app_c/sum(c/body_mass)/25400;
if hip_dy_adj(i) < -10
hip_dy_adj(i) = -10;
end
hip_y_adj(i) = hip_y_adj(i-1) + hip_dy_adj(i) * stepsecs;
end %for i
figure(3)
% plot(time,'k')
hold on
%plot(time,hip_dy2_dumb/1000)
plot(time(1:round(.9*end)+1),hip_y_nod(round(.1*end):end)*.7,'r')
%plot(time,hip_y+hip_y_adj/10)
plot(time,hip_y-hip_y_adj+hip_y_adj(1))
figure(2)
%plot(time,hip_y)
%plot(time,hip_dy_adj)
end %for j
hold on
plot(time,-hip_y_adj/25.4)
title('Device deformation during step')
xlabel('Time [s]')
ylabel('Displacement [m]')
x = 1;
flexdata_cd_dat
Provides the kinesiological data behind normal walking as well as walking in ski boots.
function [foot_theta foot_length ankle_x ankle_y hip_x hip_y lint all_y_device] = flexdata_cd_dat
lint = linspace(0,1000,1000);
hip_height = -10*cos(lint*2*3.1516/1000);
%hip_theta = [162 162 170 178 185 193 183 170 160 156 158 162];
hip_theta = [157 164 170 178 185 193 183 170 160 154 156 157];
hip_time = [0 100 200 300 400 500 600 700 800 850 900 1000];
hip_theta_cubic = interp1(hip_time,hip_theta,lint,'spline');
knee_theta = [10 5 15 5 7 45 70 20 10];
knee_time = [0 100 250 450 500 600 750 950 1000];
knee_theta_cubic = interp1(knee_time,knee_theta,lint,'spline');
%ankle_theta = [0 -5 0 22 0 -8 8 0];
%ankle_time = [0 25 50 250 440 600 900 1000];
ankle_theta = [15 15];
ankle_time = [0 1000];
ankle_theta_cubic = interp1(ankle_time,ankle_theta,lint,'spline');
foot_length = 28;
shin_length = 56;
thigh_length = 70;
%{
figure(1)
%plot(hip_time,hip_theta)
plot(lint,hip_theta_cubic)
figure(2)
%plot(knee_time,knee_theta)
plot(lint,knee_theta_cubic)
figure(3)
%plot(ankle_time,ankle_theta)
plot(lint,ankle_theta_cubic)
figure(5)
plot(lint,hip_height)
%}
%
%
% %% That's the data. Now for the motion.
%
%
pi = 3.1416;
twopi = 2*pi;
hip_theta_rad = (180-hip_theta_cubic)*pi/180;
knee_theta_rad = knee_theta_cubic*pi/180;
ankle_theta_rad = ankle_theta_cubic*pi/180;
%hip_x(1:1000) = 0;
hip_x = linspace(1,170,1000);
hip_y = hip_height;
knee_x = hip_x + thigh_length.*sin(hip_theta_rad);
knee_y = hip_y - thigh_length.*cos(hip_theta_rad);
ankle_x = knee_x + shin_length.*sin(hip_theta_rad-knee_theta_rad);
ankle_y = knee_y - shin_length.*cos(hip_theta_rad-knee_theta_rad);
toe_x = ankle_x + foot_length.*sin(hip_theta_rad-knee_theta_rad+(1.9-ankle_theta_rad));
toe_y = ankle_y - foot_length.*cos(hip_theta_rad-knee_theta_rad+(1.9-ankle_theta_rad));
device_y = [.3 2 .3];
device_x = [0 .5 1];
device_y_cubic = interp1([0 .3 .5 .8 1],[1,1.5,2,1.6,1.2],linspace(0,1,100),'spline');
%device_y_cubic = interp1(device_x, device_y,linspace(0,1,100),'spline');
foot_theta = (hip_theta_rad-knee_theta_rad+(1.9-ankle_theta_rad))'-pi/2;
[device_theta, device_phi, device_r] = cart2sph(linspace(0,foot_length,100),-device_y_cubic,zeros(1,100));
device_theta_rot = repmat(device_theta,1000,1) + repmat(foot_theta,1,100);
device_r_rot = repmat(device_r,1000,1);
[device_x_rot device_y_rot dummy2] = sph2cart(device_theta_rot,zeros(1000,100),device_r_rot);
device_y_contact = min(device_y_rot,[],2);
device_y_add = min([device_y_rot(:,1) device_y_rot(:,100)],[],2)-device_y_contact;
device_y_add(600:1000) = zeros(1,401);
%hip_y = hip_y + device_y_add' - device_y_add(10);
%figure(9)
%plot(lint,device_y_add)
all_x = [hip_x' knee_x' ankle_x' toe_x'];
all_y_raw = [hip_y' knee_y' ankle_y' toe_y'];
ankle_low = ankle_y.*(ankle_y<toe_y);
toe_low = toe_y.*(toe_y<ankle_y);
all_y_adjustment = repmat(ankle_low' + toe_low',1,4);
all_y = all_y_raw - all_y_adjustment;
all_y(600:1000,:) = all_y_raw(600:1000,:) - repmat(linspace(all_y_adjustment(600,1),all_y_adjustment(1000,1),401)',1,4);
all_y_device = all_y + repmat(device_y_add,1,4);
figure(4)
clf
step = 40;
hold on
i = 1;
k = 1;
while k < 600
plot(all_x(k,:),all_y_device(k,:))
i = i + 1;
k = k + step;
end
