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decline.m
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function decline()
addpath code
pp_L = decline_theta_L();
pp_U = decline_theta_U();
x_L = 0.2982; % fminbnd(@(x) -ppval(pp_L, x), 0, 1)
x_U = 0.8051;
my_new_figure()
my_fplot(@f_L, '#0069C0')
my_fplot(@f_U, '#BA000D')
my_legend({' Lower Leg ', ' Upper Leg '})
my_ticks([0, 90, 180])
my_xlabel('Matched Fraction of Gait Cycle')
my_ylabel('Gyroscope Pitch = $ \theta $ Below $ xy \, $-Plane (deg.)')
my_title('\textbf{Downhill}')
my_print decline_theta_LU
my_new_figure()
my_fplot(@f_K, '#087F23')
my_ticks([0, 90, 180])
my_xlabel('Matched Fraction of Gait Cycle')
my_ylabel('Knee Angle, $ \theta_K $ (deg.)')
my_title('\textbf{Downhill}')
my_print decline_theta_K
my_new_figure()
my_fplot(@(x) deg2rad(d(@f_K, x)) / 1.006547, '#087F23')
my_ticks([-10, 0, +10])
my_xlabel('Matched Fraction of Gait Cycle')
my_ylabel('Knee Anglular Velocity, $ \omega_K $ (rad/s)')
my_title('\textbf{Downhill}')
my_print plots\decline_omega_K
my_new_figure()
my_fplot(@(x) deg2rad(d(@(x) d(@f_K, x), x)) / 1.006547 ^ 2, '#087F23')
my_ticks([-100, 0, +100])
my_xlabel('Matched Fraction of Gait Cycle')
my_ylabel('Knee Angular Acceleration, $ \alpha_K $ (rad/s/s)')
my_title('\textbf{Downhill}')
my_print decline_alpha_K
H = 1.845056;
m = 1;
L_T = (0.720 - 0.530) * H;
L_U = (0.530 - 0.285) * H;
% L_L = (0.285 - 0.039) * H;
D = @(x) sqrt(L_T ^ 2 + L_U ^ 2 - 2 * L_T * L_U * cosd(f_U(x) + 90));
I = @(x) m * D(x) ^ 2;
my_new_figure()
funx = @(t) arrayfun(@(t) abs(deg2rad(d(@(t) d(@f_K, t), t)) / 1.006547 ^ 2) * I(t), t);
funy = @(t) arrayfun(@(t) abs(deg2rad(d(@f_K, t)) / 1.006547), t);
% fplot(funx, funy, [0, 1], 'k', 'LineWidth', 1.5, 'MeshDensity', 3)
% my_plot([0.000, 1.533, 19.220, 21.080, 32.100, 34.900, 37.300, 39.270, 40.680, 41.290, 41.290], ...
% [4.465, 4.465, 4.325, 4.295, 3.863, 3.731, 3.571, 3.378, 3.142, 2.842, 0.000], 'k')
% CORRECTED:
my_plot([0.000, 1.523, 19.090, 20.950, 31.890, 34.670, 37.060, 39.020, 40.410, 41.020, 41.020], ...
[4.465, 4.465, 4.325, 4.295, 3.863, 3.731, 3.571, 3.378, 3.142, 2.842, 0.000], 'k')
xticks([0, 50])
yticks([0, 5])
yticklabels(pad(string(yticks), 4, 'left'))
xlim(xticks)
ylim(yticks)
my_xlabel('Drive Torque, $ |T| $ (N-m), per 1 kg Backpack Load')
my_ylabel('Drive Speed, $ |\omega| $ (rad/s)')
my_title('\textbf{Downhill}')
my_print decline_omega_vs_T
my_new_figure()
axis off equal
xlim([-2, +1])
ylim([-2, +1])
an_K = animatedline();
an_A = animatedline();
for x = 0 : 1e-3 : 1
y_L = f_L(x);
y_U = f_U(x);
if exist('h')
delete(h)
end
x_K = - cosd(y_U);
y_K = - sind(y_U);
x_A = x_K + cosd(y_L);
y_A = y_K - sind(y_L);
h = plot([0, x_K, x_A], [0, y_K, y_A], 'k.-', 'LineWidth', 1.5);
addpoints(an_K, x_K, y_K);
addpoints(an_A, x_A, y_A);
pause(1e-3)
end
function y_L = f_L(x)
if x < 0; y_L = f_L(x + 1);
elseif x < 0.5; y_L = ppval( pp_L, x + x_L + 1 );
elseif x < 1 - x_L; y_L = ppval( pp_L, x + x_L );
elseif x < 1; y_L = ppval( pp_L, x + x_L - 1 );
else; y_L = f_L(x - 1);
end
end
function y_U = f_U(x)
if x < 0; y_U = f_U(x + 1);
elseif x < 1 - x_U; y_U = ppval( pp_U, x + x_U );
elseif x < 0.5; y_U = ppval( pp_U, x + x_U );
elseif x < 1; y_U = ppval( pp_U, x + x_U - 1 );
else; y_U = f_U(x - 1);
end
end
function y_K = f_K(x)
y_K = f_L(x) + f_U(x) - 0.8151;
end
end