a. Matlab Code

%Peak-a-Bevo Robotics_Project_V3

%Lila Bernhardt

clc; clear all; close all;

%Kinematic Analysis using a 4-Bar Crank Slider Approximation

%Origin:

Ox = 4;

Oy = 4;

%Variables:

a=1.6; 

b=6.7;

ci=4.5;

d=9.6;

Theta1=95.6;

k = 6.2;

f = 9.2;

Theta6 = 102.5;

%Initial Condition: Solve for Theta 3 and Theta 4 at Theta 2 = 0

Theta2i = 0;

[T1i,T2i,T3i,T4_i] = fourbarpos(a, b, ci, d, Theta1, Theta2i, -1);

Theta4i = T4_i + 180; %T_4 is supplementary angle of Theta0

bx=b*cosd(T3i);

L1 = bx + a;

L2 = L1 - d*cosd(Theta1);

%Position analysis of Theta 3, Theta 4, and c with input of Theta 2 = [0, 360]

for i=1:360

   T2(i) = i;

   T1(i) = Theta1;

   T3(i) = acosd((L1-a*cosd(T2(i)))/(b));

   T4(i) = atand( (d*sind(T1(i)) - b*sind(T3(i)) - a*sind(T2(i)))/ (-L2) )+180;

   c(i) = -L2/cosd(T4(i));  

end

%Plot Theta3 Theta4

figure(1)

grid on

subplot(2,1,1);

sgtitle('Theta 3 and Theta 4')

  plot(T3, 'g')

  grid on

  xlim([0 360])

  ylim([50 90])

  xlabel("Theta 2 (degrees)")

  ylabel("Theta 3 (degrees)")

subplot(2,1,2);

  plot(T4, 'r')

  grid on

  xlim([0 360])

  xlabel("Theta 2 (degrees)")

  ylabel("Theta 4 (degrees)")

  hold off

for i=1:360

   Hy(i) = a*sind(T2(i)) +b*sind(T3(i)) + k*sind(T4(i)) +3 + Oy;

   Py(i) = a*sind(T2(i)) +b*sind(T3(i)) + 1.5*sind(T4(i)) + Oy;

   T5(i) = atand((13-Py(i))/1.2);

   f(i) = 1.2/cosd(T5(i));

   Ay(i) = Py(i) + 6.5*sind(T5(i) + 25);

   Ax(i) = .6 + 6.5*cosd(T5(i) + 25);

end

figure(2)

  plot(Hy)

  hold on

  plot(Ay)

  legend('Head', 'Hands')

  grid on

  title('Vertical Movement of Head and Hands')

  xlabel("Theta 2 (degrees)")

  ylabel("y-position (cm)")

  xlim([0 360]) 

  ylim([10 19])

figure(3)

plot(Ax)

  title('Horizontal Movement of Hands')

  xlabel("Theta 2 (degrees)")

  ylabel("x-position (cm)")

  grid on

  xlim([0 360])