Question about plots using meshgrids.

I've created a plot which can show the range of the tip's movement from a 2-armed robotic arm and I hope to add one more arm.

The correct code which can plot 2 arms shows as follows:

l1 = 10; % length of first arm
l2 = 7; % length of second arm
 theta1 = 0:0.1:pi/2;% all possible theta1 values
 theta2 = 0:0.1:pi;% all possible theta2 values
[THETA1, THETA2] = meshgrid(theta1, theta2); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) ; 
for theta1 = 0:0.1:pi/2;
    for theta2 = 0:0.1:pi;
      X =  l1 * cos(THETA1) + l2 * cos(THETA1+THETA2);  % compute x coordinates
      Y =  l1 * sin(THETA1) + l2 * sin(THETA1+THETA2); 
      plot (X,Y);
      hold on 
    end
end

The result after running shows as the figure

And here's the incorrect one with 3 arms:

l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
 theta1 = 0:0.1:pi/2;% all possible theta1 values
 theta2 = 0:0.1:pi;% all possible theta2 values
 theta3 = 0:0.1:pi;
[THETA1, THETA2, THETA3] = meshgrid(theta1, theta2,theta3); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3) ; 
for theta1 = 0:0.1:pi/2;
    for theta2 = 0:0.1:pi;
        for theta3 = 0:0.1:pi;
      X =  l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3);  % compute x coordinates
      Y =  l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3); 
      plot (X,Y);
      hold on 
        end
    end
end

The error is that" Error using plot Data cannot have more than 2 dimensions."

Answer 1

[Walter Roberson]

You do not need those three nested for loops: you calculate the same thing in every iteration of the loop. You can just use

X =  l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3);  % compute x coordinates
Y =  l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3);

with no loops.

But then you end up with X and Y both three dimensional; what it means to plot that is not well defined. But you could try

X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));

plot(X1, Y1)

[Ercong Shang]

I've just modified the code as you said

l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
 theta1 = 0:0.1:pi/2;% all possible theta1 values
 theta2 = 0:0.1:pi;% all possible theta2 values
 theta3 = 0:0.1:pi;
[THETA1, THETA2] = meshgrid(theta1, theta2); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2)  ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2)  ;
for theta1 = 0:0.1:pi/2;
    for theta2 = 0:0.1:pi;
      X =  l1 * cos(THETA1) + l2 * cos(THETA1+THETA2);  % compute x coordinates
      Y =  l1 * sin(THETA1) + l2 * sin(THETA1+THETA2);
      X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
      Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));
    plot(X1,Y1)
    hold on
    end
end

But the result is the same of the previous, I hope to add another length and angle to it.

[Walter Roberson]

No loops!

l1 = 10; % length of first arm
l2 = 7; % length of second arm
l3 = 6;
 theta1 = 0:0.1:pi/2;% all possible theta1 values
 theta2 = 0:0.1:pi;% all possible theta2 values
 theta3 = 0:0.1:pi;
[THETA1, THETA2, THETA3] = meshgrid(theta1, theta2,theta3); % generate a grid of theta1 and theta2 values
X = l1 * cos(THETA1) + l2 * cos(THETA1+THETA2) + l3 * cos(THETA1+THETA2+THETA3) ; % compute x coordinates
Y = l1 * sin(THETA1) + l2 * sin(THETA1+THETA2) + l3 * sin(THETA1+THETA2+THETA3) ; 
X1 = reshape(X, size(X,1), size(X,2)*size(X,3));
Y1 = reshape(Y, size(Y,1), size(Y,2)*size(Y,3));
plot(X1, Y1);

[Ercong Shang]

Thanks a lot! By the way , where do I need to modify in order to add as many arms as I can ? Just take 4 arms as an example if possible.

[Walter Roberson]

What is the generalized expression for X and Y ? All cos for X and all sin for Y ? That does not sound like it would achieve all possible locations.

Assume that you have a numeric vector L that contains the lengths for each arm. Assume that you have a cell array thetas of the same length, each entry of which contains the list of theta values for the corresponding arm.

n_arm = length(L);
clear THETAS
[THETAS{1:n_arm}] = ndgrid(thetas{:});
X = 0;
Y = 0;
theta_sum = 0;
for arm_num = 1 : n_arm
  theta_sum = theta_sum + THETAS{arm_num};
  X = X + L(arm_num) * cos(theta_sum);
  Y = Y + L(arm_num) * sin(theta_sum);
end

X1 = reshape(X, size(X,1), []);
Y1 = reshape(Y, size(Y,1), []);
plot(X1, Y1);