How to generate 3D surface or robot workspace?

I have a 4 DOF robot with variables t1,t2,d3 and t4. I used linspace to generate values for the variables, and also I calculated the positions, resulting 90x90x90 matrices (for X, Y and Z). Now how could I do a work-space with this data? Obviously plot3 or surf does not work. I searched the answers and the one with example is no longer valid. Can please help me with some examples or code?

l1=500;l2=600;l3=400;l4=191.03;
  t1=linspace(-180,180,90)*pi/180;
  t2=linspace(-90,90,90)*pi/180;
  d3=linspace(-200,200,90);
  t4=linspace(-180,180,90)*pi/180;
  nt1=length(t1);
  nt2=length(t2);
  nd3=length(d3);
  for i=1:nt1
      for j=1:nt2
          for k=1:nd3
     xM(i,j,k)=round((-cos(t1(i)).*cos(t2(j))).*((d3(k) + l2 + l3 + l4)));
        yM(i,j,k)= round((-cos(t2(j)).*sin(t1(i))).*(d3(k) + l2 + l3 + l4));
        zM(i,j,k)=round((l1 - l4.*sin(t2(j)) - sin(t2(j)).*(d3(k) + l2 + l3)));
          end
      end
  end

Clarifications:

- What is workspace of a robot? Forward kinematics uses the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters. The dimensions of the robot and its kinematics equations define the volume of space reachable by the robot, known as its workspace. Or, as Amid said: the space that the robot gripper can reach, all way around (visualize all the points that the robot could reach, giving us a 3D space).

- The workspace using these dimensions will be a sphere. Why? The robot is a spherical robot (with two rotary joints and one prismatic).

- The parameter t4 does not appear in the equations, it's just the orientation of the final element (end-effector), thus it does not influence the workspace.

- The values of the variable parameters (t1,t2,d3) are maximum. This does not happen in real life, due to mechanical restrictions or space consideration. Modifying these parameters with more realistic values will result in a sphere with cut off top and bottom. This is normal, and that's how it should look.

Thank you very much for the help!

[Stephen23]

" Now how could I do a work-space with this data?"

What do you mean by "do a workspace" ? Do you want to plot, display, or otherwise visualize this data somehow?

[Cristina Magda]

I am adding some clarifications for future users interested in this. Thank you for your time.

[Mihir Andharia]

Can you please tell me how to plot workspace of Stewart platform?

Answer 1

[hmi amid]

Hi Cristina, I think I understand the question. You mean by workspace, the space the robot arm can reach? If yes, this is the correction you should start with. Actually, don't use 3 for loops. Never do that in Matlab... It will slow down your process. Use in this case, NDGRID. Here is the code

l1=500;l2=600;l3=400;l4=191.03;
t1=linspace(-180,180,90)*pi/180;
t2=linspace(-90,90,90)*pi/180;
d3=linspace(-200,200,90);
t4=linspace(-180,180,90)*pi/180;
[T1,T2,D3]=ndgrid(t1,t2,d3);  % This will create matrices of 90x90x90 for each variable
xM = round((-cos(T1).*cos(T2)).*((D3 + l2 + l3 + l4)));
yM = round((-cos(T2).*sin(T1)).*(D3 + l2 + l3 + l4));
zM = round((l1 - l4.*sin(T2) - sin(T2).*(D3 + l2 + l3)));
plot3(xM(:),yM(:),zM(:),'.') % This is the plot type you should be using.
% With a '.' as an argument to show only locations and not lines
% Also, (:) converts any matrix into a list of its elements in one single column.

Anyway it is interesting, the output is a sphere of about 3000 diameter. If you want to incorporate t4 also just add it in NDGRID

l1=500;l2=600;l3=400;l4=191.03;
t1=linspace(-180,180,90)*pi/180;
t2=linspace(-90,90,90)*pi/180;
d3=linspace(-200,200,90);
t4=linspace(-180,180,90)*pi/180;
[T1,T2,D3,T4]=ndgrid(t1,t2,d3,t4); % Add t4 here
xM = round((-cos(T1).*cos(T2)).*((D3 + l2 + l3 + l4))); % and use it in x y z as T4
yM = round((-cos(T2).*sin(T1)).*(D3 + l2 + l3 + l4));
zM = round((l1 - l4.*sin(T2) - sin(T2).*(D3 + l2 + l3)));
plot3(xM(:),yM(:),zM(:),'.')

Amid.

[Cristina Magda]

I never used ndgrid before. The workspace should be indeed a sphere. I will add some clarifications for future users interested in this. Thank you very much for the code and your time!

[Raul Alvarez Torrico]

Hi Cristina, can you share an image of your robot arm to see their links? I'm having trouble understanding how the parameters you are using relate to the shape of your robot. An image of your generated workspace would be helpulf also, if isn't much to ask. Thanks in advance.

[Anoop Kumar Sinha]

Hi Amid,

Is this method of plotting workspace called Monte Carlo Method?

Regrads,

Anoop

[Jacopo Podavini]

Hi Amid or whoever is reading this that used this ndgrid method, is there a way to obtain from those matrixes a vector with every position for each X,Y,Z coordinate?

Thank you very much

Answer 2

[Omer Oztoprak]

Hi Cristina and everyone

do you know now how to plot workspace

Answer 3

[Cristina Magda]

The answer selected as accepted answer (hmi amid) is the correct one. Best of luck to you all.

Answer 4

[Daniele Poli]

Ciao, purtroppo non mi torna il plot allegato, dovrei fare un workspace di un robot delta.