6-DoF Robot Elbow - A Tutorial in MATLAB and Simulink

Duy Thuc 3/26/2024
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robot

1.Draw links ( using SolidWorks software)

2.Link assembly(using SolidWorks software)

3.Forward + Inverse Kinematics

Select the base coordinate system and attach the coordinate systems to the links.

Make a table of kinematic parameters(DENAVIT HARTENBERG)

Based on kinematic parameters determine the matrices

4.Install MATLAB

5.Attach the coordinate system to the link(using SolidWorks software)

6.Export SIMCAPE MULTIBODY

7.Create interface control

Select the base coordinate system and attach the coordinate systems to the links.

The forward kinematics problem is Calculating the matrix T6


KINEMATIC  PARAMETER (DENAVIT HARTENBERG)
 

Θi :Angle of rotation about the Z axis

α : Angle of rotation of the Z axis around the X axis (positive counterclockwise)

ai : Distance between axes Z

di: Distance between axes Z


GENERAL MATRIX


An=Rot(z,θ)Trans(0,0,d)Trans(a,0,0)Rot(x,α)

                        cosθ            -sinθcosα              sinθsinα              a cosθ

                        sinθ              cosθcosα             -cosθsinα            a sinθ

 An =               0                      sinα                      cosα                  d

                        0                       0                            0                       1

          

Using MatLab to calculate the Matrix T6 

A1= [cosd(t1)    0    sind(t1)   0;sind(t1)    0  -cosd(t1)   0;0   1   0    0;0   0   0    1];

A2= [cosd(t2)   -sind(t2)    0  cosd(t2)*a2    ;sind(t2)   cosd(t2)    0   sind(t2)*a2; 0 0 1 0;0   0   0  1];

A3= [cosd(t3)   -sind(t3)    0  cosd(t3)*a3;sind(t3)     cosd(t3)   0  sind(t3)*a3 ;0  1   0  0;0  0   0  1];

A4= [cosd(t4)  0  -sind(t4)   cosd(t4)*a4;sind(t4)    0  cosd(t4)   sind(t4)*a4;0  -1   0  0;0  0   0  1];

A5= [cosd(t5)  0  sind(t5)  0;sind(t5)   0  -cosd(t5)   0;0    1   0    0;0    0    0    1];

A6= [cosd(t6)   -sind(t6)     0   0;sind(t6) cosd(t6)  0    0;0   0   1    0;0   0   0    1];

Inverse Kinematics: The inverse kinematics problem is to calculate the rotations around the joint axis  

θ1 = θ1 + 1800 

θ2 = arctg2((C3a3 + a2)p’y - S3a3p’x , (C3a3 + a2)p’x + S3a3p’y ) 

θ3 = arctg2(S3 , C3)

θ4 = θ234 - θ3 - θ2 

θ5 = arctg2(C234(C1ax + S1ay) + S234az , S1ax - C1ay) 

θ6 = arctg2(S6 , C6) 

create interface control 


function slider1_Callback(hObject, eventdata, handles)

% hObject handle to slider1 (see GCBO)

% eventdata reserved - to be defined in a future version of MATLAB

% handles structure with handles and user data (see GUIDATA)


 

% Hints: get(hObject,'Value') returns position of slider

% get(hObject,'Min') and get(hObject,'Max') to determine range of slider


 

ModelName = 'robotElbow';

global var;

t1=get(handles.slider1,'value'); %set value from slider

set(handles.edit1,'string',num2str(t1));%display value Edit

t2=get(handles.slider2,'value');

set(handles.edit2,'string',num2str(t2));

t3=get(handles.slider3,'value');

set(handles.edit3,'string',num2str(t3));

t4=get(handles.slider4,'value');

set(handles.edit4,'string',num2str(t4));

t5=get(handles.slider5,'value');

set(handles.edit5,'string',num2str(t5));

t6=get(handles.slider6,'value');

set(handles.edit6,'string',num2str(t6));

set_param([ModelName '/Gain1'],'Gain',num2str(t1)) %TRUYEN CAC THONG SO CUA CAC THANH SLIDER TRONG GUI VAO KHOI SLIDER GAIN

set_param([ModelName '/Gain2'],'Gain',num2str(t2))

set_param([ModelName '/Gain3'],'Gain',num2str(t3))

set_param([ModelName '/Gain4'],'Gain',num2str(t4))

set_param([ModelName '/Gain5'],'Gain',num2str(t5))

set_param([ModelName '/Gain6'],'Gain',num2str(t6))


 

A1= [cosd(t1) 0 sind(t1) 0;sind(t1) 0 -cosd(t1) 0;0 1 0 0;0 0 0 1];

A2= [cosd(t2) -sind(t2) 0 cosd(t2)*530 ;sind(t2) cosd(t2) 0 sind(t2)*530; 0 0 1 0;0 0 0 1];

A3= [cosd(t3) -sind(t3) 0 cosd(t3)*430;sind(t3) cosd(t3) 0 sind(t3)*430 ;0 1 0 0;0 0 0 1];

A4= [cosd(t4) 0 -sind(t4) cosd(t4)*330;sind(t4) 0 cosd(t4) sind(t4)*330;0 -1 0 0;0 0 0 1];

A5= [cosd(t5) 0 sind(t5) 0;sind(t5) 0 -cosd(t5) 0;0 1 0 0;0 0 0 1];

A6= [cosd(t6) -sind(t6) 0 0;sind(t6) cosd(t6) 0 0;0 0 1 0;0 0 0 1];


 

T=A1*A2*A3*A4*A5*A6;

Px=T(1,4);

Py=T(2,4);

Pz=T(3,4);

set(handles.edit7,'string',num2str(Px));

set(handles.edit8,'string',num2str(Py));

set(handles.edit9,'string',num2str(Pz)); 



 

function pushbutton1_Callback(hObject, eventdata, handles)

% hObject handle to pushbutton1 (see GCBO)

% eventdata reserved - to be defined in a future version of MATLAB

% handles structure with handles and user data (see GUIDATA)

ModelName = 'robotElbow';


 

% Opens the Simulink model 

open_system(ModelName);

set_param(ModelName,'BlockReduction','off');

set_param(ModelName,'StopTime','inf');

set_param(ModelName,'simulationMode','normal');

set_param(ModelName,'StartFcn','1');

set_param(ModelName, 'SimulationCommand', 'start');


 
 

https://drive.google.com/file/d/1dVklz2KRPCROHQDW1ldOMMjqTo65IyVM/view?usp=sharing

https://www.youtube.com/watch?v=Jhte3nATu8k

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