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A_Matricies.m
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A_Matricies.m
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%% Brian Bock
% ENPM662 - Modeling
% Term Project
% Fall 2019
%% Joint 1
clearvars
syms t1 t2 t3 t4 d1 d2 d3 d4 t5 d5 t6 d6 d7 t7
%%%%%% A1 %%%%%%%%%
Rotz1=[cos(t1)*cosd(90)-sin(t1)*sind(90) -(sin(t1)*cosd(90)+cos(t1)*sind(90)) 0 0;
(sin(t1)*cosd(90)+cos(t1)*sind(90)) cos(t1)*cosd(90)-sin(t1)*sind(90) 0 0;
0 0 1 0;
0 0 0 1];
Transz1=[1 0 0 0;
0 1 0 0;
0 0 1 d1;
0 0 0 1];
Transx1=eye(4);
Rotx1=[1 0 0 0;
0 cosd(90) -sind(90) 0;
0 sind(90) cosd(90) 0
0 0 0 1];
A1=Rotz1*Transz1*Transx1*Rotx1
%%%%%% A2 %%%%%%%%%
Rotz2=[cos(t2) -sin(t2) 0 0;
sin(t2) cos(t2) 0 0;
0 0 1 0;
0 0 0 1];
Transz2=[1 0 0 0;
0 1 0 0;
0 0 1 d2;
0 0 0 1];
Transx2=eye(4);
Rotx2=[1 0 0 0;
0 cosd(-90) -sind(-90) 0;
0 sind(-90) cosd(-90) 0
0 0 0 1];
A2=Rotz2*Transz2*Transx2*Rotx2
%%%%%% A3 %%%%%%%%%
Rotz3=[cos(t3) -sin(t3) 0 0;
sin(t3) cos(t3) 0 0;
0 0 1 0;
0 0 0 1];
Transz3=[1 0 0 0;
0 1 0 0;
0 0 1 d3;
0 0 0 1];
Transx3=eye(4);
Rotx3=[1 0 0 0;
0 cosd(-90) -sind(-90) 0;
0 sind(-90) cosd(-90) 0
0 0 0 1];
A3=Rotz3*Transz3*Transx3*Rotx3
%%%%%% A4 %%%%%%%%%
Rotz4=[cos(t4) -sin(t4) 0 0;
sin(t4) cos(t4) 0 0;
0 0 1 0;
0 0 0 1];
Transz4=[1 0 0 0;
0 1 0 0;
0 0 1 d4;
0 0 0 1];
Transx4=eye(4);
Rotx4=[1 0 0 0;
0 cosd(90) -sind(90) 0;
0 sind(90) cosd(90) 0
0 0 0 1];
A4=Rotz4*Transz4*Transx4*Rotx4
%%%%%% A5 %%%%%%%%%
Rotz5=[cos(t5) -sin(t5) 0 0;
sin(t5) cos(t5) 0 0;
0 0 1 0;
0 0 0 1];
Transz5=[1 0 0 0;
0 1 0 0;
0 0 1 d5;
0 0 0 1];
Transx5=eye(4);
Rotx5=[1 0 0 0;
0 cosd(90) -sind(90) 0;
0 sind(90) cosd(90) 0
0 0 0 1];
A5=Rotz5*Transz5*Transx5*Rotx5
%%%%%% A6 %%%%%%%%%
Rotz6=[cos(t6) -sin(t6) 0 0;
sin(t6) cos(t6) 0 0;
0 0 1 0;
0 0 0 1];
Transz6=[1 0 0 0;
0 1 0 0;
0 0 1 d6;
0 0 0 1];
Transx6=eye(4);
Rotx6=[1 0 0 0;
0 cosd(-90) -sind(-90) 0;
0 sind(-90) cosd(-90) 0
0 0 0 1];
A6=Rotz6*Transz6*Transx6*Rotx6
%%%%%% A7 %%%%%%%%%
Rotz7=[cos(t7)*cosd(-90)-sin(t7)*sind(-90) -(sin(t7)*cosd(-90)+cos(t7)*sind(-90)) 0 0;
(sin(t7)*cosd(-90)+cos(t7)*sind(-90)) cos(t7)*cosd(-90)-sin(t7)*sind(-90) 0 0;
0 0 1 0;
0 0 0 1];
Transz7=[1 0 0 0;
0 1 0 0;
0 0 1 d7;
0 0 0 1];
Transx7=eye(4);
Rotx7=eye(4);
A7=Rotz7*Transz7*Transx7*Rotx7
T=A1*A2*A3*A4*A5*A6*A7
%% Jacobian
o0=[0;0;0]
z0=[0;0;1]
o1=A1(1:3,4)
z1=A1(1:3,3)
A1A2=A1*A2;
o2=A1A2(1:3,4)
z2=A1A2(1:3,3)
A1A2A3=A1*A2*A3;
o3=A1A2A3(1:3,4)
z3=A1A2A3(1:3,3)
A1A2A3A4=A1*A2*A3*A4;
o4=A1A2A3A4(1:3,4)
z4=A1A2A3A4(1:3,3)
A1A2A3A4A5=A1*A2*A3*A4*A5;
o5=A1A2A3A4A5(1:3,4)
z5=A1A2A3A4A5(1:3,3)
A1A2A3A4A5A6=A1*A2*A3*A4*A5*A6;
o6=A1A2A3A4A5A6(1:3,4)
z6=A1A2A3A4A5A6(1:3,3)
A1A2A3A4A5A6A7=A1*A2*A3*A4*A5*A6*A7;
o7=A1A2A3A4A5A6A7(1:3,4)
z7=A1A2A3A4A5A6A7(1:3,3)
%cross(z1,(o7-o0))
Jv=[cross(z0,(o7-o0)) cross(z1,(o7-o1)) cross(z2,(o7-o2)) cross(z3,(o7-o3)) cross(z4,(o7-o4)) cross(z5,(o7-o5)) cross(z6,(o7-o6))]
Jw=[z0.*z0 z1.*z0 z2.*z0 z3.*z0 z4.*z0 z5.*z0 z6.*z0]
%Jacobian=[cross(z0,(o7-o0)) cross(z1,(o7-o1)) cross(z2,(o7-o2)) cross(z3,(o7-o3)) cross(z4,(o7-o4)) cross(z5,(o7-o5)) cross(z6,(o7-o6));
% z0.*z0 z1.*z0 z2.*z0 z3.*z0 z4.*z0 z5.*z0 z6.*z0];
%simplify(expand(Jacobian))