Asked by Shashank Thakker
on 2 Oct 2015

I want to generate a function which can give transformation matrix for given DH parameters. The cache is the function should valid for any number of links. It means number of links are variable. Like if I want take 4 ,5 or6 any no of links it should take dh parameters for all the links and should give the final transformation matrix.

Answer by Pushpendra Gupta
on 22 Jul 2019

syms L1 L2 L3 L4 L5 Q1 Q2 Q3 Q4 Q5

alphaa=[0,0,-90,0,+90]; % this is the alpha value for all the link

a=[L1,L2, L3, L4, L5]; % Length of the Link

d=[0,0,0,0,0]; %Offset

Q=[Q1,Q2,Q3,Q4,Q5]; % joint angle variation

%%Transformation Matrices

for i=1:5

switch i

case 1

T01= [cos(Q(1,i)),-sin(Q(1,i))*cosd(alphaa(1,i)),sind(alphaa(1,i))*sin(Q(1,i)),a(1,i)*cos(Q(1,i));sin(Q(1,i)),cos(Q(1,i)).*cosd(alphaa(1,i)),-sind(alphaa(1,i))*cos(Q(1,i)),sin(Q(1,i))*a(1,i);0,sind(alphaa(1,i)),cosd(alphaa(1,i)),d(1,i);0,0,0,1];

case 2

T12= [cos(Q(1,i)),-sin(Q(1,i))*cosd(alphaa(1,i)),sind(alphaa(1,i))*sin(Q(1,i)),a(1,i)*cos(Q(1,i));sin(Q(1,i)),cos(Q(1,i)).*cosd(alphaa(1,i)),-sind(alphaa(1,i))*cos(Q(1,i)),sin(Q(1,i))*a(1,i);0,sind(alphaa(1,i)),cosd(alphaa(1,i)),d(1,i);0,0,0,1];

case 3

T23= [cos(Q(1,i)),-sin(Q(1,i))*cosd(alphaa(1,i)),sind(alphaa(1,i))*sin(Q(1,i)),a(1,i)*cos(Q(1,i));sin(Q(1,i)),cos(Q(1,i)).*cosd(alphaa(1,i)),-sind(alphaa(1,i))*cos(Q(1,i)),sin(Q(1,i))*a(1,i);0,sind(alphaa(1,i)),cosd(alphaa(1,i)),d(1,i);0,0,0,1];

case 4

T34= [cos(Q(1,i)),-sin(Q(1,i))*cosd(alphaa(1,i)),sind(alphaa(1,i))*sin(Q(1,i)),a(1,i)*cos(Q(1,i));sin(Q(1,i)),cos(Q(1,i)).*cosd(alphaa(1,i)),-sind(alphaa(1,i))*cos(Q(1,i)),sin(Q(1,i))*a(1,i);0,sind(alphaa(1,i)),cosd(alphaa(1,i)),d(1,i);0,0,0,1];

case 5

T45= [cos(Q(1,i)),-sin(Q(1,i))*cosd(alphaa(1,i)),sind(alphaa(1,i))*sin(Q(1,i)),a(1,i)*cos(Q(1,i));sin(Q(1,i)),cos(Q(1,i)).*cosd(alphaa(1,i)),-sind(alphaa(1,i))*cos(Q(1,i)),sin(Q(1,i))*a(1,i);0,sind(alphaa(1,i)),cosd(alphaa(1,i)),d(1,i);0,0,0,1];

end

end

T01 % first link with respect to base

T02= T01*T12

you are looking for T05 then

T05= T01*T12*T23*T34*T45

This is for symbolic form in case of numeric evaluation use makehgtform

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