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Trang 1>> syms q d a al
>> H=[cos(q) -sin(q)*cos(al) sin(q)*sin(al) a*cos(q); sin(q) cos(q)*cos(al) -cos(q)*sin(al) a*sin(q); 0 sin(al) cos(al) d;
0 0 0 1]
H =
[ cos(q), -cos(al)*sin(q), sin(al)*sin(q), a*cos(q)]
[ sin(q), cos(al)*cos(q), -cos(q)*sin(al), a*sin(q)]
[ 0, sin(al), cos(al), d]
[ 0, 0, 0, 1]
>> syms q1 q2 q3 l1 l2 l3;
>> q=q1; d=l1; a=0; al=(pi/2);
>> H1=[cos(q) -sin(q)*cos(al) sin(q)*sin(al) a*cos(q); sin(q) cos(q)*cos(al) -cos(q)*sin(al) a*sin(q); 0 sin(al) cos(al) d; 0 0 0 1]
H1 =
[ cos(q1), -(4967757600021511*sin(q1))/81129638414606681695789005144064, sin(q1), 0]
[ sin(q1), (4967757600021511*cos(q1))/81129638414606681695789005144064, -cos(q1), 0]
[ 0, 1, 4967757600021511/81129638414606681695789005144064, l1] [ 0, 0, 0, 1]
>> q=q1; d=l1; a=0; al=sym(pi/2);
>> H1=[cos(q) -sin(q)*cos(al) sin(q)*sin(al) a*cos(q); sin(q) cos(q)*cos(al) -cos(q)*sin(al) a*sin(q); 0 sin(al) cos(al) d; 0 0 0 1]
H1 =
[ cos(q1), 0, sin(q1), 0]
[ sin(q1), 0, -cos(q1), 0]
[ 0, 1, 0, l1]
[ 0, 0, 0, 1]
>> q=q2; d=0; a=l2; al=0;
>> H2=[cos(q) -sin(q)*cos(al) sin(q)*sin(al) a*cos(q); sin(q) cos(q)*cos(al) -cos(q)*sin(al) a*sin(q); 0 sin(al) cos(al) d; 0 0 0 1]
H2 =
Trang 2[ cos(q2), -sin(q2), 0, l2*cos(q2)]
[ sin(q2), cos(q2), 0, l2*sin(q2)]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]
>> q=q3; d=0; a=l3; al=0;
>> H3=[cos(q) -sin(q)*cos(al) sin(q)*sin(al) a*cos(q); sin(q) cos(q)*cos(al) -cos(q)*sin(al) a*sin(q); 0 sin(al) cos(al) d; 0 0 0 1]
H3 =
[ cos(q3), -sin(q3), 0, l3*cos(q3)]
[ sin(q3), cos(q3), 0, l3*sin(q3)]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]
>> D3=H1*H2*H3
D3 =
[ cos(q1)*cos(q2)*cos(q3) - cos(q1)*sin(q2)*sin(q3), - cos(q1)*cos(q2)*sin(q3) - cos(q1)*cos(q3)*sin(q2), sin(q1), l2*cos(q1)*cos(q2) + l3*cos(q1)*cos(q2)*cos(q3) - l3*cos(q1)*sin(q2)*sin(q3)]
[ cos(q2)*cos(q3)*sin(q1) - sin(q1)*sin(q2)*sin(q3), - cos(q2)*sin(q1)*sin(q3) - cos(q3)*sin(q1)*sin(q2), -cos(q1), l2*cos(q2)*sin(q1) + l3*cos(q2)*cos(q3)*sin(q1) - l3*sin(q1)*sin(q2)*sin(q3)]
[ cos(q2)*sin(q3) + cos(q3)*sin(q2), cos(q2)*cos(q3) - sin(q2)*sin(q3), 0, l1 + l2*sin(q2) + l3*cos(q2)*sin(q3) + l3*cos(q3)*sin(q2)]
[ 0, 0, 0, 1]
>> simplify (D3)
ans =
[ cos(q2 + q3)*cos(q1), -sin(q2 + q3)*cos(q1), sin(q1), cos(q1)*(l3*cos(q2 + q3) + l2*cos(q2))]
[ cos(q2 + q3)*sin(q1), -sin(q2 + q3)*sin(q1), -cos(q1), sin(q1)*(l3*cos(q2 + q3) + l2*cos(q2))]
[ sin(q2 + q3), cos(q2 + q3), 0, l1 + l3*sin(q2 + q3) + l2*sin(q2)]
[ 0, 0, 0, 1]
>>