运动学建模的齐次坐标变换 matlab程序
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>> syms a1 a2 a3 a4 a5 a6 a7
T1=[1 0 0 0;0 1 0 0;0 0 1 0;0 0 0 1]
T2=[cos(a1) 0 sin(a1) 15;sin(a1) 0 -cos(a1) 0;0 1 0 0;0 0 0 1]
T3=[cos(a2) 0 sin(a2) 60;sin(a2) 0 -cos(a2) 0;0 1 0 0;0 0 0 1]
T4=[cos(a3) -sin(a3) 0 80;sin(a3) cos(a3) 0 0;0 0 1 0;0 0 0 1]
T5=[1 0 0 0;0 1 0 0;0 0 1 40;0 0 0 1]
T6=[cos(a4) -sin(a4) 0 -80;sin(a4) cos(a4) 0 0;0 0 1 0;0 0 0 1]
T7=[cos(a5) 0 sin(a5) -60;sin(a5) 0 -cos(a5) 0;0 1 0 0;0 0 0 1]
T8=[cos(a6) 0 sin(a6) -15;sin(a6) 0 -cos(a6) 0;0 1 0 0;0 0 0 1]
T=T1*T2*T3*T4*T5*T6*T7*T8
T1 =
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
T2 =
[ cos(a1), 0, sin(a1), 15]
[ sin(a1), 0, -cos(a1), 0]
[ 0, 1, 0, 0]
[ 0, 0, 0, 1]
T3 =
[ cos(a2), 0, sin(a2), 60]
[ sin(a2), 0, -cos(a2), 0]
[ 0, 1, 0, 0]
[ 0, 0, 0, 1]
T4 =
[ cos(a3), -sin(a3), 0, 80]
[ sin(a3), cos(a3), 0, 0]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]
T5 =
1 0 0 0
0 1 0 0
0 0 1 40
0 0 0 1
T6 =
[ cos(a4), -sin(a4), 0, -80]
[ sin(a4), cos(a4), 0, 0]
[ 0, 0, 1, 0]
[ 0, 0, 0, 1]
T7 =
[ cos(a5), 0, sin(a5), -60]
[ sin(a5), 0, -cos(a5), 0]
[ 0, 1, 0, 0]
[ 0, 0, 0, 1]
T8 =
[ cos(a6), 0, sin(a6), -15]
[ sin(a6), 0, -cos(a6), 0]
[ 0, 1, 0, 0]
[ 0, 0, 0, 1]
T =
[ (((cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*cos(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*sin(a4))*cos(a5)+(-(cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*sin(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*cos(a4))*sin(a5))*cos(a6)+cos(a1)*sin(a2)*sin(a6), ((cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*cos(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*sin(a4))*sin(a5)-(-(cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*sin(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*cos(a4))*cos(a5), (((cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))
*cos(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*sin(a4))*cos(a5)+(-(cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*sin(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*cos(a4))*sin(a5))*sin(a6)-cos(a1)*sin(a2)*cos(a6), -15*((cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*cos(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*sin(a4))*cos(a5)-15*(-(cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*sin(a4)+(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*cos(a4))*sin(a5)+15-60*(cos(a1)*cos(a2)*cos(a3)+sin(a1)*sin(a3))*cos(a4)-60*(-cos(a1)*cos(a2)*sin(a3)+sin(a1)*cos(a3))*sin(a4)-80*cos(a1)*cos(a2)*cos(a3)-80*sin(a1)*sin(a3)+40*cos(a1)*sin(a2)+80*cos(a1)*cos(a2)+60*cos(a1)]
[ (((sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*cos(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*sin(a4))*cos(a5)+(-(sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*sin(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*cos(a4))*sin(a5))*cos(a6)+sin(a1)*sin(a2)*sin(a6), ((sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*cos(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*sin(a4))*sin(a5)-(-(sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*sin(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*cos(a4))*cos(a5), (((sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*cos(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*sin(a4))*cos(a5)+(-(sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*sin(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*cos(a4))*sin(a5))*sin(a6)-sin(a1)*sin(a2)*cos(a6), -15*((sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*cos(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*sin(a4))*cos(a5)-15*(-(sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*sin(a4)+(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*cos(a4))*sin(a5)-60*(sin(a1)*cos(a2)*cos(a3)-cos(a1)*sin(a3))*cos(a4)-60*(-sin(a1)*cos(a2)*sin(a3)-cos(a1)*cos(a3))*sin(a4)-80*sin(a1)*cos(a2)*cos(a3)+80*cos(a1)*sin(a3)+40*sin(a1)*sin(a2)+80*sin(a1)*cos(a2)+60*sin(a1)]
[ ((sin(a2)*cos(a3)*cos(a4)-sin(a2)*sin(a3)*sin(a4))*cos(a5)+(-sin(a2)*cos(a3)*sin(a4)-sin(a2)*sin(a3)*cos(a4))*sin(a5))*cos(a6)-cos(a2)*sin(a6),
(sin(a2)*cos(a3)*cos(a4)-sin(a2)*sin(a3)*sin(a4))*sin(a5)-(-sin(a2)*cos(a3)*sin(a4)-sin(a2)*sin(a3)*cos(a4))*cos(a5), ((sin(a2)*cos(a3)*cos(a4)-sin(a2)*sin(a3)*sin(a4))*cos(a5)+(-sin(a2)*cos(a3)*sin(a4)-sin(a2)*sin(a3)*cos(a4))*sin(a5))*sin(a6)+cos(a2)*cos(a6), -15*(sin(a2)*cos(a3)*cos(a4)-sin(a2)*sin(a3)*sin(a4))*cos(a5)-15*(-sin(a2)*cos(a3)*sin(a4)-sin(a2)*sin(a3)*cos(a4))*sin(a5)-60*sin(a2)*cos(a3)*cos(a4)+60*sin(a2)*sin(a3)*sin(a4)-80*sin(a2)*cos(a3)-40*cos(a2)+80*sin(a2)]
[ 0, 0, 0, 1]