Question

Q-8 A frame UB was moved along its own n-axis a distance of 5 units and then rotated about its o-axis an angle of 60, followed by a rotation of about the z-axis; it was then translated about its a-axis 3 units and finally rotated about x-axis 45° a) Calculate the total transformation performed. b) What angles and movements would we have to make if we were to create the same location and orientation using Cartesian and RPY configurations?

Answer 1

Files transformations.m MATLAB Drive 1% T1-translation of 5 units along n-axis 2T1=[1 0 0 5:0 1 00;0 0 1 0;0001); 3% T2-rotation of 60 deg about o-axis 4 T2-[cosd(60) 0 sind(60) 0;010 0; -sind(60) 0 cosd(60) 0;0 0 0 1]; 5%T3-rotation of 60 deg about z-axis 6T3-[cosd(60) -sind(60) 0 0;sind (60) cosd(60) θ 0:0 θ 1 θ;θ θ θ 11: 7%T4-translation of 3 unitd along a-axis 8 T4-[1 00 0;010 0;00 13;0 0 0 1]; 9%T5-rotation of 45 deg abot x-axis 10T5-[1 0 0 0; cosd(45) -sind (45) θ:0 sind (45) 11 %total transformation-T5+T3*T1*T2*T4 12 T=T5+T3*T1*T2*T4; cosd(45) θ;00 θ 1];

Commands T1 = 1 > T2 T2 0.5000 00.8660 1.0000 0.5000 8660 1.0000 >> T3 T3= 0.5000 0.8660 0.8660 0.5000 0 0 1.0000 1·0000 > T4 T4 =

Commands T3 0.5000 0.86600.5000 0.8660 θ 1.0000 1.0000 >T4 > T5 1.0000 0 0 0.70710.7071 7071 0.7071 1.0000 s> T 0.2500 0 0.43303.7990 0.9186 0.3536 0.1768 3.5922 0.3062 0.3536 0.88395.7135 1.0000 0.8660