Question

The solution is posted with the problem but I do not understand how it was solved. Please show the steps to solve the problem

Consider the diagram of Figure 2.16. A robot is set up 1 meter from a table. The table top is 1 meter high and 1 meter square. A frame o121 is fixed to the edge of the table as shown. A cube measuring 20 cm on a side is placed in the center of the table with frame o222z2 established at the center of the cube as shown. A camera is situated directly above the center of the block 2m above the table top with frame o3x3y323 attached as shown. Find the homogeneous transformations relating each of these frames to the base frame ooaoyo20. Find the homogeneous transformation relating the frame o2r2y222 to the camera frame ozx3y323 T3 3 Tn y2 T2 TTn y0 lm lm 1m

Solution:

Answer 1

Considering the solution 1 meta squar from of 20 cm on a side of the center of table of the frame In the drawing it would appear that the origin of F_3 is on the table top however in the origin of F_3 is derived as being at the centre of the cube. H^0_1 = [1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1] H^1_2 = [1 0 0 0 0 1 0 0 0 0 1 0 -1/2 1/2 1/10 1] So H^0_2 = H^0_1 H^1_2 = [1 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1] [1 0 0 0 0 1 0 0 0 0 1 0 -1/2 1/2 1/10 1] [1 0 0 0 0 1 0 0 0 0 1 0 -1/2 3/2 11/10 1] H^2_3 = H_L1 19/10 Hy H_L1 - pi/2