HW2_sol - Texas A & M University Department of...

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Unformatted text preview: Texas A & M University Department of Mechanical Engg. MEEN-408 Intro. to Robotics Solution HW2 1. Solution to Problem 1 (a) P A = 1 , Q A = 1 1 , R A = 1 1 1 , S A = 1 1 1 P B = 1 2 3 1 , Q B = . 1744 1 . 7992 2 . 4727 1 , R B = . 5783 . 9362 2 . 1690 1 , S B = − . 2196 1 . 3355 3 . 2663 1 We know that P B = TP A , Q B = TQ A , R B = TR A , S B = TS A . Hence, we have T [ P A | Q A | R A | S A ] = [ P B | Q B | R B | S B ] ⇒ T = [ P B | Q B | R B | S B ][ P A | Q A | R A | S A ]- 1 Substituting the values for P A,B , Q A,B , R A,B , S A,B we get T = − . 8256 . 4039 − . 3940 1 − . 2008 − . 8630 − . 4637 2 − . 5273 − . 3037 . 7936 3 1 (b) We are given co-ordinates in frame B, we have to determine coordinates in frame A . Hence M A = T- 1 M B M B = 2 3 5 1 Computing T- 1 and substituing in equation above, we get M A = − 2 . 0810 − 1 . 0664 . 7293 1 . 000 2. Solution to Problem 2 (a) We have to find the transformation matrix from that relates the coordinates of point P given in body fixed frame { B } to the fixed frame { A } . The body fixed frame 1 is initially coincident with fixed frame and under goes following transformations to reach its final configuration....
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This note was uploaded on 09/10/2009 for the course MEEN MEEN612 taught by Professor Swaroopdarbha during the Spring '09 term at Texas A&M.

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HW2_sol - Texas A & M University Department of...

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