Question

2. A simple industrial robot arm has a three dimensional operating space. It has a gripping device (the hand) for picking up objects that can make only two types of moves: (1) The hand can make a move corresponding to any vector parallel to a - (1,1, 1) (2) The hand can make a move corresponding to any vector perpendicular to a. We wish to program the arm to pick up an object at position u- (0,2, 1) and move it to position v-(-1,1,2) (a) (i) By projecting an appropriate vector onto a, find vectors r and s describing the two moves the arm must make to move from the pick up position u to the release position v. (ii) Find the total travel distance of the hand as it makes the moves you found in (i) (b) Suppose that the operating space has a ceiling which prevents the vertical position of the arm from exceeding 2, so the operating space is a subset of S - [(x, y, z) E R3 2) Does this affect the order in which the arm can perform the moves corresponding to r and s to move from u to v! Explain your answer Release at v . . Pick up at u Movement direction a O (resting) Illustration of moves in part (a) of Question 2 (not to scale)

Answer 1

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