Assignment 1 Questions - Robot Manipulators | E C E 455, Assignments of Electrical and Electronics Engineering

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ECE 455/655, Fall 2009, Assignment 1 Due: in class, Tuesday 9/8/09 Draw figures to support your calculations!!! 1. What are the values of the components of the following vectors: u=[0,0,1] v=[0,2,2]° w = [33,37 in a fixed frame (x,y,z) after completing the series of rotations (positive rotations are counterclockwise): (a) first rotate 90 degrees about the z axis, the 90 degrees about the y axis (b) first rotate 90 degrees about the y axis, then 90 degrees about the z axis (c) first rotate 45 degrees about the x axis, then 30 degrees about the z axis 2. Three coordinate systems (x9, ¥y2)))(%,:94.Z,),(%,¥))2,) with their origins at the same point, are related in the following way: Frame (x,,},,2,) is obtained from frame (x,.¥,,z,) by a positive (counterclockwise) rotation of 90 degrees about the z, axis. Frame (x, ¥,.2,) is obtained from frame (x, y,,2,) by a positive (counterclockwise) rotation of 90 degrees about the y, axis. The following three vectors are expressed in terms of frame (x,, y,,2,): u=(0,0,1]" y=[0,2,2)" w=[3,3,3)° Express each of these vectors in terms of frame (Xj, ¥):2))- Consider your solution to problem 1, and comment.