(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A robot arm in a xyz coordinate system is doing three consecutive rotations, which are as follows:

1) Rotates (Pi/4) rad around the z axis

2) Rotates (Pi/3) rad around the y axis

3) Rotations -(Pi/6) rad around the x axis

Find the standard matrix for the (combined) transformation T.

2. Relevant equations

3. The attempt at a solution

I (think) I have gotten as far as finish part 1. By projecting the robot arm down to the xy plane, and by applying trigonometry, I find that the standard matrix for the rotation in 1) to be as follows (it's a 3x3 matrix, I don't know how to format properly):

[cos (Pi/4) | -sin(Pi/4) | 0]

[sin (Pi/4) | cos(Pi/4) | 0]

[0 | 0 | 1] [||1]

which is:

[1/2[tex]\sqrt{}2[/tex] | -1/2[tex]\sqrt{}2[/tex] | 0]

[1/2[tex]\sqrt{}2[/tex] | 1/2[tex]\sqrt{}2[/tex] | 0]

[0 | 0 | 1]

Hopefully that is the right answer to question 1), but my answer really is how do I go from here? I've found the first standard matrix, but how do I go forth in trying to find the standard matrix for the entire set of 3 rotations?

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# Homework Help: Linear transformation: Rotations in R3

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