ECE 417 --- ROBOTICS
Homework 1, Fall 2018

 For the rotation matrix:
 

XYZRUVW

[

2/7

-6/7

3/7

]

6/7

3/7

2/7

-3/7

2/7

6/7

  1. Show that XYZRUVW  is a proper rotation matrix.

  2. Show that R-1 is equal to RT where (R is shorthand for XYZRUVW).  HINT: taking the inverse is not required.

  3. Compute R A where matrix A is given by



A  

[

3/7

2/7

6/7

]

2/7

6/7

-3/7

-6/7

3/7

2/7

  1. If PUVW = (1,2,3)T, what is PXYZ given (using XYZRUVW above)

  2. If PXYZ = (1,2,3)T, what is PUVW? given (using XYZRUVW above)

  3. If the OUVW system has basis vectors U = (1/√2, 0, 1/√2)T, V = (-1/√2, 0, 1/√2)T, W = (0, -1, 0)T, and the OXYZ system has basis vectors X = (1, 0, 0)T, Y = (0, 1/√2, -1/√2)T, Z = (0, 1/√2, 1/√2)T, then what is the corresponding rotation matrix between the two systems?