Robotics 1
Rotation Matrices
Quiz
Your ID Code:
Question 2: Which of these matrices represents a rotation of theta around the Z axis?
Question 3: Which of these matrices represents a rotation of theta around the X axis?
Question 4: Which of these matrices represents a rotation of theta around the Y axis?
Question 5: Suppose that we rotate a frame 30 degrees around X, then rotate 60 degrees around the new (rotated) Y axis. Which of these matrices is the rotation matrix for these two rotations?
Question 6: Suppose I know the rotation of the 1 frame relative to the 0 frame, and I know the rotation of the 2 frame relative to the 1 frame. How can I find the rotation of the 2 frame relative to the 0 frame?
Question 7: Which of these rotation matrices means 'no rotation'?
Question 8: Shown here is a kinematic diagram. Which of these rotation matrices represents the rotation of frame 1 relative to frame 0?
Question 9: Shown here is a kinematic diagram. Which of these rotation matrices represents the rotation of frame 2 relative to frame 1?
Question 10: Shown here is a kinematic diagram. When both joints turn to the 90 degree position, which of these rotation matrices represents the rotation from frame 0 to frame 2?
Undergraduate/Graduate Questions (both undergraduates AND graduates should answer these questions):
Questions 11-15: Shown here is a 6-DoF kinematic diagram. Find the complete rotation matrix from frame 0 to frame 6. Then, assume that all angles have a value of 15 degrees. Fill in the five of the missing values in the rotation matrix. You can use any combination of hand calculations and Python programming to answer this question. Round your answers to 4 significant digits.
Question 1: Suppose I have a rotation matrix showing the rotation of frame 1 relative to frame 0, as shown here. What is the projection of X1 on Z0?
0.866
0.50
0
-0.50
Graduate Questions (ONLY graduates need to answer these questions):
1