{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ME427MTS

# ME427MTS - Isik University Faculty of the College of...

This preview shows pages 1–5. Sign up to view the full content.

Isik University Faculty of the College of Engineering Mechanical Engineering Department ME 427 INTRODUCTION TO ROBOTICS MIDTERM EXAMINATION Date: Saturday, April 23, 2011 Time Allowed: 120 Minutes Student’s Name:_ _______________________________________________ Student’s No.___________________________________________________ Scoring Box Question Number Maximum Score Obtained Score Q1 20 Points Q2 15 Points Q3 10 Points Q4 10 Points Q5 10 Points Q6 15 Points Q7 20 Points Total Score 100 points

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Q1. A) Write the matrix product that will give the resulting rotation matrix (do not perform the matrix multiplication). Consider the following sequence of rotations: (a) Rotate by φ about the world x-axis. (b) Rotate by θ about the current z-axis. (c) Rotate by ψ about the current x-axis. (d) Rotate by about the world z-axis. Solution Rule: For fixed or world frame pre-multiply and for current axes post multiply , , , , x z x z R R R R R B) Write the matrix product that will give the resulting rotation matrix (do not perform the matrix multiplication). Consider the following sequence of rotations: (a) Rotate by φ about the world x-axis. (b) Rotate by θ about the world z-axis. (c) Rotate by ψ about the current x-axis. (d) Rotate by about the world z-axis. Solution Rule: For fixed or world frame pre-multiply and for current axes post multiply , , , , x x z z R R R R R C) Write the matrix product that will give the resulting rotation matrix (do not perform the matrix multiplication). Find the rotation matrix representing a roll of 45° followed by a yaw of 45° followed by a pitch of 45°. Solution Rule: fixed axis rotation with order yaw about x, pitch about y, and roll about z 45 , 45 , 45 , x y z R R R R
D) Suppose that three coordinate frames {1}, {2}, and {3} are given, and suppose 0 0 1 0 1 0 1 0 0 R and 2 1 2 3 0 2 3 2 1 0 0 0 1 R 1 3 1 2 Find R 3 2 0 2 3 2 1 0 2 1 2 3 1 0 0 0 0 1 0 1 0 1 0 0 2 1 2 3 0 2 3 2 1 0 0 0 1 Therefore, 2 1 2 3 0 2 3 2 1 0 0 0 1 where Solution 2 3 1 2 1 1 2 2 1 1 3 2 1 1 3 1 2 2 3 R R R R R R R R R T T

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
E) Let 90 and 1) 1, , 1 ( 3 1 k . Find R(k, θ)
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern