ME5286 Robotics Spring 2013 Quiz 1

Transcription

1 Page 1 of 7 ME5286 Robotics Spring 2013 Quiz 1 Total Points: 36 You are responsible for following these instructions. Please take a minute and read them completely. 1. Put your name on this page, any other page you write on, and your blue book. 2. This quiz has 7 pages (including this cover page) and contains 2 problems. 3. This quiz is open book and open notes. You may use a calculator. You may not use any device that is capable of wireless communication. 4. To get full credit, your response must have a single, correct solution reported with appropriate units. Partial credit is awarded, so be sure to show your work. 5. If you believe a problem statement is missing a necessary parameter, make an assumption and carry on. Be sure to specify the exact nature of your assumption. 6. If you get stuck and cannot derive the solution to one part that you will need for a subsequent part, assume an answer and carry on. 7. If you can t get an answer, or you believe your answer is incorrect, and cannot find the problem in the time available, write a brief explanation of what you think is wrong, why you don t believe your answer is correct, and how you would continue to find the correct solution. Name: Student ID:

2 Page 2 of 7 PROBLEM 1 (18 points) The BH8-series BarrettHand is a multi-fingered programmable grasper with the dexterity to secure target objects of different sizes, shapes, and orientations. The BarrettHand weighs about 1.2 kg and is totally self-contained. Figure 1.1 shows the BarrettHand in different configurations. Figure 1.1. The BarrettHand in two different configurations joint configuration. The second finger of the Bar- Figure 1.2 shows the BarrettHand in the retthand is the subject of this quiz Figure 1.2. The BarrettHand in the joint configuration A. (2 points) Write the unit vectors for each of the joint axes for the shown figures (Figures 1.3 and 1.4), as expressed in the base coordinate frame (also shown in Figure 1.4). The direction of these vectors should be determined from the joints rotational sense as shown, along with the righthand rule.

3 Page 3 of 7 B. (2 points) The base coordinate frame is shown in Figures 1.3 and 1.4 (at the base of the wrist). Clearly draw and label the remaining link coordinate frames in Figure 1.5 and 1.6. Note that the endeffector s finger vector and the location of the end effector finger tip s coordinate frame origin are also shown in Figures 1.3 and Figure 1.3. The BarrettHand in the joint configuration top view (units in mm) Figure 1.4. The BarrettHand in the joint configuration side view (units in mm)

4 Page 4 of 7 Figure 1.5. Blank copy of Figure 1.3 for you to draw coordinate frames on for part B top view Figure 1.6. Blank copy of Figure 1.4 for you to draw coordinate frames on for part B side view

5 Page 5 of 7 C. (5 points) The elements of the matrices from the ( ) to the joint can be calculated using the Denavit-Hartenburg convention. Fill in the table below with the Denavit-Hartenburg variables for each of the matrices. Use the appropriate geometric dimensions from Figure 1.3 and 1.4. Joint i θ (degrees) d (mm) a (mm) α (degrees) D. (3 points) At one instant in time, the joints move through their zero positions (as shown in Figures 1.3 and 1.4). Compute the matrices,, and using the Denavit-Hartenburg variables from part C for this instant. E. (4 points) Find the homogeneous transformation matrix from the base coordinate frame to the coordinate frame after the end effector finger coordinate frame has been shifted by to the finger surface. F. (2 points) Express, in words, the significance each of the columns in the homogeneous transformation matrix. In other words, what does each column represent?

6 Page 6 of 7 Problem 2 (18 points) A robotic arm with 3 joints is depicted in Figure 2.1 in its non-zero joint configuration. Figure 2.1 Three-joint robot arm in non-zero configuration The first two joints are rotational joints and the third joint is prismatic. Assume that the first joint is located at the origin. Observe that and are unit vectors defined in the world coordinate frame ( ). Notice the second axis of rotation is sitting in a horizontal plane, parallel to the ( ) plane. The prismatic joint (joint 3) is constrained to a minimum length of. Assume, the end effector vector, is pointing along with its origin at. A. (4 points) Fill in the Denavit-Hartenberg table symbolically using the values given in Figure 2.1. Joint i θ d a α 1 2 3

7 Page 7 of 7 B. (3 points) Compute each A matrix ( ) using the values found in the Denavit-Hartenberg table from part A. Write the matrix elements as functions of the variables and. Substitute the following values; and. C. (3 points) Find the homogeneous transformation matrix from frame 0 to frame E in terms of the variables and. For parts D-F, assume that each joint is varying between certain discrete positions. Your goal is to determine the volume swept by the end effector. Assume that is varying by between and is varying by between and is varying by between. D. (2 points) How many vertices do you need to specify in order to accurately describe the bounding shape of the swept volume? E. (4 points) Provide the coordinates of the bounding vertices of the swept volume (in the ( ) coordinate frame). F. (2 points) Sketch out the shape of the swept volume as described above. Use both a top view and a side view to depict the shape of the volume.