Introduction to Robotics 236927 – Winter 2014-2015
Homework assignment 2
Submission Date – 18.12.2014
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Question 1:
1. Write down DH parameters for the following robot:
You can assume the initial angle between xi and xi 1 is 0
i

ai
di
1
2
3
4
5
6
2. Find the origin of frame {2} in terms of frame {1}.
3. Find the origin of frame {3} in terms of frame {2}.
4. Find the origin of frame {3} in terms of frame {1}.
i
i
Question 2:
Given the above SCARA Robot,
Note: For better understanding the SCARA robot, you are welcome to visit the ISL Lab (Taub,
1st floor).
1. Draw a schematic of this manipulator (as seen in Question 1), with the axis of frame {1}
through {4} labeled. Also, include the parameters 1 ,2 , d 3 ,4 on your schematic.
2. Write down the Denavit-Hartenberg parameters for this manipulator. Assume the initial
angle between xi and xi 1 is 0 :
i

ai
i
di
i
1
2
3
4
3. Use the Robotic Toolbox, and build the SCARA robot. Use the following parameters:
d1  1, a1  2, a2  2 all other parameters are derived from DH table. Animate the robot,

 

2
4 4
5
with starting point ( , 0, 0, 0) to ( , , 6, ) with the following time vector [0:0.056:2]
(use fkine,jtraj and plot)
Question 3:
1. Put coordinate system for each one of the joints. Note that the first and last CS is given.
2. Write down DH parameters:
i

ai
di
i
i
1
2
3
3. Write down the transformation matrices 01T , 21T , 23T and 03T .
4. Solve the IK problem for this robot, that is to say, given a point ( x, y, z ) what would be
the configuration of the robot in order to reach this point.
Note that the height of the bottom disk is 0 and not as shown in the figure; also, note that,
when   0 the robot arm points towards x0 , when   0 the robot arm is parallel to the
ground, and when L  0 then the 3rd coordinate system is adjacent to the cylinder with radios
R2 .
Question 4:
The purpose of this question is to better understand the IK problem. You’ll solve the IK
problem for the following robot:
1. Complete the coordinate system for each one of the joints and the end effector that
the system is solvable by DH
2. Write down the DH parameters for this manipulator
i

ai
di
i
i
1
2
3
3. Compute the Workspace of the manipulator by a function of b, L1 and L2
4. What is the Dextrous workspace of the manipulator for:
a. L1  L2
b. L1  L2
5. Solve the IK problem of the manipulator
Hint1 : Use the side view, and the Top view to help you solve the question.
Hint2: Why 0 is trivial?
Hint3: Look at the lecture and tutorial and see how we solved the RR arm.
Hint4: what is d in Top view?
Question 5:
A small humanoid robot is being programmed to place a hat on its head. The objective is
to place the hat in the position shown by the dashed outline in the figure below. Assume
that the arm is composed of 3 revolute joints and is constrained to move in the plane of
the page. The arm consists of 3 links with dimensions: L1  0.4, L2  0.3, L3  0.1 .
In order to place the hat on its head, assume that we must place the edge of the hat
brim at a location of 0.5m above its shoulder joint. The hat brim should be in a
horizontal position and is gripped at its edge by the hand and is aligned with the last link
of the arm.
a. (3 pts.) Complete the coordinate systems for each one of the joints.
b. (6 pts.) Write down the Denavit-Hartenberg parameters for this robot.
i
1
2
3

ai
di
i
i
c. (6 pts.) Write down 02T
General Notes:
1. The homework has to be submitted in pairs
2. Whoever gets caught copying will get 0 automatically!
3. Submit all your code with one zip file named: hw2_<your_id>.zip