Homework 2

Course	Introduction to Robotics
Course Number	00350001

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Question 1

Part a

Figure HW2.1: Manipulator schema.

First, we’ll define the -axes according to the D–H method:

Figure HW2.2: Marking axes along the joints’ axes.

Now we can complete the other frames, starting from the world frame:

Figure HW2.3: Assigning all the frames according to the convention.

Therefore, the D–H Parameters are:

For each joint, the transformation matrix is:

Therefore:

Now we calculate step by step:

Step 1:

Step 2:

Step 3:

Therefore:

Part b

Figure HW2.4: Manipulator schema.

First, we’ll define the -axes according to the
D–H method:

Figure HW2.5: Marking axes along the joints’ axes.

Now we can complete the other frames, starting from the world frame:

Figure HW2.6: Assigning all the frames according to the convention.

Defining

the D–H Parameters are:

Therefore:

Which gives us:

Part c

Figure HW2.7: Manipulator schema.

First, we’ll define the -axes according to the D–H method:

Figure HW2.8: Marking axes along the joints’ axes.

Now we can complete the other frames, starting from the world frame:

Figure HW2.9: Assigning all the frames according to the convention.

Therefore, the D–H Parameters are:

Therefore:

Which gives us:

Question 2

We have:

The manipulator schema would be:

Figure HW2.10: Assigning all the frames according to the convention.