1. PROBLEM SET 6
1. What is the Jacobian for translational velocities of point “P” for the following robot? X0 Y0 Y1
X1, Y2 X2 X3 Y3 P 1
What is the velocity of point “P” after 1 second if all the joints are rotating at

2. (2=-90° at home position) (3=-90° at home position)
Problem 1
Link i
Twist i
Link length ai
Link offset di
Joint angle i
i=0 …
i=1
A1=1 1
(1=90° at home position)
i=2
A2=1 2
(2=-90° at home position)
i=3 3
(3=-90° at home position)

3. Problem 1

4. Problem 1
The transformation matrix for is

5. Problem 1
The transformation matrix of point “P” w.r.t. frame {3} is

6. Problem 1

7. Problem 1
Note: A1=1, A2=1:
At t=1,

8. Problem 1 X0 Y0 Y1
X1, Y2 X2 X3 Y3 P 1
We should get the same answer if we used the transformation matrices.