Robotics 2
Jacobian Matrix
Quiz
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Question 2: The Jacobian matrix relates end-effector velocities to the joint velocities. Which of these expresses the correct relationship between these three things?
Question 3: True or false: the positions of the joints have no effect on the velocity of the end-effector.
Questions 4-7: Shown here is a kinematic diagram. Find the Jacobian matrix, then use the drop-down boxes to fill in the missing values.
Question 8: Which of these equations does come from the Jacobian matrix in questions 4-7?
Question 10: Based on the Jacobian matrix in Questions 4-7, which of these end-effector velocities is controlled by only one joint?
Question 1: I have a 4-degree-of-freedom manipulator. What should be the dimensions of my Jacobian matrix?
Question 9: Based on the Jacobian matrix in Questions 4-7, which of these end-effector velocities will always be zero, no matter what the values of the joint variables are?
(a2+a3+d2)sin(Theta1)
-(a2+a3+d2)sin(Theta1)
(a2+a3+d2)cos(Theta1)
-(a2+a3+d2)cos(Theta1)
sin(Theta1)
cos(Theta1)
-sin(Theta1)
-cos(Theta1)
Theta2 dot
d2 dot
Theta2
d2
6 rows and 4 columns
4 rows and 6 columns
2 rows and 4 columns
4 rows and 2 columns
Jacobian Matrix = End-effector velocities * Joint velocities
Jacobian Matrix = Joint velocities * End-effector velocities
Joint velocities = Jacobian Matrix * End-effector velocities
End-effector velocities = Jacobian Matrix * Joint velocities
True
False
The linear velocity in the Y direction
The linear velocity in the X direction
The rotational velocity around Z
The rotational velocity around X
The linear velocity in the Y direction
The linear velocity in the X direction
The rotational velocity around Z
The rotational velocity around X
(a2+a3+d2)sin(Theta1)
-(a2+a3+d2)sin(Theta1)
(a2+a3+d2)cos(Theta1)
-(a2+a3+d2)cos(Theta1)