Problem 2: Find the Jacobian of the manipulator with three degrees of freedom shown below. Write it in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}. Ja 9₂ TOT
Problem 2: Find the Jacobian of the manipulator with three degrees of freedom shown below. Write it in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}. Ja 9₂ TOT
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Problem 2:**
Find the Jacobian of the manipulator with three degrees of freedom shown below. Write it in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}.
**Diagram Explanation:**
The diagram illustrates a robotic manipulator with three segments.
- The base segment is horizontal, indicated with a rotational joint labeled as θ₁, driving motion around a vertical axis. The length of this segment is L₁.
- The second segment extends upwards from the end of the first segment and is connected with a rotational joint labeled θ₂. This joint allows rotation in a vertical plane. The length of the second segment is L₂.
- The third segment continues from the second joint, also in a vertical plane, with an angular movement denoted by θ₃, similarly to θ₂.
The aim is to determine the Jacobian matrix that correlates the manipulator's joint velocities with its end-effector velocity, represented in a frame {4} at the tip of the hand, sharing the orientation with frame {3}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbba9f6c6-d2a1-4bca-bdf9-0111cddb17f4%2Fa7b83a46-610d-4236-878a-6179ba665721%2Fc1g83ol_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2:**
Find the Jacobian of the manipulator with three degrees of freedom shown below. Write it in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}.
**Diagram Explanation:**
The diagram illustrates a robotic manipulator with three segments.
- The base segment is horizontal, indicated with a rotational joint labeled as θ₁, driving motion around a vertical axis. The length of this segment is L₁.
- The second segment extends upwards from the end of the first segment and is connected with a rotational joint labeled θ₂. This joint allows rotation in a vertical plane. The length of the second segment is L₂.
- The third segment continues from the second joint, also in a vertical plane, with an angular movement denoted by θ₃, similarly to θ₂.
The aim is to determine the Jacobian matrix that correlates the manipulator's joint velocities with its end-effector velocity, represented in a frame {4} at the tip of the hand, sharing the orientation with frame {3}.
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