Answered: onsider the robotic arm shown below,…

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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Question

Consider the robotic arm shown below, made up of individual arms ?B and ?C. The weight of
the arms AB and ?C are each 160 N, and the resultant weight force is shown to act through each
arm’s center of gravity as shown. You may assume that the center of gravity is occurring along the
midpoint of each arm’s length. The robotic arm is picking up a package that weighs 40 N, and the
40 N weight force acts through the package’s center of gravity at the location shown.

a) A servomotor at point B is exerting a torque value to resist the rotation induced
by the weight force of the robotic arm BC and the weight force of the 40 N package.
Calculate the required torque at point B necessary to resist the moment caused by the
robotic arm BC and the 40 N package. Indicate the direction of the required torque (↺ or
↻). Report your answer in N-m.
b) A servomotor at point C is exerting a torque value to resist the rotation induced
by the weight force of the 40 N package. Calculate the required torque at point C necessary
to resist the moment caused by the 40 N package. Indicate the direction of the required
torque (↺ or ↻). Report your answer in N-m.
c) Consider the 3 servomotors at A, B, and C. Explain which servomotor is
subjected to the largest demand and justify your explanation.
d) Consider the 3 servomotors at A, B, and C. Explain how you might adjust the
capacity at each location where a servomotor is located such that larger weight forces might
be allowable (e.g., enabling the robotic arm to pick up a 140 N package).

The image depicts a robotic arm with labeled segments, forces, and angles illustrating its structure.

Features:
1. **Base (A):** The arm is anchored at the base point A.
2. **Segments:** The arm consists of two main segments:
- The first segment is 600 mm long, extending from point A to point B₀.
- The second segment is also 600 mm long, extending from point B₀ to point C.
3. **Small Extension:** An additional 150 mm extension projects from point C.
4. **Angles:**
- The angle between the first segment and the vertical line drawn from the joint at A is 40 degrees.
- The angle between the second segment and the horizontal line at point B₀ is 20 degrees.
5. **Forces:**
- A downward force of 160 N acts at point B₀.
- Another 160 N force acts downward on the segment between B₀ and C.
- A 40 N force acts downward at the end of the extension.
6. **Joints:** Movable joints are located at points A, B₀, and C, allowing rotational movement, depicted by circular markings.

This diagram illustrates an example of static forces and the geometrical configuration involved in the design of mechanical arms, useful for educational purposes in physics and engineering.

Expert Solution

Step 1: Write the given data with suitable variables-

$A B equals 600 space mm B C equals 600 space mm$

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