Answered: 600 mm 160 N Bo 40° 600 mm 150 mm 160 N…

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 mechanical arm consisting of several segments with applied forces and dimensions clearly labeled. The arm is hinged at different points, and angles between segments are specified. Here’s a detailed breakdown:

1. **Hinges and Segments:**
- The arm is hinged at three points: A, B\(_0\), and C.
- The segments between these points are labeled with their respective lengths:
- Segment A to B\(_0\) is 600 mm.
- Segment B\(_0\) to C is 600 mm.
- The final segment beyond point C is 150 mm.

2. **Forces:**
- There are several forces applied to different parts of the arm:
- A downward force of 160 N is applied at point B\(_0\).
- Another 160 N force is applied downward at the middle of the segment B\(_0\) to C.
- A downward force of 40 N is applied at the end of the segment extending from point C.

3. **Angles:**
- The angle between segment A to B\(_0\) and the vertical is 40°.
- The angle between segment B\(_0\) to C is 20° with respect to the previous segment.

This detailed information is crucial for understanding the mechanical behavior of the arm, as well as for performing analyses related to statics or dynamics to understand how the forces affect the movement and stress distribution within the arm.

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