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Can you please explain how to find the velocity using the methods described? And also why it's done that way?

Can you please explain how to find the velocity using the methods described? And also why it's done that way?

Elements Of Electromagnetics
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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Can you please explain how to find the velocity using the methods described? And also why it's done that way? This is from Introduction to robotics mecahnics and controls. Please help ;( !

In Fig. 7.4, we have made a reasonable choice of joint velocities at the via points, as indicated with small line segments representing tangents to the curve at each via point. This choice is the result of applying a conceptually and computationally simple heuristic. Imagine the via points connected with straight line segments. If the 208 Chapter 7 Trajectory generation Од |მი to tA tB 0с tc tD FIGURE 7.4: Via points with desired velocities at the points indicated by tangents. slope of these lines changes sign at the via point, choose zero velocity; if the slope of these lines does not change sign, choose the average of the two slopes as the via velocity. In this way, from specification of the desired via points alone, the system can choose the velocity at each point.
Transcribed Image Text:In Fig. 7.4, we have made a reasonable choice of joint velocities at the via points, as indicated with small line segments representing tangents to the curve at each via point. This choice is the result of applying a conceptually and computationally simple heuristic. Imagine the via points connected with straight line segments. If the 208 Chapter 7 Trajectory generation Од |მი to tA tB 0с tc tD FIGURE 7.4: Via points with desired velocities at the points indicated by tangents. slope of these lines changes sign at the via point, choose zero velocity; if the slope of these lines does not change sign, choose the average of the two slopes as the via velocity. In this way, from specification of the desired via points alone, the system can choose the velocity at each point.
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