The tip of a one-link robot is located at? = 3 ?∕4 rad at time t = 0 s as shownin Fig. P6.5. It takes 2 s for the robot tomove from ? = 3 ?∕4 rad to ? = 3 ?∕4 +2 ?rad. If l = 15 cm, plot the x- andy-components as a function of time. **6-4.** The tip of a one-link robot is located at \(\theta = \pi/2\) rad at \(t = 0\) s as shown in Fig. P6.4. It takes 4 s for the robot to move from \(\theta = \pi/2\) rad to \(\theta = \pi/2 + 2\pi \text{ rad}\). If \(l = 10\) cm, plot the \(x\)- and \(y\)-components as a function of time. Also find the amplitude, frequency, period, phase angle, and time shift.**Figure P6.4** Rotating one-link robot starting at \(\theta = 90^\circ\).**Explanation of Diagram:**The diagram illustrates a one-link robot arm positioned in a two-dimensional coordinate system (x, y). At \(t = 0\), the arm is positioned at an angle of \(\pi/2\) radians (or 90 degrees) from the x-axis. The arm’s length, \(l\), is labeled, and the path of rotation is indicated by an arrow curving from the initial position, suggesting the movement of the arm as it rotates through 2\(\pi\) radians over 4 seconds.

Given: (i) The tip of one-link robot is located at θ=π2rad at t=0. (ii) It atkes 4 sec for the robot…

6-4. The tip of a one-link robot is located at 0 = 1/2 rad at t=0 s as shown in Fig. P6.4. It takes 4 s for the robot to move from 0 = 1/2 rad to 0 = π/2+ 2 rad. If = 10 cm, plot the x- and y-components as a function of time. Also find the amplitude, frequency, period, phase angle, and time shift. 1=0 π/2 x gure P6.4 Rotating one-link robot starting at = 90°.

6-4. The tip of a one-link robot is located at 0 = 1/2 rad at t=0 s as shown in Fig. P6.4. It takes 4 s for the robot to move from 0 = 1/2 rad to 0 = π/2+ 2 rad. If = 10 cm, plot the x- and y-components as a function of time. Also find the amplitude, frequency, period, phase angle, and time shift. 1=0 π/2 x gure P6.4 Rotating one-link robot starting at = 90°.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The tip of a one-link robot is located at
? = 3 ?∕4 rad at time t = 0 s as shown
in Fig. P6.5. It takes 2 s for the robot to
move from ? = 3 ?∕4 rad to ? = 3 ?∕4 +
2 ?rad. If l = 15 cm, plot the x- and
y-components as a function of time.

**6-4.** The tip of a one-link robot is located at \(\theta = \pi/2\) rad at \(t = 0\) s as shown in Fig. P6.4. It takes 4 s for the robot to move from \(\theta = \pi/2\) rad to \(\theta = \pi/2 + 2\pi \text{ rad}\). If \(l = 10\) cm, plot the \(x\)- and \(y\)-components as a function of time. Also find the amplitude, frequency, period, phase angle, and time shift.

**Figure P6.4** Rotating one-link robot starting at \(\theta = 90^\circ\).

**Explanation of Diagram:**

The diagram illustrates a one-link robot arm positioned in a two-dimensional coordinate system (x, y). At \(t = 0\), the arm is positioned at an angle of \(\pi/2\) radians (or 90 degrees) from the x-axis. The arm’s length, \(l\), is labeled, and the path of rotation is indicated by an arrow curving from the initial position, suggesting the movement of the arm as it rotates through 2\(\pi\) radians over 4 seconds.

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