The telescoping arm of a certain robot obtains its vertical motion by rotating (R) about a horizontal axis. The total range of the rotation is 90
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- The robot's telescoping arm rotates about a horizontal axis with a range of 90°. - The robot has a 10-bit storage capacity for this axis. - When fully extended, the arm measures 50 inches from the pivot point. - When fully retracted, the arm measures 30 inches Show more…
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The member $O A$ of the industrial robot telescopes and pivots about the fixed axis at point $O$. At the instant shown, $\theta=60^{\circ}, \dot{\theta}=1.2 \mathrm{rad} / \mathrm{s}, \ddot{\theta}=0.8$ $\operatorname{rad} / \mathrm{s}^{2}, \quad \overline{O A}=0.9 \mathrm{m}, \quad \dot{\overline{O A}}=0.5 \mathrm{m} / \mathrm{s},$ and $\overrightarrow{O A}=$ $-6 \mathrm{m} / \mathrm{s}^{2} .$ Determine the magnitudes of the velocity and acceleration of joint $A$ of the robot. Also, sketch the velocity and acceleration of $A$ and determine the angles which these vectors make with the positive $x$ -axis. The base of the robot does not revolve about a vertical axis.
The robotic device consists of the stationary pedes$\operatorname{tal} O A, \operatorname{arm} A B$ pivoted at $A,$ and arm $B C$ pivoted at $B .$ The rotation axes are normal to the plane of the figure. Estimate $(a)$ the moment $M_{A}$ applied to arm $A B$ required to rotate it about joint $A$ at $4 \mathrm{rad} / \mathrm{s}^{2}$ counterclockwise from the position shown with joint $B$ locked and $(b)$ the moment $M_{B}$ applied to arm $B C$ required to rotate it about joint $B$ at the same rate with joint $A$ locked. The mass of arm $A B$ is $25 \mathrm{kg}$ and that of $B C$ is $4 \mathrm{kg}$, with the stationary portion of joint $A$ excluded entirely and the mass of joint $B$ divided equally between the two arms. Assume that the centers of mass $G_{1}$ and $G_{2}$ are in the geometric centers of the arms and model the arms as slender rods.
Robotic movement Refer to Exercise 71 . (a) Suppose the wrist joint of the robot's arm is allowed to rotate at the joint connection $S$ and the arm is located as shown in the first figure. The upper arm has a length of 15 inches; the forearm, without the hand, has a length of 10 inches; and the hand has a length of 7 inches. Approximate the coordinates of $R$ by using $\mathbf{a}+\mathbf{b}+\mathbf{c}$ (Figure can't copy) (b) Suppose the robot's upper arm is rotated $75^{\circ},$ and then the forearm is rotated $-80^{\circ},$ and finally the hand is rotated an additional $40^{\circ},$ as shown in the second figure. Approximate the new coordinates of $R$ by using $\mathbf{d}+\mathbf{e}+\mathbf{f}$ (Figure can't copy)
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