Explanation Given information: The robotic arm is as follows The given angles are: α = 47 ∘ , β = 17 ∘ Calculation: We need to find the position of hand H with respect to shoulder O as pole. Now, segment OE measures 14 inches and make an angle α with the horizontal. Hence we can write vector O E as: In polar coordinates ( r , θ ) of E are ( 14 , α ) The relationship between rectangular coordinates ( x , y ) and polar coordinates ( r , θ ) is given as: x = r cos θ ....... (1) y = r sin θ ....... (2) Using equations (1), (2), we get: O E = 〈 14 cos α , 14 sin α 〉 Similarly we get: E H = 〈 8 cos β , 8 sin β 〉 We know that: O H = O E + E H O H = 〈 14 cos α , 14 sin α 〉 + 〈 8 cos β , 8 sin β 〉 Doing vector addition, we get: O H = 〈 14 cos α + 8 cos β , 14 sin α + 8 sin β 〉 Plugging in the value α = 47 ∘ , β = 17 ∘ , we get: O H = 〈 14 cos 47 ∘ + 8 cos 17 ∘ , 14 sin 47 ∘ + 8 sin 17 ∘ 〉 So the rectangular coordinates ( x , y ) of H are: x = 14 cos 47 ∘ + 8 cos 17 ∘ ⇒ x = 14 × 0

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Chapter 6.6, Problem 88E

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Determine the position of the hand relative to the shoulder by considering the robotic arm given in the picture. Round all answers to the nearest tenth

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Chapter 6.6, Problem 87E

Chapter 6.6, Problem 89E

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Determine the position of the hand relative to the shoulder by considering the robotic arm given in the picture. Round all answers to the nearest tenth

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To calculate: Determine the position of the hand relative to the shoulder by considering the robotic arm given in the picture. Round all answers to the nearest tenth

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To calculate:

Determine the position of the hand relative to the shoulder by considering the robotic arm given in the picture. Round all answers to the nearest tenth