Explanation Write the position vector B with respect to O ( r O B ) . r O B = ( − 0.18 i + 0.1 k ) m Write the position vector A with respect to O ( r O A ) . r O A = ( − 0.08 i + 0.1 k ) m Write the position vector A with respect to B ( r A / B ) . r A / B = 0.1 i m Write the expression to determine the angular velocity of the arm O C B ( Ω ) . Ω = 2 π N 1 60 j (I) Here, speed of the arms is N 1 . Write the expression to determine the angular velocity of the disk ( p ) . p = 2 π N 2 60 k (II) Here, speed of the arms is N 2 . Write the expression to detemine the velocity at B ( v B ) . v B = Ω × ( r O B ) (III) Write the expression to determine the relative velocity of the disk ( v r e l ) . v r e l = p × ( r A / B ) (IV) Write the expression to detemine the velocity at A ( v A ) . v A = v B + Ω × ( r A / B ) + ( v r e l ) (V) Write the expression to detemine the acceleration at B ( a B ) . a B = Ω × Ω × ( r O B ) (VI) Write the expression to determine the relative acceleration of the disk ( v r e l ) . a r e l = α × ( r A / B ) + p × p × ( r A / B ) (IV) Write the expression to determine the acceleration at point A ( a A ) . a A = a O + ( Ω ˙ × r A / B ) + Ω × ( Ω × r A / B ) + ( 2 Ω × v r e l ) + a r e l (VIII) Conclusion: Substitute 30 rev / min for N 1 in Equation (I). Ω = 2 π × 30 rev / min 60 j = π j rad / s Substitute 240 rev / min for N 2 in Equation (II). p = 2 π × 240 rev / min 60 k = 8 π k rad / s Substitute π j rad / s for Ω and ( − 0.18 i + 0.1 k ) m for r O B in Equation (III). v B = π j rad / s × ( − 0.18 i + 0.1 k ) m = π ( − 0.18 k + 0.1 i ) m / s Substitute 0.1 i m for r A / B and 8 π k rad / s for p in Equation (IV). v r e l = 8 π k rad / s × 0

8th Edition

ISBN: 9781119047315

Author: Bolton

Publisher: VST

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Chapter 7.6, Problem 43P

To determine

The velocity at point A

The acceleration at A

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Chapter 7.6, Problem 42P

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The velocity at point A The acceleration at A