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The peg B fixed on the gear slides freely along the slot in the link AB. If the gear's center O moves with the velocity and acceleration shown in the figure, determine the angular velocity and angular acceleration of the link AB at this instant. a) using the relative motion analysis and the contact conditions. 150 mm Vo = 3 m/s ao = 1.5 m/s² 150 mm u 600 mm

The peg B fixed on the gear slides freely along the slot in the link AB. If the gear's center O moves with the velocity and acceleration shown in the figure, determine the angular velocity and angular acceleration of the link AB at this instant. a) using the relative motion analysis and the contact conditions. 150 mm Vo = 3 m/s ao = 1.5 m/s² 150 mm u 600 mm

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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I'm trying to understand this problem is there an easier way to solve  other than the the solution I attached? That just doesn't look like a relative acceleration equation it is so complicated any help is so appreciated thanks.

Apply the relative acceleration equation. Aß = ªд + WẠb × VB/A + WAB × (WAB × rbia) + 2wab × (Vrel)x'y'z' + (Arel)x'y'z' (XI) Substitute {-50.46i – 32.60j} m/s² for ab, 0 for aд, -αABk for @AB, {0.6j} m for rB/A, -a -WABK for WAB and {-5.196j} m/s for (Vrel)x'y'z' in Equation (XI). -50.46i - 32.60j = [ 0 + (−¤µßk) × (0.6j) + (−wabk) × (-wabk × 0.6j) [ 0.60] +2 (−wabk) × (−5.196j) + (Arel)x'y'z' Substitute 5 rad/s for @AB in Equation (XII). -50.461 - 32.60j = = [ 0 + (−¤abk) × (0.6j) + (−5k) × (−5k × 0.6j) +2 (−5k) × (-5.196j) + (arel)x'y'z' - = (0.6αaß − 51.96)i + [(Arel)x'y'z' − 15] j (XII) (XIII)
Transcribed Image Text:Apply the relative acceleration equation. Aß = ªд + WẠb × VB/A + WAB × (WAB × rbia) + 2wab × (Vrel)x'y'z' + (Arel)x'y'z' (XI) Substitute {-50.46i – 32.60j} m/s² for ab, 0 for aд, -αABk for @AB, {0.6j} m for rB/A, -a -WABK for WAB and {-5.196j} m/s for (Vrel)x'y'z' in Equation (XI). -50.46i - 32.60j = [ 0 + (−¤µßk) × (0.6j) + (−wabk) × (-wabk × 0.6j) [ 0.60] +2 (−wabk) × (−5.196j) + (Arel)x'y'z' Substitute 5 rad/s for @AB in Equation (XII). -50.461 - 32.60j = = [ 0 + (−¤abk) × (0.6j) + (−5k) × (−5k × 0.6j) +2 (−5k) × (-5.196j) + (arel)x'y'z' - = (0.6αaß − 51.96)i + [(Arel)x'y'z' − 15] j (XII) (XIII)
The peg B fixed on the gear slides freely along the slot in the link AB. If the gear's center O moves with the velocity and acceleration shown in the figure, determine the angular velocity and angular acceleration of the link AB at this instant. a) using the relative motion analysis and the contact conditions. 150 mm Vo = 3 m/s ao = 1.5 m/s² 150 mm r B --- 600 mm
Transcribed Image Text:The peg B fixed on the gear slides freely along the slot in the link AB. If the gear's center O moves with the velocity and acceleration shown in the figure, determine the angular velocity and angular acceleration of the link AB at this instant. a) using the relative motion analysis and the contact conditions. 150 mm Vo = 3 m/s ao = 1.5 m/s² 150 mm r B --- 600 mm
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