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chap_II_hwk - Chapter II: Planar Rigid Body Kinematics...

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Unformatted text preview: Chapter II: Planar Rigid Body Kinematics Homework Chapter II Planar Rigid Body Kinematics Homework II-1 II-2 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems Chapter II: Planar Rigid Body Kinematics Homework ME 274 II-3 Problem II.1 Problem II-1 Given: The rectangular BCD ABCD rotates about about a pivot at point If, At the instant shown, The rectangular plate A plate freely freely rotates a pivot at point A. A. at the acceleration of point C ispoint C is￿ C = axby ay ˆ.= ax i + ay j , determine the angular i shown, the acceleration of given by agiven ˆ + a j C velocity ! and angular acceleration " of the plate. Find: Determine the angular velocity ω and angular acceleration α of the plate. ￿ ￿ y B C 0.25 m A D 0.5 m x Use the following parameters in your analysis: ax = 0 and ay = −20m/sec2 . Use the following: ax = !10 m / sec 2 and ay = 0 . aC II-4 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.2 Problem The pulley shown below freely rotates about point C and interacts with two rubber belts Given: II-2 (one horizontal, one vertical). The velocity of point A on the drive belt is measured to be ￿A = vAˆ, v i The pulley shown belowpoint Brotates aboutbelt is C and interacts ￿ B = two ,rubber belts do not with aB ˆ and the belts and the acceleration of freely on the load point measured to be a j (one horizontal, one vertical). If the velocity of point A on the drive belt is measured to slip. be v A = vA i , the acceleration of point B on the load belt is measured to be a B = aB j , and Find: do not slip, find the velocity and acceleration of D on the the belts Determine the velocity and acceleration of point point D. pulley. y A D C x 0.1 m 0.025 m B Usese the following vA = 10 m / secyour analysis:2vm =sec 2 . U the following: parameters in and aB = ! A / 20m/sec and aB = −5m/sec2 . Chapter II: Planar Rigid Body Kinematics Homework r Kinematics Homework Problems II-5 ME 274 Problem II.3 blem II-3 Given: The car lift shown below is controlled by a horizontally-mounted hydraulic cylinder attached to point A. The by a horizontally a constant speed v . cylinder car lift shown below is controlled cylinder extends at-mounted hydraulic Assume the upper platform remains horizontal cylinder extends at a constant speed v, find the vertical hed to point A. If the and all joints are pinned. ponent of the platform’s velocity for an arbitrary value of !. Assume the upper Find: Determine the vertical component of the platforms velocity for an arbitrary value of θ. orm remains horizontal and all joints are pinned. II-6 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.4 Given: The compound wheel assembly shown below is driven by a cable attached to the outer rim Problem II-4 of the assembly at point A. The wheel rolls without slip at point B, and the acceleration at point A isThe compound xwheel ˆassembly shown below is driven by a cable attached to the outer given by ￿ = a ˆ + ay j a i rim of the assembly at point A. Assuming that the wheel rolls without slip about point B, and the acceleration at point A is given by a A = ax i + ay j , determine the acceleration of Find: Determine the acceleration of the center point C of the pulley. point C. y A ! x C 0.025 m B 0.1 m Use Use following parameters in your analysis: sec 2 0,ndx a 8m/sec2sec 2 . ay = 12m/sec2 . the the following: ! = 36.87° , a = 8 m / φ = a a = = 6 m / and x y Chapter II: Planar Rigid Body Kinematics Homework II-7 Planar Kinematics Homework Problems ME 274 Problem II.5 Problem II-5 Given: The wheel shown below rolls without slip on cart A. The cart has velocity ￿A = vAˆ and v i ˆ. The center of without slip onvelocity ￿Assuming that the cart has C = aCˆ. ˆ and acceleration ￿ velocity acceleration ￿ A =shown below rolls the wheel has cart A. vC = vC i a a i The wheel aA i v A = vA i and acceleration a A = aA i , and the center of the wheel has velocity vC = vC i and acceleration aC = aC i , determine the velocity and acceleration of point B. Find: Determine the velocity and acceleration of point B. y r B C x A aA Use the following parameters in your analysis: r = 0.5m, vA = 5m/sec, vC = −10m/sec, aA = −8m/sec2 and aC = −6m/sec2 . Use the following: r = 2 ft , vA = 10 ft / sec , vC = !5 ft / sec , aA = !10 ft / sec 2 and aC = !6 ft / sec 2 . II-8 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.6 Problem II-6 Given: At the instant shown, the piston has velocity ￿A = vAˆ. v i If, at the instant shown, the piston has velocity v A = vA i , determine the resulting angular Find: Determine the resulting angular velocity ωBC of the crankshaft. ￿ velocity ! CB of the crankshaft. B 0.06 m C y ! A x 0.03 m Use the following parameters in your analysis: φ = 30◦ and vA = −50m/sec. Use the following: ! = 53.13° and vA = !20 m / sec . v Chapter II: Planar Rigid Body Kinematics Homework II-9 Problem II.7 Consider the four mechanisms shown below. Respond to the questions posed. Feel free to draw directly on these sheets and submit for your homework solution. Use a straight edge when making ics Homework Problems ME 274 your drawings. -7 MECHANISM NO. 1 four mechanisms shown below. Respond to the questions posed. Feel free to Link OA is rotating in the clockwise sense. Determine the y on these sheets and submit for your homework solution. Use a straight location of the instant center (IC) of link AB. aking your drawings. From the location of this IC, determine the sense of rotation for links AB and BC. Justify your answers in words. #1 rotating in the clockwise sense. he location of the instant center (IC) of m the location of this IC, determine the tion for links AB and BC. Justify your ords. #2 he location of the instant center AD. From the location of this IC, e sense of rotation for links AD tify your answers in words. II-10 Chapter II: Planar Rigid Body Kinematics Homework MECHANISM NO. 2 Determine the location of the instant center (IC) of link AD. From the location of this IC, determine the sense of rotation for links AD and DB. Justify your answers in words. #2 he location of the instant center AD. From the location of this IC, he sense of rotation for links AD stify your answers in words. Chapter II: Planar Rigid Body Kinematics Homework II-11 MECHANISM NO. 3 Link OA is rotating in the clockwise sense. Determine the location of the instant center (IC) of link cs Homework Problems AB. From the location of this IC, determine the sense E 274 M of rotation for link AB and the sense of translation for the piston. Justify your answers in words. #3 otating in the clockwise sense. e location of the instant center (IC) rom the location of this IC, e sense of rotation for link AB and translation for the piston. Justify your ords. #4 B are moving in the directions he speeds provided. Assume that the t slip on the racks. Determine the e instant center (IC) of the gear. ation of this IC, determine the sense r the gear. Justify your answers with words. vA = 0.8 m/s vB = 0.6 m/s II-12 Chapter II: Planar Rigid Body Kinematics Homework MECHANISM NO. 4 Racks A and B are moving in the directions shown with the speeds provided. Assume that the gear does not slip on the racks. Determine the location of the instant center (IC) of the gear. From the location of this IC, determine the sense of rotation for the gear. Justify your answers with numbers and words. are moving in the directions speeds provided. Assume that the ip on the racks. Determine the nstant center (IC) of the gear. n of this IC, determine the sense he gear. Justify your answers with rds. vA = 0.8 m/s vB = 0.6 m/s Chapter II: Planar Rigid Body Kinematics Homework II-13 lanar Kinematics Homework Problems ME 274 Problem II.8 roblem II-8 Given: The mechanism below is driven by a motor at point A, which produces an angular velocity of ωAB in the direction shown. ￿ he mechanism below is driven by a motor at point A, which produces an angular elocity of ! ABFind: Using the shown. of instantaneous centers, find the velocity of find C. in the direction method Using the method of instantaneous centers, point e velocity of point C. ! AB B 0.2 m C 0.1 m A " # Use the following parameters in your analysis: φ = 0, θ = 60◦ and ωAB = 5rad/sec. se the following: BC is horizontal, ! = 0 , ! = 30° and ! AB = 8 rad / sec . II-14 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.9 P The sliding Given: roblem II-9 collar moves horizontally along the shaft producing an oscillation in AB. At the instant shown, AB and BC are horizontal and vertical, respectively, and the velocity of C is The sliding collar moves C moves to the right. not changing (vC = constant) ashorizontally along the shaft producing an oscillation in AB. If, at the instant shown, AB and BC are horizontal and vertical, respectively, and the velocity f C is not changing ( vC = cons ant ) Find: oDetermine the angular acceleration tof AB.as C moves to the right, find the angular acceleration of AB. A r B L C vC Use the following: L = 0.6 m , r = 0.8 m and v = 25 m / sec . Use the following parameters in your analysis: L = 2fC, r = 1.5f t and vC = 40f t/sec. t Chapter II: PlanarHomework Problems Planar Kinematics Rigid Body Kinematics Homework II-15 ME 274 Problem II.10-10 Problem II Given: The mechanism below is drivenby a motor at point A,A, which produces angular velocity The mechanism below is driven by a motor at point which produces an an angular of ωAB and angular acceleration of αAB . BCE and CD are horizontal and vertical, respectively, at ￿ ￿ velocity of ! A and angular acceleration of ! AB . Provided BCE and CD are horizontal the instant shown. B and vertical, respectively, at the instant shown, find the velocity and acceleration vectors of Determine the velocity and acceleration vectors of point E. Find: point E. 0.3 m Use the following parameters in your analysis: ωAB = 3rad/sec, αAB = 0 and φ = 36.87◦ . Use the following: ! AB = 8 rad / sec , ! AB = "5 rad / sec 2 and ! = 53.13° . II-16 Chapter II: Planar Rigid Body Kinematics Homework Problem II.11 Given: Bar OP rotates about a shaft passing through end O of the bar. At the instant shown, the angular velocity and angular acceleration of OP are given by ω and α. ￿ atics Homework Problems ME 274￿ II-11 (5/12) Find: Determine the velocity and acceleration of end P. Write your answers as vectors. tates about a shaft passing d O of the bar. At the instant e angular velocity and angular n of OP are given by ! and ! . the velocity and acceleration of ite your answers as vectors. y P rotation of bar h O b x Use the following parameters in your analysis: ω = 2rad/sec (CCW), αAB = 3rad/sec2 (CW), b ) ! mm and h c 2 ( CW ) rad / sec ( CCW= ,500= 3 rad / se= 200mm,. b = 500 mm and h = 200 mm in sis. Chapter II: Planar Rigid Body Kinematics Homework II-17 Problem II.12 Given: Point A of plate ABC moves to the right with a speed of vA as the plate rotates with an angular speed of ω . Find: For the instant shown, determine the velocity of point C on the plate. Write your answer ME 274 as a vector. omework Problems (5/61) ABC moves to the right with a the plate rotates with an angular r the instant shown, determine the t C on the plate. Write your answer Use the following parameters in your analysis: vA = 3f t/sec and ω = 5rad/sec (CCW). sec and ! = 5 rad / sec ( CCW ) in your analysis. II-18 Chapter II: Planar Rigid Body Kinematics Homework Problem II.13 Given: Link OA of the mechanism shown rotates with an angular speed of ω0 . At the position shown, link BC is vertical, and the coordinates of pin A are given by (xA , yA ). omework ProblemsFind: (5/88) ME of For this position, determine the angular velocities 274 links AB and BC. Write your answers as vectors. mechanism shown rotates with an f ! 0 . At the position shown, link BC the coordinates of pin A are given by is position, determine the angular ks AB and BC. Write your answers as Use the following parameters in your analysis: ω0 = 10rad/sec and (xA , yA ) = (−60, 80) mm. d / sec and ( x A , yB ) = ( !60, 80 ) mm in your analysis. Chapter II: Planar Rigid Body Kinematics Homework II-19 Problem II.14 mework Problems Given: The vertical control rod of the mechanism shown moves downward with a speed of v. ME 274 5/108) Find: Use the method of instant centers to determine the velocity of end C of link ABC. rol rod of the mechanism shown moves speed of v. Use the method of instant ine the velocity of end C of link ABC. our analysis. Use the following parameter in your analysis: θ = 60◦ . II-20 Chapter II: Planar Rigid Body Kinematics Homework Problem II.15 Given: Link OA rotates at a constant rate of ω . At the instant shown, link OA is aligned with the horizontal line of OC and link AB is vertical. Find: For this position, determine the angular accelerations of links AB and BC. Write your ME 274 answers as vectors. tics Homework Problems -15 (5/137) tates at a constant rate of ! . At the n, link OA is aligned with the ine of OC and link AB is vertical. ition, determine the angular s of links AB and BC. Write your ectors. Chapter II: Planar Rigid Body Kinematics Homework II-21 Problem II.16 Given: The orientation angle θ for the circular disk of radius R is given by: θ (t) = π sinπ t (with 3 θ in radians and t in seconds). Find: Determine the velocity and acceleration vectors for point A on the outer edge of the disk for: • t=0 mework Problems • t = 1/3seconds ME 274 Make sketches of these vectors for the above two instants in time. ngle ! for the circular disk of radius R is " sin" t (with ! in radians and t in 3 ine the velocity and acceleration vectors e outer edge of the disk for: A ! R O conds these vectors for the above two instants Use the following parameter in your analysis: R = 0.5m our analysis. II-22 Chapter II: Planar Rigid Body Kinematics Homework Problem II.17 Given: Thin bar AB (having a length of L) moves in a way that ends A and B slide along straight, fixed guides as shown in the figure. End A has a constant speed of vA to the right as the bar moves. omework Problems ME 274 Find: Determine the velocity and acceleration of end B. ving a length of L) moves in a way B slide along straight, fixed guides as ure. End A has a constant speed of s the bar moves. B elocity and acceleration of end B. L ! ! A vA Use the following parameters in your analysis: L = 2f t, vA = 4f t/sec, θ = 36.87◦ and φ = 120◦ . rs , vA = 3 m / sec , ! = 90° and ! = 36.87° in your analysis. Chapter II: Planar Rigid Body Kinematics Homework II-23 Problem II.18 Given: Wedge A moves to left with a speed of vA . A circular disk is able to roll without slipping on the inclined surface of the wedge. At the instant shown, the velocity of the center of the disk O is moving straight down with an unknown speed of vO . Find: For this problem: • Determine the angular velocity of the disk and the velocity of O. Write your answers as vectors. • Determine the velocity of point B on the disk that is directly above O on the outer surface of the disk. Write your answer as a vector. nematics Homework Problems ME 274 m II-18 B A moves to left with a speed of ircular disk is able to roll slipping on the inclined surface edge. At the instant shown, the of the center of the disk O is straight down with an unknown f vO . O R no slip vA A vO ! Determine the angular velocity of the disk and the velocity of O. Write your answers as vectors. Use the following parameters in your analysis: R = 2f t, vA = 40f t/sec and θ = 36.87◦ . Determine the velocity of point B on the disk that is directly above O on the outer surface of the disk. Write your answer as a vector. = 0.4 meters , vA = 20 m / sec and ! = 53.13° in your analysis. II-24 Chapter II: Planar Rigid Body Kinematics Homework ar Kinematics Homework Problems blem II-19 ME 274 Problem II.19 echanism is made up of links AB, BD and DE. At the instant shown, links AB the instant shown, links AB and Given: A mechanism is made up of links AB, BD and DE. At and are aligned horizontally, and link DE is vertical. ForDE isposition: BD are aligned horizontally, and link this vertical. a) locate the instant center for link BD. Find: For this position: b) determine the angular velocities of links BD and DE. Write your answers as • locate the instant center for link BD. vectors. L = 1 ft and ! AB• =determinesthe iangularanalysis. of links BD and DE. Write your answers as vectors. "4 rad / ec n your velocities E 2L ! AB L 2L A B D Use the following parameters in your analysis: L = 1f t and ωAB = 8rad/sec. atics Homework Problems II-20 ME 274 Chapter II: Planar Rigid Body Kinematics Homework II-25 Problem II.20 ism is made up of links AB, BD and DE. At the instant shown, links AB and rtical, and link BD is horizontal. For this position: Given: A mechanism is made up of links AB, BD and DE. At the instant shown, links AB and termine the angular velocities of links AB and horizontal. your answers as BD. Write DE are vertical, and link BD is ctors. Find: For this position: termine the angular accelerations of links AB and BD. Write your answers as ctors. • determine the angular velocities of links AB and BD. Write your answers as vectors. ft and ! DE = 2 r• determineonstant in your analysis. of links AB and BD. Write your answers as vectors. ad / sec = c the angular accelerations E ! DE 2L B 2L D L A Use the following parameters in your analysis: L = 3f t and ωDE = 3rad/sec. II-26 Chapter II: Planar Rigid Body Kinematics Homework Problem II.21 Given: Link OB rotates with a constant rate of ωOB . At the instant shown, link OB is vertical. omework Problems (5/143) ME 274 Find: Determine the angular acceleration of link AC at this instant. Write your answer as a vector. with a constant rate of ! OB . At the ink OB is vertical. Determine the tion of link AC at this instant. Write a vector. Use the following parameters in your analysis: ωOB = 0.5rad/sec (CW) and tanθ = 4/3. rad / sec ( CW ) and tan! = 4 / 3 in your analysis. Chapter II: Planar Rigid Body Kinematics Homework II-27 Problem II.22 Given: Link OA of the mechanism shown rotates with a constant angular speed of ω0 . At the position shown, link BC is vertical, and the coordinates of pin A are given by (xA , yA ). Find: s Homework Problems 22 (5/145) For this position, determine the angular acceleration of link AB. Write your answer as a ME 274 vector. he mechanism shown rotates with an lar speed of ! 0 . At the position C is vertical, and the coordinates of en by ( x A , yB ) . For this position, angular acceleration of link AB. swer as a vector. Use the following parameters in your analysis: ω0 = 10rad/sec and (xA , yA ) = (−60, 80) mm. rad / sec and ( x A , yB ) = ( !60, 80 ) mm in your analysis. II-28 Chapter II: Planar Rigid Body Kinematics Homework Problem II.23 Planar Kinematics Homework Problems ME 274 Given: -23 Problem IIA mechanism is made up of links AB and BD, with point A being pinned to ground and point B being a pin joint connecting links AB and BD. A slider is connected to BD at pin D with A mechanismbeing constrained to AB and BD, with point A being radius of R. At the position shown the slider is made up of links move on a circular path with a pinned to ground and point B being aAB is vertical, link BD is horizontal andA slider is connected to BD at pin position, below, link pin joint connecting links AB and BD. D is directly above point O. At this D with the slider being constraineda constant speed of vD path with a radius of 2.5 meters. D is traveling to the right with to move on a circular . At the position shown below, link AB is vertical, link BD is horizontal and D is directly above point O.this this position, D is traveling to the right with a constant speed of 5 Find: For At position: m/sec. For the position shown, find: • determine the angular velocities of links AB and BD. Write your answers as vectors. i) the angular velocity of links AB and BD, and ii) t• determine the angularoaccelerations of BD. AB and BD. Write your answers as vectors. he angular acceleration f links AB and links y x A d vD D L B R O Use the following parameters in your analysis: R = 0.5m, L = 2m, d = 1.5m and vD = 5m/sec. Chapter II: Planar Rigid Body Kinematics Homework II-29 Problem II.24 Given: The mechanism shown below is made up of links AB, BE and CE. Links AB and CE are pinned to ground at pins A and C, respectively. Link BE is pinned to links AB and CE at pins B and E, respectively. Link AB is rotating CCW at a constant rate of ωAB . In the position shown Planar Kinematics Homework Problems ME 274 link AB is horizontal, and link CE is vertical. Problem II-24 Given: The mechanism shown below is made up of links AB, BE and CE. Links AB • determine nd CE are pinned to ground at pins A CE. C, respectively. Link BE is pinned a the angular velocity for links BE and and to links AB and CE at pins B and E, respectively. Link AB is rotating CCW at • determine the angular acceleration forIn the BE and CE. a constant rate of 4 rad/sec. links position shown link AB is horizontal, and link CE is vertical. Find: For this position: E L d !AB r A B C Use the following parameters in your analysis: r = 0.2f t, L = 0.5f t, d = 0.4f t and ωAB = 4rad/sec. Find: For the position shown above: a) Find the angular velocity for links BE and CE. b) Find the angular acceleration for links BE and CE. Write your final answers as vectors. Planar Kinematics Homework Problems II-30 ME 274 Chapter II: Planar Rigid Body Kinematics Homework Problem II-25 Problem II.25 Given: A mechanism is made up of two links AB and BC pinned together at point B, and with link AB pinned to ground at point A. Link BC is Given: inned to a block that upconstrained ABmoveBC pinned together at point B, and with p A mechanism is made is of two links to and on a horizontal plane. At link ABhe instant ground at pointvertical, BC ispoint Cto a block that the right t pinned to shown, AB is A. Link and pinned is moving to is constrained to move on 2 a horizontal a speed of 10 instant shown, AB is vertical,at a rate ofC is moving to the right with with plane. At the m/sec and slowing down and point 3 m/sec . a speed of vC with this speed changing at a rate of vC . ˙ Find: At the instant shown, a) determine the angular velocity of links AB and BC. Write your answers as vectors. • determine the angular velocity of links AB and BC. Write your answers as vectors. b) determine the angular acceleration of links AB and BC. Write your • determine the angular acceleration of links AB and BC. Write your answers as vectors. answers as vectors. Find: For this position: B L r A C vC Use the following parameters in your analysis: r = 1m, L = 2m, d = 0.4m, vC = 10m/sec and vC = −3m/sec2 . ˙ Planar Kinematics Homework Problems ME 274 Problem II-26 Given: II: Planar Rigid Body Kinematics Homework BC and a wheel pinned to A mechanism is made up of links AB and Chapter BC at the wheel’s center C. The wheel rolls without slipping on a horizontal surface. Link AB rotates counterclockwise with a constant Problem rate of 3 rad/sec. At the instant shown, link AB is vertical. II.26 II-31 Find: A At the instant shown, links AB and BC and a wheel pinned to BC at the wheels center Given: mechanism is made up of C. The wheela) determine the angular velocities surface. BC and the wheel. rolls without slipping on a horizontal of link Link AB rotates counterclockwise with a constant rate of ωAB . At the instant shown, link AB is vertical. b) determine the angular accelerations of link BC and the wheel. c) determine the velocity and acceleration of point E on the perimeter Find: For this position: of the wheel (at the instant shown, E is on the same horizontal line as C). • determine the angular velocity of links AB and BC. Write your answers as vectors. • determine the angular acceleration of links AB and BC. Write your answers as vectors. Write your answers as vectors. B r d !AB E no slip L A C Use the following parameters in your analysis: r = 0.5m, L = 2m, d = 1m and ωAB = 3rad/sec. II-32 Chapter II: Planar Rigid Body Kinematics Homework PProblem II.27 lanar Kinematics Homework Problems ME 274 Given: I 27 ProblemAI-mechanism is made up of links OA, AB and BD. At the instant shown, link OA is vertical and links AB and BD are horizontally aligned. At this instant, link BD is rotating CW at Given: A mechanism is made up of at α OA, AB and BD. At the instant shown, link links . ωBD with this angular speed changing BD OA is vertical and links AB and BD are horizontally aligned. At this instant, 2 Find: Forlink BD is rotating CW at 6 rad/sec with this rate increasing at 4 rad/sec . this position: Find: showFthethe instant shown, or location of the instant center for link AB in the figure below. • a) show the location of the instant center for link AB in the figure below. • determine the angular velocity of links OA and AB. b) determine the angular velocity of links OA and AB. • determine the angular the angular accelerationandlinks OA and AB. c) determine acceleration of links OA of AB. A L B d D !BD r O Use the following parameters in your analysis: r = 2f t, L = 3f t, d = 1f t, ωBD = 6rad/sec and αBD = 4rad/sec2 . Planar Kinematics Homework Problems ME 274 Chapter II: Planar Rigid Body Kinematics Homework II-33 PProblemIIII.28 roblem -28 Given: A mechanism is made up of links AE, BD, and DE. Links AE and BD are p mechanism is made up of links AE, BD, and DE. Links is pinned to are Given: A inned to ground at pins A and B, respectively, and link DE AE and BD links pinned to ground atAE and BD at pins D and E, and link DE is pinned to links AE link AE is pins D and pins A and B, respectively, respectively. At the instant shown, and BD at vertical and link BD shown, link Also vertical and link BD is horizontal. E, respectively. At the instant is horizontal.AE is at this instant, link BD is rotating Also at this instant, link BD is rotating CW atateconstant= 6 rad/sec. . clockwise at a constant r a of !BD rate of ωBD FFind: ForFthis position: shown: ind: or the position a) determine the angular links AE f links AE • determine the angular velocity of velocity oand DE. and DE. b) determine the angular acceleration of links AE and DE. • determine the angular acceleration of links AE and DE. E !BD b B D a A c d Use the following parameters in your analysis: a = 5f t, b = 3f t, c = 4f t, d = 5f t and ωBD = 6rad/sec. II-34 Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems ME 274 Problem II.29 Problem II-29 Given: A mechanism shown is made up of links OA and AB with a slider pinned to link AB at Given: A mechanism shown is made up of links OA and AB with a slider pinned to B. The slider is constrained to move within a fixed slot at a constant speed of vB in the direction link AB at is oriented at constrained to move within a fixed the at a shown. The slotB. The slider isan angle θ from the horizontal. At slot instant shown, link OA is constant speed of vB = 2 vertical and AB is horizontal. 0 ft/sec in the direction shown. The slot is oriented at a 36.87° angle from the horizontal. At the instant shown, link OA is vertical a For this horizontal. Find: nd AB is position: Find: • For the instant shown, velocity of links OA and AB. determine the angular d) determine the angular velocity of links OA and AB. e) determine the angular acceleration of links OA and AB. • determine the angular acceleration of links OA and AB. A B L ! vB r O Use the following parameters in your analysis: r = 2f t, L = 3f t, θ = 36.87◦ and vB = 20f t/sec. Chapter II: Planar Rigid Body Kinematics Homework Planar Kinematics Homework Problems II-35 ME 274 Problem II.30 Problem II-30 Given: The simple mechanism shown below consists of a flywheel pinned at O and an attached Given: The simple mechanism shown below consists of a flywheel pinned at O and member AB pinned on the outer edge of the flywheel at A. At this moment in time the flywheel an attached member AB pinned on the outer edge of the flywheel at A. At this has a constant angular velocity of ω in the clockwise direction, and OA is horizontal. Assume that moment in time the flywheel has a constant surface aligned of ! in the point B remains in contact with the horizontalangular velocity with the bottom of the flywheel, as clockwise direction, and OA is horizontal . Assume that point B remains in shown below. contact with the horizontal surface aligned with the bottom of the flywheel, as shown below. Find: For this moment in time: Find: • this moment in time, For determine the velocity of B. a) determine the velocity of B (write your answer as a vector). • show the location of the instant center of link AB in the figure below. Use this location to b) show the location of the instantof B foundlink AB in the figure below. verify the direction of the velocity center of above. Use this location to verify the direction of the velocity of B found in a) above. • determine the acceleration of B. c) determine the acceleration of B (write your answer as a vector). ...
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