Homework 2.A

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.

Find: Determine the velocity and acceleration of end P. Write your answers as vectors.

Planar Kinematics Homework Problems ME 274

Problem II-11 (5/12) 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 ! and ! . Determine the velocity and acceleration of end P. Write your answers as vectors. Use ! = 2 rad / sec CCW( ) , ! = 3 rad / sec2 CW( ) , b = 500 mm and h = 200 mm in your analysis.

O

P rotation of bar

b

h

x

y

Use the following parameters in your analysis: ω = 2 rad/s (CCW), α = 3 rad/s2 (CW), b = 500mm and h = 200 mm.

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Homework 2.B

Given: The rectangular plate ABCD freely rotates about a pivot at point A. At the instant shown,the acceleration of point C is given by ~aC = axi+ ay j.

Find: Determine the angular velocity ~ω and angular acceleration ~α of the plate.

A

B C

Dx

y

0.25 m

0.5 m

Use the following parameters in your analysis: ax = 0 and ay = -20 m/s2.

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Homework 2.C

Given: The wheel shown below rolls without slip on cart A. The cart has velocity ~vA = vAi andacceleration ~aA = aAi. The center of the wheel has velocity ~vC = vC i and acceleration ~aC = aC i.

Find: Determine the velocity and acceleration of point B.

Planar Kinematics Homework Problems ME 274

Problem II-5 The wheel shown below rolls without slip on cart A. Assuming that the cart has velocity vA = vA i and acceleration aA = aA i , and the center of the wheel has velocity vC = vC i and accelerationaC = aC i , determine the velocity and acceleration of point B.

Use the following: r = 2 ft , vA = 10 ft / sec , vC = !5 ft / sec , aA = !10 ft / sec2 and

aC = !6 ft / sec2 .

x

y

A

B C

aA

r

Use the following parameters in your analysis: r = 0.5 m, vA = 5 m/s, vC = -10 m/s, aA = -8 m/s2

and aC = -6 m/s2.

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Homework 2.D

Given: The sliding collar moves horizontally along the shaft producing an oscillation in AB. Atthe instant shown, AB and BC are horizontal and vertical, respectively, and the velocity of C isnot changing (vC is constant) as C moves to the right.

Find: Determine the angular acceleration of AB.

Planar Kinematics Homework Problems ME 274

Problem II-9 The sliding collar moves horizontally along the shaft producing an oscillation in AB. If, at the instant shown, AB and BC are horizontal and vertical, respectively, and the velocity of C is not changing (vC = constant ) as C moves to the right, find the angular acceleration of AB.

Use the following: L = 0.6 m , r = 0.8 m and vC = 25 m / sec .

L

C

B A

C

B A r

vC

Use the following parameters in your analysis: L = 2 ft, r = 1.5 ft and vC = 40 ft/s.

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Homework 2.E

Given: A mechanism is made up of links AB, BD and DE. At the instant shown, links AB andDE are vertical, and link BD is horizontal.

Find: For this position:

(a) Determine the angular velocities of links AB and BD. Write your answers as vectors.

(b) Determine the angular accelerations of links AB and BD. Write your answers as vectors.

Planar Kinematics Homework Problems ME 274

Problem II-20 A mechanism is made up of links AB, BD and DE. At the instant shown, links AB and DE are vertical, and link BD is horizontal. For this position:

a) determine the angular velocities of links AB and BD. Write your answers as vectors.

b) determine the angular accelerations of links AB and BD. Write your answers as vectors.

Use L = 3 ft and !DE = 2 rad / sec = constant in your analysis.

!DE

A

B

D

E

2L

2L

L

Use the following parameters in your analysis: L = 3 ft and ωDE = 3 rad/s = constant.

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Homework 2.F

Given: A mechanism is made up of links AB and BD, with point A being pinned to ground andpoint B being a pin joint connecting links AB and BD. A slider is connected to BD at pin D withthe slider being constrained to move on a circular path with a radius of R. At the position shownbelow, link AB is vertical, link BD is horizontal and D is directly above point O. At this position,D is traveling to the right with a constant speed of vD.

Find: For this position:

(a) Determine the angular velocities of links AB and BD. Write your answers as vectors.

(b) Determine the angular accelerations of links AB and BD. Write your answers as vectors.

Planar Kinematics Homework Problems ME 274

Problem II-23

A 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 the slider being constrained to move on a circular path with a radius of 2.5 meters. At the position shown below, link AB is vertical, link BD is horizontal and D is directly above point O. At this position, D is traveling to the right with a constant speed of 5 m/sec. For the position shown, find:

i) the angular velocity of links AB and BD, and

ii) the angular acceleration of links AB and BD.

d

L v D

A

B

D

x

y

O

R

Use the following parameters in your analysis: R = 0.5 m, L = 2 m, d = 1.5 m and vD = 5 m/s.

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Homework 2.G

Given: A mechanism is made up of links AB, BD and DE. At the instant shown, links AB andBD are aligned horizontally, and link DE is vertical.

Find: For this position:

(a) Locate the instant center for link BD.

(b) Determine the angular velocities of links BD and DE. Write your answers as vectors.

Planar Kinematics Homework Problems ME 274

Problem II-19 A mechanism is made up of links AB, BD and DE. At the instant shown, links AB and BD are aligned horizontally, and link DE is vertical. For this position:

a) locate the instant center for link BD.

b) determine the angular velocities of links BD and DE. Write your answers as vectors.

Use L = 1 ft and !AB = "4 rad / sec in your analysis.

!AB

AB D

E

2L

2LL

Use the following parameters in your analysis: L = 1 ft and ωAB = 8 rad/s.

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Homework 2.H

Consider the four mechanisms shown below. Respond to the questions posed. Feel free to drawdirectly on these sheets and submit for your homework solution. Use a straight edge when makingyour drawings.

MECHANISM NO. 1Link OA is rotating in the clockwise sense. Determine the location of the instant center (IC) oflink AB. From the location of this IC, determine the sense of rotation for links AB and BC. Justifyyour answers in words.

AB

C

O

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MECHANISM NO. 2Determine the location of the instant center (IC) of link AD. From the location of this IC, determinethe sense of rotation for links AD and DB. Justify your answers in words.

A

B

D

CO

v

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MECHANISM NO. 3Link OA is rotating in the clockwise sense. Determine the location of the instant center (IC) oflink AB. From the location of this IC, determine the sense of rotation for link AB and the sense oftranslation for the piston. Justify your answers in words.

O

A

B

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MECHANISM NO. 4Racks A and B are moving in the directions shown with the speeds provided. Assume that the geardoes not slip on the racks. Determine the location of the instant center (IC) of the gear. From thelocation of this IC, determine the sense of rotation for the gear. Justify your answers with numbersand words.

O

A

B

0.1 m

0.2 m

vA = 0.3 m/s

vB = 0.1 m/s

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Homework 3.A

Given: Particle P moves within a straight slot cut into a rotating disk with the x-position of Pincreasing at a constant rate of x. The disk is rotating with counter-clockwise sense at a speed ofΩ, changing at a rate of Ω. The xyz coordinate system is attached to the disk with its origin atthe center O of the disk.

Find: For this problem:

(a) Determine the velocity and acceleration of particle P. Express your answers as vectors in termsof their x-y components.

(b) Make a sketch of the velocity and acceleration vectors found above.

Moving Reference Frame Kinematics Homework Problems ME 274

Problem III-1 A particle P moves within a straight slot cut into a rotating disk with the x-position of P increasing at a constant rate of !x . The disk is rotating with counter-clockwise sense at a speed of ! , with ! changing at a rate of !! . The xyz coordinate system is attached to the disk with its origin at the center O of the disk.

a) Determine the velocity and acceleration of particle P. Express your answers as vectors in terms of their x-y components.

b) Make a sketch of the velocity and acceleration vectors found in a) above.

Use the following parameters in your analysis: x = 0.8 ft , h = 0.6 ft , !x = 15 ft / s , ! = 10 rad / s and !! = "5 rad / s2 .

O

P

x

y

h

x !

Use the following parameters in your analysis: x = 1.5 ft, h = 0.6 ft, x = -10 ft/s, Ω = 6 rad/s andΩ = -4 rad/s2.

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Homework 3.B

Given: An L-shaped arm OBE is pinned to ground at O (section OB is perpendicular to sectionBE of OBE). Arm OBE is known to be rotating in the counterclockwise sense with a constantrotational speed of Ω. Rigid link AP is pinned to ground at A, and with P able to slide within aslot that is cut into section BE of arm OBE, as shown. The xyz coordinate system is attached toarm OBE with its origin at pin O. For the position shown, section OB is aligned with the directionof OA, and P is at a position of yP within the slot.

Find: For this position:

(a) Determine the angular velocity of link AP. Write your answer as a vector.

(b) Determine the angular acceleration of link AP. Write your answer as a vector.

Moving Reference Frame Kinematics Homework Problems ME 274

Problem III-3 An L-shaped arm OBE is pinned to ground at O (section OB is perpendicular to section BE of OBE). Arm OBE is known to be rotating in the counterclockwise sense with a constant rotational speed of !. Rigid link AP is pinned to ground at A, and with P able to slide within a slot that is cut into section BE of arm OBE, as shown. The xyz coordinate system is attached to arm OBE with its origin at pin O. For the position shown, section OB is aligned with the direction of OA, and P is at a position of yP within the slot. For this position:

a) Determine the angular velocity of link AP. Write your answer as a vector.

b) Determine the angular acceleration of link AP. Write your answer as a vector.

Use the following parameters in your analysis: ! = 2 rad / sec , yP = 2 ft , L = 2.5 ft and b = 5 ft .

P

O A

L

x

y

b

! B

E

yP

Use the following parameters in your analysis: Ω = 4 rad/s, yP = 2 ft, L = 5 ft and b = 3 ft.

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