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Instantaneous Center of Zero Velocity Problems

Instantaneous Center of Zero Velocity Problemskisi.deu.edu.tr/emine.cinar/DYNAMICS/FALL 2018/G18... · 2018-12-14 · instant considered. The disk contacts the surface at point C

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Text of Instantaneous Center of Zero Velocity Problemskisi.deu.edu.tr/emine.cinar/DYNAMICS/FALL...

  • Instantaneous Center of Zero Velocity

    Problems

  • PROBLEMS

    1. A device which tests the resistance to wear of two materials A and B is shown. If the link EO has a velocity of 1.2 m/s to the right when q = 45°, determine the rubbing velocity vA.

  • PROBLEMS vEO =1.2 m/s to the right when q = 45°, determine the rubbing velocity vA.

    P wOAD C300

    DP

    O

    45 125

  • PROBLEMS 2. Horizontal oscillation of the spring loaded plunger E is controlled by varying the air pressure in the horizontal pneumatic cylinder F. If the plunger has a velocity of 2 m/s to the right when q = 30°, determine the downward velocity of vD of roller D in the vertical guide and find the angular velocity w of ABD for this position.

  • PROBLEMS vE = 2 m/s to the right when q = 30°, determine the downward velocity of vD of roller D and w of ABD .

    P

    30°

    30°

    200

    2.173

    2.173100

    30°

  • PROBLEMS

    3. If the center O of the gear is given a velocity of vO = 10 m/s, determine the velocity of the slider block B at the instant shown.

  • PROBLEMS

    mBP

    mABAP

    ABBPAP

    039.130cos)6.0(2

    6.0

    30sin120sin30sin

    sm

    v

    srad

    gearA

    gear

    /143.17

    175.0125.0

    /143.57175.0

    10

    300.0

    w

    w

    smBPv

    sradAP

    v

    ABB

    AAB

    /69.29

    /57.28

    w

    w

    vO = 10 m/s, determine vB .

    vO

    A vA

    C

    vB

    P

    30°

    wAB

    120°

    30° B

  • PROBLEMS 4. The mechanism used in a marine engine consists of a single crank AB and two connecting rods BC and BD. Determine the velocity of the pistons at C and D and angular velocities of rods BC and BD when the crank is in the position shown and has an angular velocity of 5 rad/s.

    s/m.ABv ABB 1205 w

    Cv

    Dv

    P2 (IC of link BD)

    P1 (IC of link BC)

    0.5 m

  • s/m.ABv ABB 1205 w

    Cv

    Dv

    P2 (IC for link BD)

    P1 (IC for link BC) P2

    D

    B

    30o

    105o

    45o

    0.6

    83 m

    s/m.v

    s/rad.

    .

    v

    .

    v

    m.DP

    m.BP

    sin

    DP

    sin

    BP

    sin

    .

    D

    BD

    DBBD

    5180

    4641

    35406830

    1

    3540

    6830

    3010545

    50

    2

    2

    22

    w

    w

    P1

    C

    B 60o

    75o

    45o

    0.5

    46 m

    smv

    srad

    vv

    mBP

    mCP

    BPCP

    C

    BC

    CBBC

    /896.0

    /8315.1

    489.0546.0

    1

    546.0

    489.0

    75sin60sin45sin4.0

    1

    1

    11

    w

    w

    0.5 m

  • PROBLEMS 5. The mechanism shown is used at a riveting machine. The mechanism consists of a drive piston A, three links and sliding block D. If the velocity of piston at the instant shown is vA = 20 m/s, determine the angular velocity of link CD and the velocity of block D, vD. Use the Method of Instantaneous Center of Zero Velocity.

    20 m/s

  • 15

    PROBLEMS

    vA = 20 m/s, wCD = ?, vD = ?

    20 m/s

    20 m/s

    45

    PAC

    PDC

  • PROBLEMS 6. The center O of the stepped disk which rolls on the horizontal surface without slipping has a velocity of 6 m/s to the right at the instant considered. The disk contacts the surface at point C. Rod AB, attached to the disk with a pin connection at point A is also pin connected to a small roller at B. The roller B can move freely on the circular road which has a radius of 120 cm. Determine the angular velocity of rod AB (wAB) and the velocity of roller B (vB) for this instant.

    O vO=6 m/s

    r

    R

    60o

    240 cm

    100 cm

    A

    C

    120 cm

    B

    37o

    r=30 cm R= 50 cm

  • PROBLEMS v0 = 6 m/s (→), wAB = ? vB = ?

    O vO=6 m/s

    r

    R

    60o

    240 cm

    100 cm

    A

    C

    120 cm

    B

    37o

    r=30 cm R= 50 cm

    A

    O

    C

    60

    30

    50

    120

    79.5190

    21.38,6186.0sin,120sin

    70sin50

    70

    120cos305023050 222

    cmAC

    AC

    A

    B

    100

    240

    62.22

    417.0240100

    tan

    cmAB 260100240 22

    P

    A

    B

    P

    C79.51

    3721.38

    62.75

    260

    Bv

    Av