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Rogelio Daro Gutirrez Carrillo

UNAM,FACULTADDEINGENIER

A

Semestre2012-I

Dinmica de Maquinaria


2/13



If the collar atA is moving downward with an acceleration aA= {~5k}

ft/s2

, at the instant its speed is VA= 8 ft/s, determine the velocity andacceleration of the collar at B at this instant.

vA=8ft/s


A

Semestre2012-I


3/13



Cuando la barraAB est en la posicin que se muestra, el collarn se

mueve a una velocidad de A= {3i} m s y aceleracin de aA= {0.5i} m/s

2

.Determine la aceleracin del collarn B en este instante. Suponga que la

velocidad y aceleracin angulares deAB son perpendiculares a la

barra.


A

Semestre2012-I


4/13


La manivelaAB se utiliza para convertir movimiento rotacional en traslacin del

collarn C. La barra BC de 150 mm esta conectada a la manivela y al collarn

con juntas de bola y receptculo. Si la manivela tiene una aceleracin angularde 2 rad/s2partiendo del reposo en la posicin que se muestra en la figura,

determine lavelocidad y la aceleracin del collarn.


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I


5/13


The rodAC is attached to collars at its ends by ball-and-socket joints. If

diskA has an angular velocity of

A= 10 rad/s, determine the angularvelocity of the rod andthe velocity of collar B at the instant shown.

Assume angular velocity of the rod is directed perpendicular to the rod


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I


6/13


At the instant shown, the cab of the excavator is rotating about the z axis

with a constant angular velocity of Z= 0.3 rad/s. At the same instant

= 60

, and boom OBC has an angular velocity of = 0.6 rad/s, which isincreasing at = 0.2 rad/s2, both measured relative the cab. Determine the

velocity and acceleration of point C on the grapple at this instant


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I


7/13Rogelio Daro Gutirrez Carrillo

At the instant shown, the arm OA of the conveyor belt is rotating about the z axis with

a constant angular velocity 1= 6 rad/s, while at the same instant the arm is rotatingupward at a constant rate 2= 4 rad/s. If the conveyor is running at a constant rate

= 5 ft/s, determine the velocity and acceleration of the package P at the instant

shown. Neglect the size of the package.

1= 6 rad/s

If the conveyor is running at a rate = 5

ft/s, which is increasing at a = 8 ft/s2,

determine the velocity and acceleration

of the package P at the instant shown.

Ans vp= -25.5i -13.4j +20.5k ft/s

ap= 161i -249j -39.9k ft/s2

Ans vp= -25.5i -13.4j +20.5k ft/sap= 161i -243j -33.9k ft/s

2


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I



At the instant shown, the helicopter is moving upwards with a velocity vh=

4 ft/s and has an acceleration aH= 2 ft/s2. At the same instant the frame H,

not the horizontal blade, is rotating about a vertical axis with a constant angularvelocity h= 0.9 rad/s. If the tail blade B is rotating with a constant angular

velocity b/h=180 rad/s, measured relative to H, determine the velocity and

acceleration of point P, located on the tip of the blade, at the instant the blade is

in the vertical position.


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I



At the instant shown, the boom is rotating about the z axis with an angular velocity

1= 2 rad/s and angular acceleration 1= 0.8 rad/s2

. At this same instant the swivelis rotating at 2 = 3 rad/s when 2= 2 rad/s

2, both measured relative to the boom.

Determine the velocity and" acceleration of point P on the pipe at this instant.

Ans vp= 2i + 20j m/s

ap= -101i -14.8j m/s2


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I



The triangular plateABC is supported atA by a ball-and-socket joint and at C by the

xz plane. The sideAB lies in thex-y plane. At the instant = 60, = 2 rad/s, = 3

rad/s2

, and point C has the coordinates shown. Determine the angular acceleration ofthe plate and the acceleration of point C at this instant.

Ans ac = 99.6i117k ft/s2

= 10.4i + 30j +3k rad/s2


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I



At the instant shown, the industrial manipulator is rotating about the z axis at 1= 5rad/s,

and about joint B at 2= 2 rad/s. Determine the velocity and acceleration of the gripA at

this instant, when =30 = 45and r = 1.6m.

Ans vA= -8.66i + 2.26j + 2.26k m/s

aA= -22.6 -47.8j + 4.53k m/s2


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I



At a given instant, the antenna has an angular motion 1= 3 rad/s and 1= 2 rad/s2

about the z axis. At this same instant = 30, the angular motion about thex axis is

2= 1.5 rad/s, and 2= 4 rad/s2. Determine the velocity and acceleration of the

signal hornA at this instant. The distance from O toA is d = 3 ft.

Ans vA= -7.79i -2.25j +3.9k ft/s

aA= 8.3i -35.2j + 7.02k ft/s2


UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I




UNAM,FAC

ULTADDEINGENIER

A

Semestre2012-I

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