chương 7 hợp chuyển động của điểm cơ lí thuyết spkt

chương 7 hợp chuyển động của điểm cơ lí thuyết spk đây là tài liệu dành cho những bạn họ cơ lí thuyêt, tài liệu rất đầy đủ, dễ hiểu, giúp các ạn nứm vững kiến thức các bạn có thể tải về để phục phụ việc hoc

LOGO trangtantrien@hcmute.edu.vn

https://sites.google.com/site/trangtantrien/

MỤC TIÊU CỦA CHƯƠNG

* Nhận biết được những bài toán hợp chuyển động.

* Xác định được các thành phần vận tốc tuyệt đối, vận tốc tương đối và vận tốc kéo theo Thiết lập được mối quan hệ giữa chúng.

* Ứng dụng Matlab, Maple để phân tích bài toán hợp chuyển động.

* Xác định được các thành phần gia tốc tuyệt đối, gia tốc tương đối, gia tốc kéo theo và gia tốc Coriolis Thiết lập được mối quan

hệ giữa chúng.

* Xây dựng được sơ đồ tính phù hợp cho các bài toán kỹ thuật.

1 Khái Niệm

1 Khái Niệm

* x 1 y 1 là hệ tọa độ vừa tịnh tiến,

vừa quay đối với hệ trục cố định

=> Ở mỗi thời điểm, vận tốc tuyệt đối

Example: The disk rotates

ω=2rad/s The small ball

A is moving along the

radial slot with speed

u=100mm/s relative to the

absolute velocity of the

ball and state the angle β

between this velocity

vector and the positive

x-axis

Example: Collar C moves along rod BA with a constant velocity of

v=3m/s and measured relative to the rod At the same instant, rod AB

rotates with the angular velocity and angular acceleration shown.Determine the collar’s velocity at this instant



the hoop, while the

hoop rotates with the

angular velocity and

Example: The disk rotates

about a fixed axis through O

ω=5rad/s and angular

acceleration ε=2rad/s 2 at the

instant represented, in the

directions shown The slider

A moves in the straight slot.

Determine the absolute

velocity of A for the same

instant, when y=16cm;

Example: The disk rotates

about a fixed axis through O

with angular velocity

ω=5rad/s and angular

acceleration ε=3rad/s 2 in the

directions shown at a certain

instant The small sphere A

moves in the circular slot,

and at the same instant,

β=300,

Determine the absolute

velocity of A at this instant.

2

2rad s/ ; 4rad s/



Example: The small collar A is sliding on the bent bar with speed u relative to the bar as shown Simultaneously, the bar is rotating with angular velocity ω about the fixed pivot B Determine the absolute velocity of A at this instant

Example: The bar DC rotates uniformly about the shaft at D with a constant angular velocity ω = 10 rad/s Determine the velocity of the bar

AB at the instant θ = 300, which is confined by the guides to move

vertically CD = l = 10 cm.

Example: At the instant θ = 600, the slotted guide is moving upward

with a velocity of 2m/s Determine the angular velocity of link AB at this

instant

Example: The bridge girder G of a bascule bridge is raised and lowered using the drive mechanism shown If the hydraulic cylinder AB shortens

at a constant rate of 0.15m/s, determine the angular velocity of the bridge girder at the instant θ = 60°.

Example: Peg B mounted on hydraulic cylinder BD slides freely along the slot in link AC If the hydraulic cylinder extends at a constant rate of 0.5m/s, determine the angular velocity of the link at the instant θ = 30°.

Example: Block B of the

mechanism is confined tomove within the slot member

CD If AB is rotating at a

constant rate of ω AB = 3 rad/s,

determine the angular velocity

of member CD at the instant

shown

Example: The

consists of a crank AB,

slider block B, and slotted

link CD If the crank has

the angular motion shown,

determine the angular

velocity of the slotted link

at this instant



Example: At the instant shown rod AB has an angular velocity

ω AB and an angular acceleration ε AB Determine the angular velocity of

rod CD at this instant The collar at C is pin connected to CD and slides freely along AB.



Example: At the instant θ = 45°, link DC has an angular velocity of ω DC =4rad/s and an angular acceleration of ε DC =2rad/s 2.

Determine the angular velocity of rod AB at this instant The collar at C

is pin connected to DC and slides freely along AB.



Example: Peg B fixed to crank AB slides freely along the slot in member CDE If AB rotates with the motion

shown, determine the angular velocity of CDE at the

instant shown.



Example: At a given instant, rod AB has the angular motions shown Determine the angular velocity of rod CD at this instant There is a collar

at C.



Example: The pin A of the hinged link AC is confined to move in the rotating slot of link OD The angular velocity of OD is ω=2rad/s

clockwise and is constant for the interval of motion concerned For the

position where θ=450 with AC horizontal, determine the angular velocity of AC.

Example: For the instantrepresented, link CB isrotating counterclockwise at

a constant rate N=4rad/s.

Determine the angular

velocity of ODE for this

instant

Example: The disk rotates about a fixed axis through point O with a clockwise angular velocity ω0=20rad/s and a counterclockwise angular acceleration ε0=5rad/s 2 at the instant under consideration The value of r

is 200 mm Pin A is fixed to the disk but slides freely within the slotted member BC Determine the velocity of A relative to slotted member BC and the angular velocity of BC.

Example: The crank OA revolves clockwise with a constant

angular velocity of 10 rad/s within a limited arc of its motion For the

position θ=450, determine the angular velocity of the slotted link CB.

Example: Theslotted yoke is

pinned at A while end B is used to move the ram R

horizontally If thedisk rotates with aconstant angular

rad/s, determine the

velocity of the ram

at the instant θ=90° The crank pin C is

fixed to the diskand turns with it

Example: Peg B on the gear slides freely along the slot in link AB If the gear’s center O moves with the velocity and acceleration shown, determine the angular velocity of the link AB at this instant.

Example: The gear has the angular motion shown Determine the

angular velocity of the slotted link BC at this instant The peg at A is

fixed to the gear



Example: The gear has the angular motion shown Determine the

angular velocity of the slotted link BC at this instant The peg at A is

fixed to the gear



Example: The disk rolls without slipping and at a given instant has theangular motion shown Determine the angular velocity of the slotted

link BC at this instant The peg at A is fixed to the disk.



Example: The disk rolls without slipping on the horizontal surface If

the disk has a clockwise angular velocity of 20rad/s and a counterclockwise angular acceleration of 5rad/s2, determine the velocity

of pin A relative to the slotted member BC and the angular velocity of

BC The value of r is 200 mm Neglect the distance from the center of

pin A to the edge of the disk

Example: The dumpster pivots about C and is operated by the hydraulic cylinder AB If the cylinder is extending at a constant rate of 0.5ft/s,

determine the angular velocity of the container at the instant it is in thehorizontal position shown

Example: The cars onthe amusement-parkride rotate around the

velocity ω A/f =2rad/s

measured relative to

the frame AB At the

same time the framerotates around the main

axle support at B with

a constant angularvelocity ω f =1rad/s Determine the velocity

of the passenger at C at

the instant shown

Example: If the piston is moving with a velocity of v A and acceleration

of a A, determine the angular velocity of the slotted link at the instant

shown Link AB slides freely along its slot on the fixed peg C.

Example: The wheel is rotating with the angular velocity and angularacceleration at the instant shown Determine the angular velocity of therod at this instant The rod slides freely through the smooth collar.



Example: The figureillustrates a commonly usedquickreturn mechanismwhich produces a slowcutting stroke of the tool

(attached to D) and a rapid

return stroke If the driving

crank OA is turning at the

determine the magnitude of

the velocity of point B for the instant when θ=300

3 rad s /

  

Example: For the

AC For this same

horizontal and DE is

vertical Determinethe angular velocity

of DE at this instant.

Example: The crank OB revolves clockwise at the constant rate ω0 of 5rad/s For the instant when θ=900, determine the angular

velocity of the rod BD, which slides through the pivoted collar at C.

Example: The Geneva wheel is a mechanism for producing

intermittent rotation Pin P in the integral unit of wheel A and locking plate B engages the radial slots in wheel C, thus turning wheel C one-

fourth of a revolution for each revolution of the pin Determine the

angular velocity of wheel C for the instant when θ=200 Wheel A has a

constant clockwise angular velocity of 2rad/s

Example: The pin A in the bell crank AOD is guided by the flanges of the collar B, which slides with a constant velocity v B of 3ft/s along thefixed shaft for an interval of motion For the position θ=300, determine

the velocity of the plunger CE, whose upper end is positioned by the

radial slot in the bell crank

Example: The Geneva

packaging system to convertconstant angular motion intointermittent angular motion The

star wheel A makes one sixth of a

revolution of the driving wheel B and the attached guide C To do this, pin P, which is attached to

B, slides into one of the radial

slots of A, thereby turning wheel

A, and then exits the slot If B has

a constant angular velocity of

ω B =4rad/s, determine angular

velocity of wheel A at the instant

shown

: gia tốc của điểm B so với hệ động là chuyển động kéo tương đối.

3 Hợp Gia Tốc Của Điểm

=> Ở mỗi thời điểm, gia tốc tuyệt

đối của điểm B bằng tổng hình học

gia tốc tương đối, gia tốc theo và

gia tốc Coriolis của nó.

3 Hợp Gia Tốc Của Điểm

* Trong thực hành sử dụng qui tắc sau đây để xác định gia tốc Côriôlis :

r

v 

+ Khi vuông góc với , ta quay theo chiều một góc 900

ta được phương và chiều của véc tơ , độ lớn của nó được xác địnhbởi công thức: ac=2ωevr

* Trong thực hành sử dụng qui tắc sau đây để xác định gia tốc Côriôlis :

r

v 

+ Khi không vuông góc với ,ta chiếu lên mặt phẳng vuông

phương và chiều của véctơ , độ lớn của nó được xác định bởi côngthức: ac=2ωevr sinα

* Trường hợp đặc biệt: a c = 0 (ω e = 0)

3 Hợp Gia Tốc Của Điểm

* Ảnh hưởng của gia tốc Coriolis

3 Hợp Gia Tốc Của Điểm

Example: The disk rotates

about a fixed axis through O

ω=5rad/s and angular

acceleration ε=2rad/s 2 at the

instant represented, in the

directions shown The slider

A moves in the straight slot.

Determine the absolute

velocity and acceleration of

A for the same instant, when

y=16cm; y  50cm s y/ ;   10cm s/ 2

10cm



Example: Collar C moves along rod BA with a constant velocity of

v=3m/s and measured relative to the rod At the same instant, rod AB

rotates with the angular velocity and angular acceleration shown

Determine the velocity and acceleration of collar C at this instant.



the hoop, while the

hoop rotates with the

angular velocity and

Example: The disk rotates

about a fixed axis through O

with angular velocity

ω=5rad/s and angular

acceleration ε=3rad/s 2 in the

directions shown at a certain

instant The small sphere A

moves in the circular slot,

and at the same instant,

β=300,

Determine the absolute

velocity and acceleration of

Example: The bar DC rotates uniformly about the shaft at D with a constant angular velocity ω = 10 rad/s Determine the velocity and acceleration of the bar AB at the instant θ = 300, which is confined by the

guides to move vertically CD = 10 cm.

Example: At the instant θ = 600, the slotted guide is moving upwardwith an acceleration of 3m/s 2 and a velocity of 2m/s.

Determine the angular acceleration and angular velocity of

link AB at this instant.

Example: The bridge girder G of a bascule bridge is raised and lowered using the drive mechanism shown If the hydraulic cylinder AB shortens

at a constant rate of 0.15m/s, determine the angular velocity of the bridge girder at the instant θ = 60°.

Example: Peg B mounted on hydraulic cylinder BD slides freely along the slot in link AC If the hydraulic cylinder extends at a constant rate of 0.5m/s, determine the angular velocity and angular acceleration of the link at the instant θ = 30°.

Example: Block B of the

mechanism is confined tomove within the slot member

CD If AB is rotating at a

constant rate of ω AB = 3 rad/s,

determine the angular velocityand angular acceleration of

member CD at the instant

shown

Example: The

consists of a crank AB,

slider block B, and slotted

link CD If the crank has

the angular motion shown,

determine the angular

motion of the slotted link

at this instant



Example: At the instant shown rod AB has an angular velocity

ω AB and an angular acceleration ε AB Determine the angular velocity and

angular acceleration of rod CD at this instant The collar at C is pin connected to CD and slides freely along AB.



Example: Peg B on the gear slides freely along the slot in link AB If the gear’s center O moves with the velocity and acceleration shown,

determine the angular velocity and angular acceleration of the link atthis instant

Example: At the instant θ = 45°, link DC has an angular velocity of ω DC =4rad/s and an angular acceleration of ε DC =2rad/s 2.

Determine the angular velocity and angular acceleration of rod AB at this instant The collar at C is pin connected to DC and slides freely along AB.



Example: Peg B fixed to crank AB slides freely along the slot in member CDE If AB rotates with the motion

shown, determine the angular velocity of CDE at the

instant shown.



Example: At a given instant, rod AB has the angular motions shown Determine the angular velocity and angular acceleration of rod CD at this instant There is a collar at C.



Example: The dumpster pivots about C and is operated by the hydraulic cylinder AB If the cylinder is extending at a constant rate of 0.5ft/s,

determine the angular velocity of the container at the instant it is in thehorizontal position shown

Example: The cars onthe amusement-parkride rotate around the

velocity ω A/f =2rad/s

measured relative to

the frame AB At the

same time the framerotates around the main

axle support at B with

a constant angularvelocity ω f =1rad/s Determine the velocityand acceleration of the

passenger at C at the

instant shown

Example: If the piston is moving with a velocity of v A and acceleration

of a A, determine the angular velocity and angular acceleration of the

slotted link at the instant shown Link AB slides freely along its slot on the fixed peg C.

Example: The wheel is rotating with the angular velocity and angularacceleration at the instant shown Determine the angular velocity andangular acceleration of the rod at this instant The rod slides freelythrough the smooth collar.



Example: The gear has the angular motion shown Determine the

angular velocity and angular acceleration of the slotted link BC at this instant The peg at A is fixed to the gear.



Example: The gear has the angular motion shown Determine the

angular velocity and angular acceleration of the slotted link BC at this instant The peg at A is fixed to the gear.



Example: The disk rolls without slipping and at a given instant has theangular motion shown Determine the angular velocity and angular

acceleration of the slotted link BC at this instant The peg at A is fixed to

the disk



Example: The pin A of the hinged link AC is confined to move in the rotating slot of link OD The angular velocity of OD is ω=2rad/s

clockwise and is constant for the interval of motion concerned For the

position where θ=450 with AC horizontal, determine the angular velocity and angular accelaeratin of AC.