Chapter 1 mechanism

Chi tiết máy là gì? Dấu hiệu để nhận biết chi tiết máy là phần tử có cấu tạo hoàn chỉnh và không thể tháo rời ra được hơn nữa. – Các chi tiết máy sau khi gia công xong cần được lắp ghép với nhau theo một cách nào đó để tạo thành sản phẩm hoàn chỉnh. – Các chi tiết máy được lắp ghép với nhau như sau: Các chi tiết máy được ghép với nhau bằng mối ghép cố định và mối ghép động. + Mối ghép cố định là những mối ghép mà các chi tiết được ghép không có chuyển động tương đối với nhau. Gồm hai loại là mối ghép tháo được như ghép bằng vít, ren, then, chốt…và mối ghép không tháo được như ghép bằng đinh tán, bằng hàn. Mối ghép bằng đinh tán thường được dùng khi vật liệu tấm ghép không hàn được hoặc khó hàn, mối ghép phải chịu được nhiệt độ cao, chịu lực lớn và chấn động mạnh. Ứng dụng: soong, nồi, giàn cần trục,… + Mối ghép động là những mối ghép mà chi tiết được ghép có thể xoay, trượt, lăn và ăn khớp với nhau, các chi tiết có chuyển động tương đối với nhau.

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Mechanisms and Machine Components

Design CHAPTER 1: Mechanism

HOCHIMINH CITY UNIVERSITY OF TECHNOLOGY

AND EDUCATION

TS Phan Công Bình binhpc@hcmute.edu.vn binhpc.tpm@gmail.com

Theoretical contents

I Machines and Mechanisms

II Mobility or Degrees of freedom

of mechanisms

III Inversion of Mechanisms

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3

I Mechanisms

1 General

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TS Phan Công Bình binhpc@hcmute.edu.vn binhpc.tpm@gmail.com 11-Sep-2311-Sep-23

1 General

1.1 Machinery parts

 Machinery parts (elements) are basic mechanical parts and features used as the

building blocks of most machine

I Mechanisms

TS Phan Công Bình binhpc@hcmute.edu.vn binhpc.tpm@gmail.com 11-Sep-23

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1 General

1.2 Mechanical linkage

I Mechanisms

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 A link is defined as a rigid body having one or more pairing elements which

connect it to other bodies for the purpose transmitting force or motion

1 General

1.2 Link

I Mechanisms

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 Degrees of freedom (DOF) of mechanical system is the number of

independent parameters that define its configuration or state

 Kinematic constraints: Are constraints between rigid bodies that

result in the decrease of the freedom of rigid body system

 Kinematic pair: is a connection between two physical object that

imposes constraints on their relative movement

 Classification of kinematic pair:

• Number of kinematic constraint

• Contact surface:

 Higher pairs –point or line contact.

 Lower pairs –surface contact.

1 General

1.3 Kinematic pair

I Mechanisms

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1 General

1.3 Kinematic pair

I Mechanisms

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Kinematic chain is an assembly of rigid bodies connected by joints

to provide constrained (or desired) motion

1 General

1.3 Kinematic chain, mechanism and machine

I Mechanisms

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 Mechanism:

Kinematic chain consists of 1 permanent link (Fixed link)

 Input or drive link is provided motion to move (Input link)

 Another link move follow Input link (follower)

1 General

I Mechanisms

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1 General

Application of four-bar mechanism

I Mechanisms

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 Machine: One or multi mechanisms are assembled to transmit or transform energy

1 General

I Mechanisms

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2 Degree of freedom

I Mechanisms

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 Definition:

An unrestrained rigid body in space has six degrees of freedom:

Z

X

Y

2 Degree of freedom

2.1 Space mechanism

- Three translating motion along

x, y and z axes

- Rotary motion around

x, y and z axes respectively

I Mechanisms

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 Coincide constraint:

• Constraint generated (when two stitches are linked by kinematic

couple) coincide with the available constraints of the joining linkage.

 Ví dụ:

• 3 Coincide constraint

 Translating z axis

 Rotating x axis

 Rotating y axis

2 Degree of freedom

2.1 Space mechanisms

I Mechanisms

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 Redundancy constraint:

• Degree of freedom but redundancy

in kinematics

 Example:

• Linkage CD - 3

→ Note: Constrain of dimension and

positions

2 Degree of freedom

2.1 Space mechanism

I Mechanisms

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 Redundancy degree of freedom:

• Degree of freedom but unnecessary

in kinematics

 Example:

• The roller rolls around its center

→ Note: Self motion without affecting the

movement of the other.

2 Degree of freedom

2.1 Space mechanism

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5

1

6 ( k th tr ) th

W  n   k p   r r  w

n: Number of kinematic link

pk: K constraint

rth: Redundancy constraint

rtr: Coincide constraint

wth: Redundancy of DOF

2 Degree of freedom

2.1 Space mechanism

I Mechanisms

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2 Degree of freedom

2.2 Planar mechanism

 Definition :

• All of the relative motions of the rigid bodies are in one plane or in

parallel planes

Y

X

I Mechanisms

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3 ( 2 th ) w th

W  n  p  p  r 

n: Number of kinematic link (số khâu động có thể di chuyển)

p4: Higher pairs (two degrees of freedom)

(tiếp xúc cung tròn vd: cam, con lăn, bánh răng…)

p5: Lower pairs (one degrees of freedom)

(tiếp xúc mặt: khớp bản lề xoay hoặc trượt tịnh tiến)

rth: Redundancy constraint (hình bình hành)

Wth: Redundancy degree of freedom (con lăn)

2 Degree of freedom

2.2 Planar mechanism

I Mechanisms

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 Q 1 : predict DOF of the given mechanism?

1

2

3

𝑛 = 3, 𝑃 = 4, 𝑃 = 0 𝑊 = 0

⇒ 𝑊 = 3.3 − 0 + 2.4 − 0 − 0 = 1

2 Degree of freedom

2.3 Problems

I Mechanisms

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𝑛 = 7, 𝑃 = 9 , 𝑃 = 1, 𝑊 = 1

⇒ 𝑊 = 3.7 − 2.9 + 1 − 1 = 1

2 Degree of freedom

2.3 Problems

I Mechanisms

1 2 3 4

5

6 7 2P5

P5

P4

P5

Wth

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1 2

3 4 5

6 7

2

1

2

𝑛 = 7, 𝑃 = 10, 𝑃 = 0, 𝑊 = 0

𝑊 = 3.7 − 2.10 + 0 − 0 = 1

2 Degree of freedom

2.3 Problems

I Mechanisms

TS Phan Công Bình binhpc@hcmute.edu.vn binhpc.tpm@gmail.com

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5 1

1

𝑛 = 5, 𝑃 = 7, 𝑃 = 0 , 𝑊 = 0, 𝑟 = 0

𝑊 = 3.5 − 7.2 + 0 − 0 − 0 = 1

2 Degree of freedom

2.3 Problems

I Mechanisms

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𝑛 = 8, 𝑃 = 11, 𝑃 = 0 , 𝑊 = 0, 𝑟 = 0

𝑊 = 3.8 − 11.2 + 0 − 0 − 0 = 2

2 Degree of freedom

2.3 Problems

I Mechanisms

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 Drive link (input link) connected to the fixed link by one or many

kinematic chains ( DOF = 0).

3 Principle of creating a mechanism

3.1 Definition

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 A chain have W=0 ( DOF = 0).

 The simplest chain.

1.3 Classification of Atxua chains

 Type 2 : 2 links - 3 joints

3.2 Atxua chains

I Mechanisms

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 Type 3 : 4 links 6 joints

 Type n : n link polygon

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3.3 Classification of Atxua chains

I Mechanisms

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I Mechanisms

3.4 Principles for separating

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 Replacing higher pair by lower pair P4 P5 :

A

B 2

1

B

A 1

3.4 Principles for separating

I Mechanisms

B

A

1

A

1

2

`

A

B

1

2

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 Q 1 : Separating Atxua chain of the given mechanism

Atxua chain type 2 ( 2 x2’ ) Drive link 1

3 5 Problems

I Mechanisms

𝑛 = 2, 𝑃 = 2, 𝑃 = 1

𝑊 = 3𝑛 − 2𝑃 + 𝑃 = 1

2

1

2

2’

1P5

1P5 A

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 Q 2 : Separating Atxua chain of the given mechanism.

𝑊 = 3.7 − 2.10 + 0 + 0 − 0 = 1

Tính theo tách Atxua 𝑊 = 1 + 0 + 0 + 0 = 1

3 Atxua chain type 2 Input link1

3.5 Problems

I Mechanisms

A

2’

4

5 6 7

3

2'

1

33

𝑊 = 3.7 − 2.10 + 0 + 0 − 0 = 1

𝑊 = 1 + 0 = 1

3 Atxua chains type 2 Driving link 1

3.5 Problems

I Mechanisms

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3.5 Problems

𝑛 = 6, 𝑃 = 8, 𝑃 = 1, 𝑟 = 0, 𝑊 = 0

𝑊 = 3.6 − 8.2 + 1 + 0 − 0 = 1

I Mechanisms

2

3

4

5

6

1

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 Q 4

3.5 Problems

Atxua chain type 3 (3, 4 ,5,6) Atxua chain type 2 (2, 2

Input link 1

I Mechanisms

1

2

3

4

5

6 3P5

P5

P1

P2 2' 3P5

P5

O2ω2

W

P1

ω1

O1

P2

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Planar mechanism: All of the relative motions of rigid bodies are

in one plane or parallel planes

Four-bar Mechanism

II Mechanisms with lower pair

1 General

1.1 Definition

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Types of four-bar mechanism following those principle :

• Changing dimension of the links.

• Changing the fixed link.

1) Change dimension Four-bar mechanism

(Link 3 moves translate và D at infinity)

x

B

1

2 3 4

D∞ a) Slider-crank off-center mechanism

1 General

1.2 Other types of four-bar mechanism

4

3

2

1

A

B

C

D

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(b change 1 into fixed link)

ω1

A

v

B

C

3

D

d) Sin mechanism

(In c A translate to infinity)

B

C D 2 3

4 v

1 A

v

e) Elip mechanism

In b, A & D to infinity

1 General

ω

A

1

4

ω1

B

C

4

1

3

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1 General

a) Four-bar mechanism

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1 General

c) Slider-crank mechanism

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1 General

b) Slider-crank off-center mechanism

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1 General

d) Culit mechanism

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1 General

e) Sin mechanism

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1 General

f) Elip mechanism

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• Mechanism has 2 link rotate

Link 1 and link 3 rotate same clockwise

4

3 2

1

A

D

• Mechanism has 1 link rotate and 1 link shake (Crushed stone machine)

Link 1 rotate, link 5 swing

A

F

B

C D E

Đá

1

2

3 4

5

1 General

1.3 Application of four-bar mechanism

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In four-bar mechanism, 1 link can rotate fully if total length of the shortest

link and the longest link ≤ total link of 2 rest links There are 3 cases:

• If the link connected the shortest link is fixed, the shortest link can rotate

and opposite link can swing

• If the shortest link is fixed, 2 connected fixed links can rotate

• If the link opposite the shortest link is fixed link, 2 link connecting fixed link

can swing and the shortest link rotates

=> Purpose: Confirm movement of links connecting fixed link

2 Laws of mechanisms

2.1 Grahof’s law

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2.1 Grahof’s law

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B

C

D

A

9,625"

7,187"

8,375"

2"

11,625

18,562

• Mechanism diagram

A

B

C D

8"

14"

47,5"

12"

76"

2.1 Grahof’s law

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Transmission ratio mechanism

4

3

2

1

A

D

1 13 3





2.2 Transmission ratio mechanism

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• Point at B

• ┴ AB

• Follow direction ω1

• VB = ω1.lAB

B

v

Vector vận tốc

Mechanism ABCD, ω1, ω3 BC cut AD at point P 1

13 3

Definition u

PA



2.3 Villis’s law



F

1

2

3

4

αB

A B

C

D

αC vc

B

v

P

αC

αB E

Cos

B

c

AE

AB

DF

CD





1

13

3

u



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Content of law:

Link BC divides link AD into 2 segments that inversely proportional to the angular

velcoity of 2 link connect link AD

Comment:

• When mechanism moves , P changes => PD

and PA change (

• If P out of AD => ω1 and ω3 have same

rotate clockwise.

• If P in AD => ω1 and ω3 have contrary

rotate

D A

1 13 3

/ /

1

BC AD P

PD PA AD u

PA PA



  



2.3 Villis’s law

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Tiêu đề	Chapter 1: Mechanism
Tác giả	TS. Phan Công Bình
Trường học	Hochiminh City University of Technology and Education
Chuyên ngành	Mechanisms and Machine Components Design
Thể loại	theoretical contents
Năm xuất bản	2023
Thành phố	Hochiminh City

Định dạng
Số trang	18
Dung lượng	2 MB