The homework

1. Pay attention to the symbols of the links and kinematic pairing

2. Label out the primary drive3. Pay attention to the scale of your sketch4. For the collinear pairing, use the center

line to present them out.5. For the system, you must analyze the

functions of the machine.

The homework

1. Label out the link and pairing with different Number series

2. Pay attention to the redundant constraint

3. Pay attention to the compound hinges

4. Compare it with the real model.

Summary of QAs

• 共同约束＝公共约束• 杆组的主要应用是机构的机械分析• 机构自由度的计算公式通用化问题• 答疑问题需要大家积极参加！！！• 欢迎大家给我的 TA与我发送电子邮件！• 课代表整理出班机的电子邮件发送给我们！

Summary of last class

1) General Character of a four-bar linkage

2) Basic Form of Four-bar Linakage

3) Grashof Criterion (Conditions of a Crank)

4) Inversions of Four-bar Linkage

5) Kinematic Design of Four-bar Linkage

Today’s Main Topic

• General task of kinematic analysis

• 1. Velocity Analysis of four bar linkage with graphic method

• 2. The Velocity Analysis of Four-bar linkage with Computer program

Velocity Analysis of four bar linkage with graphic method

• 1.1 Aronhold-Kennedy Theorem

• 1.2 Apply the Instant center to basic four bar linkage

• 1.3 Apply the instant center to slide crank mechanism

• 1.4 The general method of application

• 1.5 Shortcomings of the graphic method

1.1 Aronhold-Kennedy Theorem

Definition of Instant Center

Two bodies moves in a planar motion, there is two coincident points, the absolute velocities of which are the same

At the instant, the pair of coincident points with the same velocities is defined as the instantaneous center of relative motion

1.1 Aronhold-Kennedy Theorem

Character of Instant center1) Two body with relative motion2) The instant center may be changing all the

time3) The Velocity Vector is perpendicular to the

rotating radius3) If one link is a frame, the instant center is the rotating center

1.1 Aronhold-Kennedy Theorem

Number of instant centers of a Mechanism

Two links have one instant center

Three links have 3 instant centers

Four links C24

n links will have Cn2

1.1 Aronhold-Kennedy Theorem

• Location of the Instant Center of two links connected by a Kinematic pair

• 1) Revolute pair

• 2) Pure rolling pair

• 3) Sliding pair

• 4) higher pairing• Textbook pp 56

1.1 Aronhold-Kennedy Theorem

• The Theorem:Any three links have three instant centers, the

three instant centers must lie on a straight line

ProofUse the contradiction methodPp 57

1.2 Apply the Instant center to basic four bar linkage

• Pp57

• Given the crank rotating velocity

• The links length and the position

• Find the rotating speed of 3 and 4

4= 3* p12p24/p14p24

1.3 Apply the instant center to slide crank mechanism

Given the dimension of the links, the position of the links and the rotating speed of crank.

Find out the sliding speed of the slider.

V4=Vp24= 2* p12p24

1.4 The general method of application

Given the dimension of the links and angular velocity of crank one.

Find out the rotating speed of rocker three

Find out the speed of point F on coupler two

1.5 Shortcomings of the graphic method

1)Each position should have a analysis, For the whole procedure need much work

2) The instant center may be far away from the drawing paper

3) Some instant center is not easy to find out

4) Can use the vector method

5) Analytical method may be easy to use.

Velocity Analysis of four bar linkage with graphic method

• 1.1 Aronhold-Kennedy Theorem

• 1.2 Apply the Instant center to basic four bar linkage

• 1.3 Apply the instant center to slide crank mechanism

• 1.4 The general method of application

• 1.5 Shortcomings of the graphic method

2. The Velocity Analysis of Four-bar linkage with Computer program

The slide crank mechanism

2. The Velocity Analysis of Four-bar linkage with Computer program

The basic form of four bar linkage

L1

L4

L3L2

phi1

phi2

2. The Velocity Analysis of Four-bar linkage with Computer program

The more general method of Kinematic Analysis is the Assur group method

Find out the basic Component of the linkage system.

The program out the basic subroutine.You just call them when you want to

Calculate

2. The Velocity Analysis of Four-bar linkage with Computer program

The basic Dyad

RRRRRP

RPR

2. The Velocity Analysis of Four-bar linkage with Computer program

Basic Kinematic Analysis

Position Analysis

Velocity Analysis

Acceleration AnalysisSee Textbook pp59

2. The Velocity Analysis of Four-bar linkage with Computer program

Given The position of link A and Link B

The angular velocity of point A, B

Find out the angular velocity of link B and velocity of point C

LA

LB

CA B

2. The Velocity Analysis of Four-bar linkage with Computer program

The PRP dyad

Given: the Position and Angular parameters of Point A and Point C

Find out the kinematic parameters of the Guide bar

See pp 35 of the reference book

What have we dealt with today

• General tasks and methods of kinematic analysis

• 1. Velocity Analysis of four bar linkage with graphic method

• 2. The Velocity Analysis of Four-bar linkage with Computer program

Homework for Today

Textbook pp 40

1) 2.8 be abide by the ratio of the links if you draw the kinematic sketch by hand.

2) 2.11 the crank has an angle with line AC for 30 degrees.