W2 Mobility Four Bar Slider Crank Mechanism 20140724

-Mobility -Four Bar Linkage

Noor Aliah Abdul Majid Dept. of Mechanical & Manufacturing Eng.

Mobility & Four Bar Linkage, N. Aliah A. M Sept 2014

KNJ 2222: Analysis of Mechanics and machines

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1

Mobility (Degree of Freedom)

2

Types of Links

3

Four Bar Mechanism

4

Slider- Crank Mechanism


Contents

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RECALL • How many LINKS are there in this mechanism?


• Identify what type of JOINTS available.

3

RECALL • How many LINKS are there in this mechanism?


• Identify what type of JOINTS available.

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The students will be able to: 1. Compute the number of degrees of freedom of a mechanism. 2. Identify the types of mechanical drives


Objectives of this chapter

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MOBILITY

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What is the meaning of Mobility?

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MOBILITY (M) • number of independent inputs required to precisely positions all links of the mechanism with respect to the ground • number of actuators needed to operate the mechanism A mechanism actuator could be manually moving one link to another position, connecting a motor to the shaft of one link, or pushing a piston of a hydraulic cylinder.


• number of degrees of freedom (DOF) of the linkage

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MOBILITY (M)

You need at least x,y and θ

What if you take the pencil up in the air?


How to define the position of the pencil if it is constrained on the paper?

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MOBILITY (M) • Gruebler’s equation to calculate Mobility

• n = number of links • jp = number of primary joints (lower order joints) • jh = number of higher order joints • M = 1 constrained mechanism • M < 1 locked mechanism

Lower order joints have a surface or planar contact, such as a pin joint or a sliding joint Higher order joints have a line or point contact, such as a cam or a gear


M = 3(n-1) – 2jp – jh

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Spherical

Revolute / Hinge / Pin

Planar

Prismatic / Sliding joint

Cylindrical

Screw


Types of Lower Order Joints

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Mobility Mechanism b) Locked mechanism (M=0) • Mechanism with zero or negative DOF • These mechanism are unable to move and form a structure c) Unconstrained or multi degree of freedom (M=2) • Need more than one driver to precisely operate them • Example: Robotic arm


a) Constrained mechanism or single degree of freedom (M=1) • A single degree of freedom

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• An actuator or driver device is required to provide the input motion and energy. • One driver is required for each DOF exhibited. • Examples: Electric motors (AC), electric motors (DC), engines, servomotors, air or hydraulic motors, hydraulic or pneumatic cylinders, screw actuators, manual or hand operated mechanism and etc.


Actuators and Drivers

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Example 1.3


Figure below shows a toggle clamp. Draw a kinematics diagram, using the clamping jaw and the handle as point of interest. Also compute the DOF for the clamp.

Toggle clamp movement

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Example 1.3 (cont.)

1.

Identify the Frame • •

2.

The component that is bolted to the table is designated as the frame The frame is numbered as link 1

Identify All Other Links • • •


Solution:

Handle (Link 2) Arm that serves as the clamping jaw (Link 3) Bar that connects the clamping arm and handle (Link 4)

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Example 1.3 (cont.) 3. Identify the Joints • •

Four pin joints are used to connect these different parts These joints are lettered A through D

• •

5.

The motion of the clamping jaw is desired. This is designated as “Point of Interest X” The motion of the end of the handle, is designated as Y

Draw the Kinematic Diagram 2

3


4. Identify Any Points of Interest

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Example 1.3 (cont.) 6. Calculate Mobility Gruebler’s Equation

where (links = 4, pin joints = 4) n= 4, jp = 4, jh = 0 M = 3(n-1) – 2jp – jh =3(4-1)-2(4)-0 =1 ….the clamp mechanism is constrained


M = 3(n-1) – 2jp – jh

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Figure 1

Figure 2

A folding chair that is commonly used in stadiums is shown in figure 1 above. A sketch of a lift platform is shown in figure 2. For both figures: i. Specify the number of links and the number of joints and; ii. Calculate the mobility for the mechanism.


Now You Try!

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Special Cases of Mobility Equation

a) Three rotating links

b) Two rotating and one sliding link

Solution: The joint will be considered as two joints instead of one. Therefore, (Fig. b) becomes one slider and one pin joint.


Case 1: Coincident joints – i.e. three links connected at a common pin joint (by definition, a pin joint connects two links)

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Special Cases of Mobility Equation (cont.) Case 2:

Exception to Gruebler’s equation

M = 3( n-1 ) – 2jp – jh =3( 5-1 ) – 2(6) =12-12 = 0 (mechanism is locked??)

According to Gruebler’s equation, this linkage should have zero DOF. However, this mechanism are capable of motion with 1 DOF.

Problem!! The Gruebler equation does not account for link geometry.


Links = 5, Pin = 6

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FOUR BAR LINKAGE

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The Four – Bar Mechanism


• The simplest and most common linkage is the four-bar mechanism. • It is a combination of four links, one as a frame, and connected by four pin joints.

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The four-bar mechanism (cont.) • The mobility of a four-bar mechanism is as below:

and M = 3(n - 1) – 2 jp – jh = 3(4 - 1) – 2(4) – 0 =1


n = 4, jp = 4 pins, jh = 0

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The Grashof’s criterion • Used to determine the category of the four bar mechanism

• The following nomenclature is used to describe the length of the four links. Let

S =length of the shortest link L =length of the longest link

P =length of one of the intermediate links Q =length of the other intermediate links


• Used to predict the rotation behavior of a four-bar linkage’s inversion based only on the link lengths

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The Grashof’s criterion Grashof’s theorem states that a four-bar mechanism has at least one revolving link if

S = length of the shortest link L = length of the longest link P = length of one of the intermediate links Q = length of the other intermediate links


S+L  P+Q

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Categories of Four-Bar Mechanism • All four-bar mechanism fall into 5 category:

Criteria

Shortest link

S+L < P+Q

Frame

Double crank

Side

Crankrocker

S+L < P+Q

S+L = P+Q S+L > P+Q

Coupler

Any

Any

Grashof double rocker

(b) Crank - Rocker (a) Double Crank

(c) Double Rocker

Change point Triplerocker


S+L < P+Q

Category

(d) Change Point

(e) Triple Rocker

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Crank – Rocker Mechanism

- Its one type of four bar mechanism

Coupler coupler

follower (or rocker)

Rocker (Follower)

crank Crank

ground

Ground • Crank (input link) • A link that makes a complete revolution and is pivoted to ground. • Rocker (output link) • A link that has oscillatory (back and forth) rotation and is pivoted to ground.

• Coupler (connecting rod) • A link that has complex motion (non moving) with respect to the reference frame. • Ground

• Any link that are fixed (non moving) with respect to the reference frame.


shorter side link revolves and the other one rocks

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Example Problem 1.9

80 cm

66 cm


A nose wheel assembly for a small aircraft is shown below. Classify the motion of this four bar mechanism based on the configuration of the links.

76 cm 40 cm

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Example Problem 1.9 (cont.)

1. Distinguish the Links Based on Length • • • •

The motion of the wheel assembly would be determined relative to the body of the aircraft The aircraft body will be designated as the frame The tip of the wheel was designated as point of interest X The lengths of the link are: S = 30cm, L= 80cm, P = 76cm, Q = 66cm


Solution:

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Example Problem 1.9 (cont.)

3.

Compare to Criteria • The shortest link is a side to the frame Check the Crank-Rocker Criteria S+L< P+Q (30 + 80) < (76+66) 110 < 142 … True!  It’s a Crank – Rocker Mechanism

Kinematic Diagram


2.

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Slider – Crank Mechanism

connecting rod crank slider


• This is a four-bar linkage with 3 revolute joints and one sliding joint. • This mechanism converts rotary motion into reciprocating linear motion, or vice versa.

ground

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Slider – Crank Mechanism Example


• Example: manual water pump

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Discussion

Discuss with your friends and give examples of these two types of mechanism.


What’s the difference between four – bar mechanism and slider – crank mechanism??

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• Traditional Drafting Techniques • The equipment used included triangles, parallel straight edges, compasses, protectors etc. • CAD Systems • AutoCAD, Microstation, Unigraphics and ProEngineer • Analytical Techniques • Mathematical functions, geometry, trigonometry and graphical mechanism analysis • Computer Methods


Techniques of Mechanism Analysis

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EXTRA EXERCISE

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W2 Mobility Four Bar Slider Crank Mechanism 20140724

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