Crank And Slotted Lever Mechanism Engineering Essay

In a kinematic chain when one link is fixed, then that chain is known as mechanism. It may be used for transmitting or transforming motion for example engine indicators, typewriters etc.[1]

A mechanism which has four links is known as simple mechanism, and a mechanism which has more than four links is known as complex mechanism. A mechanism which is required to transmit some particular type of work is knows as machines. In certain cased the elements have to be designed to withstand the forces safely.

A mechanism is a kinematic chain in which kinematic pairs are connected in such a way that first link is joined to the last link to transmit a predetermined constrained motion

The various parts of the mechanism are called as links or elements. When two links are in contact and a relative motion is possible, then they are known as a pair. An arbitrary set of a link which forms a closed chain which is capable of relative motion and that can be made into a rigid structure by adding a single link is known as kinematics chain. To form a mechanism from a kinematics chain one of the link must be fixed. The technique obtaining different mechanism by fixing the various link in turn is knows as inversion. [2]

Fig 1.1-Chart illustrating kinematic pair makes up a machine

CHAPTER 2

KINEMATIC PAIRS

Two links that can move with respect to each other by a mechanical constraint between them, with one or more degrees of freedom

The relative motion between two links of a pair can take different form. Three types of pair are identified as lower pairs and these are the commonly occurring ones.

Sliding: Such as occurs between a piston and a cylinder

Turning: Such occurs with a wheel on an axle

Screw Motion: Such as occurs between a nut and a bolt

All other cases are considered to be combination of sliding and rolling is called higher pairs. Screw pair is higher pair as it combines turning and sliding.

2.1 Classification of Kinematic Pairs

Since kinematics pairs deals with relative motion between two links then can be classifies based on the characteristics of relative motion between two bodies.

The type of relative motion between the elements

The type of contact between the elements

The type of closure[1]

The type of relative motion between the elements

The kinematic pair according to type of relative motion can classified as below

Sliding Pair

Turning Pair

Rolling Pair

Screw Pair

Spherical Pair

2.1.2 The type of contact between the elements

The kinematic pair according to type of contact between the elements can be classified

Lower Pair

Higher Pair

2.1.3 The type of closure

The kinematic pair according to type of closure between the elements can be classified as

Self -Closed Pair

Force -Closed Pair

2.2 GRUBLERS CRITERION FOR PLANAR MECHANISM

The Grubler’s criterion applies to mechanism with only single degree of freedom joints where the overall movability of the mechanism is unity.Subtituting n=1 and h=0 in kutzbach equation we have [3]

F= 3 (n-1) – 2j – h

The equation is known as Grubler’s criterion for plane mechanisms with constrained motion.

2j-3n+h+4=0

Where, F=number of degrees of freedom of a chain

j= number of lower kinematic pairs

h = number of higher kinematic pairs

n= number of links

When F=1, the linkage is called a mechanism.

When F=0 it forms a structure. That is an application of external force does not produce relative motion between any links of a linkage

When F>1 the linkage will require more than one external driving force 2 obtain constrained motion

When F<1 there is one redundant member and that the chain is statically indeterminate structure

2.3 KINEMATIC CHAIN

A Kinematic Chain is defined as a closed network of links, connected by kinematic pairs so that the motion is constrained.

First a network of links to give constrained motion, certain conditions are to be satisfied. Minimum number of three links is required to form a closed chain .The three links are connected with turning pairs.

Fig.2.1 (a) A Five-Link Kinematic Chain (b) Six-Link Kinematic Mechanism

2.3.1 Types of kinematic chains

The most important kinematic chains are those which consists of four lower pairs, each pair being a sliding pair or a turning pair

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Four Bar Chain or Quadric Cyclic Chain

Single Slider Crank chain

Double slider crank chain

2.3.2 Inversions

Inversion is a method of obtaining different mechanisms by fixing different links in a kinematic chain. A particular inversion of a mechanism may give rise to different mechanism of practical unity, when the proportions of the link are changed [2].

CHAPTER 3

SLOTTED LINK QUICK RETURN MECHANISM

Slotted link mechanism which is commonly used in shaper mechanism. The mechanism which converts rotary motion of electric motor and gear box into the reciprocating motion of ram which is the most simple and compact machine.[3]

Fig 3.1 : Slotted link mechanism

The slotted link mechanism which is mainly divided into seven main parts .They are

A – Clamping nut

B – Ram

C – Link D

D – Crankpin A

E – Slotted crank B

F – Bull Wheel

G – Glot

Slotted link mechanism gives ram the higher velocity during the return stroke (i.e. Non cutting stroke) .Then the forward stroke which reduces the wasting during the return stroke. [4]

When the bull wheel is rotated the crank pin A is also rotated side by side through the slot the crank B. This makes the slotted crank B.This makes the slotted crank to oscillate about one end C.The oscillation motion of slotted crank makes ram to reciprocate. The intermediate D is required to accommodate the rise and fall of the crank.

Crank Pin A decides the length of the strokes of the shaper. The further it’s away from the center of the bull wheel longer is its stroke.

The cutting stroke of the ram is complete while crank pin moves from A to A1 and slotted link goes from left to right.

During return stroke pin moves from A1 to A and link moves from right to left

Cutting Time/Idle Time = Angle of AZA1/ Angles of AZA2

3.1 SHAPER MECHANISM

The working of a shaper mechanism is that it has two stokes. One is forward stroke and the other is return stroke. Clearing up more about these two strokes is that in the forward stroke the material is feeded, where as in the return stroke is an idle stroke when no material is feeded.[6]

Fig 3.2 : Shaper Mechanism

Shaping process which involves only short setup time and uses only inexpensive tools. Shaping is used for the production of gears ,splined shafts racks etc. it can produce one or two such parts in a shaper less time that is required to setup for production. Other alternatively equipment with a higher output rate is required. [5]

The cost per cubic cm of metal removal by shaping may be as five times more than that of the removal by milling or broaching. Shaping machines are mainly used in tool rooms or model shops.

3.2 SHAPER CUTTING SPEED

The cutting speed depends on

The type of material used.

The amount of material removed.

The kinds of tool material.

The rigidity of machine.

3.4 DIFFERENCE BETWEEN WHITHWORTH AS WELL AS QUICK RETURN MECHANISM

Maximum pressure is holding the ram down the slides so that steadying is most necessary on entering the cut

In Whitworth motion, the main pressure is in the correct place, less pressure is required in center of stroke.

Slotted link motion is opposite to all the points explained above.

Not withstanding the recompense stated above for the Whitworth motion, constructional difficulty make it more suitable for traversing head shaping machines and slotting machines, so that the crank motion, despite its restrictions finds universal adaptation for the pillar style of shaping machines.[6]

CHAPTER 4

DESIGN OF CRANK AND SLOTTED LEVER MECHANISM

Design and fabrication of crank and slotted lever mechanism and also doing the structural and thermal analysis of crank shaft. Drawing the velocity diagram of the mechanism.

Fig 4.1 : Dimensions for the components using AutoCAD

DESIGNING USING CATIA

The design of different components is explained here using Catia.

SLOTTED LEVER

Slotted lever connected to the crank shaft which provides the forward and backward motion of the tool post. The drawing is done as per the dimensions shown above. Different view of the slotted lever is also explained

Fig 4.2: Design of slotted lever

FIG4.3: Different angle view of slotted lever

CRANK SHAFT

Crank shaft which is connected to flywheel with the help of a motor , which provides the rotation of the crank shaft as well as the rotation of the slotted lever connected to it. The drawing is done as per the dimensions shown above. Different view of the crank shaft is also explained

Fig 4.4: DESIGN of crank shaft

Fig 4.5: Different angle view of crank shaft

TOOL POST

Tool post which is connected to slotted lever, where the tool is connected to it which is used for the cutting of materials. The drawing is done as per the dimensions shown above. Different view of the Tool post is also explained

Fig 4.6: Design of tool post

Fig 4.7: Different angle view of tool post

TOOL CUTTER

Tool cutter is connected to the tool which is used to cut the material. The design is done as per assumed dimensions. Different view of the Tool is also explained.

Fig 4.8: Design of tool

Fig 4.9: Different angle view of tool

5.2 FABRICATION OF CRANK AND SLOTTED LEVER

With the help of above design of different components it has been combined together to form a crank and slotted lever mechanism which is seen mainly in shaper machines.

Fig4.10: Design of crank and slotted lever mechanism

The final fabrication model will be represented as shown below.

Fig4.11: Final Design of crank and slotted lever mechanism

4.3 MODEL FABRICATION

To conclude my Assigned project I hereby affix few photos of crank and slotted quick return mechanism indicating the functioning the same.

Fig 4.12: FABRICATED MODEL OF CRANK AND SLOTTED LEVER

Fig 4.13: SLOTTED LEVER CONNECTED TO THE LEVER

CHAPTER 5

STRUCTURAL AND THERMAL ANALYSIS OF CRANK SHAFT

Crank and slotted lever mechanism, crank shaft which acts as the rotating device which helps the slotted lever forward and backward movement. Therefore analyzing the different propertied which take place in a crank shaft

5.1 STRUCTURAL ANALYSIS

Fig 5.1: Crank shaft used for analysis

Units

TABLE 1

Unit System

Metric (m, kg, N, s, V, A) Degrees rad/s Celsius

Angle

Degrees

Rotational Velocity

rad/s

Temperature

Celsius

Model (C4)

Geometry

TABLE 2

Model (C4) > Geometry

Object Name

Geometry

State

Fully Defined

Definition

Source

C:UsersPATRICKDesktopPAPArollcageSUDEEPPart1.CATPart

Type

Catia5

Length Unit

Millimeters

Element Control

Program Controlled

Display Style

Part Color

Bounding Box

Length X

2.e-002 m

Length Y

0.20055 m

Length Z

0.19999 m

Properties

Volume

6.2904e-004 m³

Mass

4.938 kg

Scale Factor Value

1.

Statistics

Bodies

1

Active Bodies

1

Nodes

3258

Elements

556

Mesh Metric

None

Preferences

Import Solid Bodies

Yes

Import Surface Bodies

Yes

Import Line Bodies

No

Parameter Processing

Yes

Personal Parameter Key

DS

CAD Attribute Transfer

No

Named Selection Processing

No

Material Properties Transfer

No

CAD Associatively

Yes

Import Coordinate Systems

No

Reader Save Part File

No

Import Using Instances

Yes

Do Smart Update

No

Attach File Via Temp File

Yes

Temporary Directory

C:UsersPATRICKAppDataLocalTemp

Analysis Type

3-D

Mixed Import Resolution

None

Enclosure and Symmetry Processing

Yes

TABLE 3

Model (C4) > Geometry > Parts

Object Name

Part 1

State

Meshed

Graphics Properties

Visible

Yes

Transparency

1

Definition

Suppressed

No

Stiffness Behavior

Flexible

Coordinate System

Default Coordinate System

Reference Temperature

By Environment

Material

Assignment

Structural Steel

Nonlinear Effects

Yes

Thermal Strain Effects

Yes

Bounding Box

Length X

2.e-002 m

Length Y

0.20055 m

Length Z

0.19999 m

Properties

Volume

6.2904e-004 m³

Mass

4.938 kg

Centroid X

1.e-002 m

Centroid Y

-1.9072e-004 m

Centroid Z

-1.9565e-004 m

Moment of Inertia Ip1

2.4661e-002 kg·m²

Moment of Inertia Ip2

1.2451e-002 kg·m²

Moment of Inertia Ip3

1.2537e-002 kg·m²

Statistics

Nodes

3258

Elements

556

Mesh Metric

None

Coordinate Systems

TABLE 4

Model (C4) > Coordinate Systems > Coordinate System

Object Name

Global Coordinate System

State

Fully Defined

Definition

Type

Cartesian

Ansys System Number

0.

Origin

Origin X

0. m

Origin Y

0. m

Origin Z

0. m

Directional Vectors

X Axis Data

[ 1. 0. 0. ]

Y Axis Data

[ 0. 1. 0. ]

Z Axis Data

[ 0. 0. 1. ]

Mesh

TABLE 5

Model (C4) > Mesh

Object Name

Mesh

State

Solved

Defaults

Physics Preference

Mechanical

Relevance

0

Sizing

Use Advanced Size Function

Off

Relevance Center

Coarse

Element Size

Default

Initial Size Seed

Active Assembly

Smoothing

Medium

Transition

Fast

Span Angle Center

Coarse

Minimum Edge Length

2.e-002 m

Inflation

Use Automatic Tet Inflation

None

Inflation Option

Smooth Transition

Transition Ratio

0.272

Maximum Layers

5

Growth Rate

1.2

Inflation Algorithm

Pre

View Advanced Options

No

Advanced

Shape Checking

Standard Mechanical

Element Midside Nodes

Program Controlled

Straight Sided Elements

No

Number of Retries

Default (4)

Rigid Body Behavior

Dimensionally Reduced

Mesh Morphing

Disabled

Pinch

Pinch Tolerance

Please Define

Generate on Refresh

No

Statistics

Nodes

3258

Elements

556

Mesh Metric

None

Static Structural (C5)

TABLE 6

Model (C4) > Analysis

Object Name

Static Structural (C5)

State

Solved

Definition

Physics Type

Structural

Analysis Type

Static Structural

Solver Target

ANSYS Mechanical

Options

Environment Temperature

22. °C

Generate Input Only

No

TABLE 7

Model (C4) > Static Structural (C5) > Analysis Settings

Object Name

Analysis Settings

State

Fully Defined

Step Controls

Number Of Steps

1.

Current Step Number

1.

Step End Time

1. s

Auto Time Stepping

Program Controlled

Solver Controls

Solver Type

Program Controlled

Weak Springs

Program Controlled

Large Deflection

Off

Inertia Relief

Off

Nonlinear Controls

Force Convergence

Program Controlled

Moment Convergence

Program Controlled

Displacement Convergence

Program Controlled

Rotation Convergence

Program Controlled

Line Search

Program Controlled

Output Controls

Calculate Stress

Yes

Calculate Strain

Yes

Calculate Results At

All Time Points

Analysis Data Management

Solver Files Directory

F:ansyshallo_filesdp0SYS-1MECH

Future Analysis

None

Scratch Solver Files Directory

Save ANSYS db

No

Delete Unneeded Files

Yes

Nonlinear Solution

No

Solver Units

Active System

Solver Unit System

mks

TABLE 8

Model (C4) > Static Structural (C5) > Rotations

Object Name

Rotational Velocity

State

Fully Defined

Scope

Geometry

All Bodies

Definition

Define By

Vector

Magnitude

200. rad/s (ramped)

Axis

Defined

Suppressed

No

Fig 5.2 : Graph showing rotational velocity

TABLE 9

Model (C4) > Static Structural (C5) > Loads

Object Name

Frictionless Support

State

Fully Defined

Scope

Scoping Method

Geometry Selection

Geometry

1 Face

Definition

Type

Frictionless Support

Suppressed

No

Solution (C6)

TABLE 10

Model (C4) > Static Structural (C5) > Solution

Object Name

Solution (C6)

State

Solved

Adaptive Mesh Refinement

Max Refinement Loops

1.

Refinement Depth

2.

TABLE 11

Model (C4) > Static Structural (C5) > Solution (C6) > Solution Information

Object Name

Solution Information

State

Solved

Solution Information

Solution Output

Solver Output

Newton-Raphson Residuals

0

Update Interval

2.5 s

Display Points

All

TABLE 12

Model (C4) > Static Structural (C5) > Solution (C6) > Results

Object Name

Total Deformation

Minimum Principal Elastic Strain

Stress Intensity

Middle Principal Stress

Equivalent Stress

State

Solved

Scope

Scoping Method

Geometry Selection

Geometry

All Bodies

Definition

Type

Total Deformation

Minimum Principal Elastic Strain

Stress Intensity

Middle Principal Stress

Equivalent (von-Mises) Stress

By

Time

Display Time

Last

Calculate Time History

Yes

Identifier

Use Average

 

Yes

Results

Minimum

8.5255e-009 m

-8.1173e-006 m/m

5.3895e+005 Pa

-4.8689e+005 Pa

5.3642e+005 Pa

Maximum

7.9016e-007 m

-8.1177e-007 m/m

3.0171e+006 Pa

1.2909e+006 Pa

2.7325e+006 Pa

Information

Time

1. s

Load Step

1

Substep

1

Iteration Number

1

TABLE 13

Model (C4) > Static Structural (C5) > Solution (C6) > Results

Object Name

Shear Stress

Vector Principal Elastic Strain

Strain Energy

State

Solved

Scope

Scoping Method

Geometry Selection

Geometry

All Bodies

Definition

Type

Shear Stress

Vector Principal Elastic Strain

Strain Energy

Orientation

XY Plane

 

By

Time

Display Time

Last

Coordinate System

Global Coordinate System

 

Calculate Time History

Yes

Use Average

Yes

 

Identifier

Results

Minimum

-3.4345e+005 Pa

 

5.6327e-007 J

Maximum

3.4345e+005 Pa

 

1.1931e-005 J

Information

Time

1. s

Load Step

1

Substep

1

Iteration Number

1

Material Data

Structural Steel

TABLE 14

Structural Steel > Constants

Density

7850 kg m^-3

Coefficient of Thermal Expansion

1.2e-005 C^-1

Specific Heat

434 J kg^-1 C^-1

Thermal Conductivity

60.5 W m^-1 C^-1

Resistivity

1.7e-007 ohm m

TABLE 15

Structural Steel > Compressive Ultimate Strength

Compressive Ultimate Strength Pa

0

TABLE 16

Structural Steel > Compressive Yield Strength

Compressive Yield Strength Pa

2.5e+008

TABLE 17

Structural Steel > Tensile Yield Strength

Tensile Yield Strength Pa

2.5e+008

TABLE 18

Structural Steel > Tensile Ultimate Strength

Tensile Ultimate Strength Pa

4.6e+008

TABLE 19

Structural Steel > Alternating Stress

Alternating Stress Pa

Cycles

Mean Stress Pa

3.999e+009

10

0

2.827e+009

20

0

1.896e+009

50

0

1.413e+009

100

0

1.069e+009

200

0

4.41e+008

2000

0

2.62e+008

10000

0

2.14e+008

20000

0

1.38e+008

1.e+005

0

1.14e+008

2.e+005

0

8.62e+007

1.e+006

0

TABLE 20

Structural Steel > Strain-Life Parameters

Strength Coefficient Pa

Strength Exponent

Ductility Coefficient

Ductility Exponent

Cyclic Strength Coefficient Pa

Cyclic Strain Hardening Exponent

9.2e+008

-0.106

0.213

-0.47

1.e+009

0.2

TABLE 21

Structural Steel > Relative Permeability

Relative Permeability

10000

TABLE 22

Structural Steel > Isotropic Elasticity

Temperature C

Young’s Modulus Pa

Poisson’s Ratio

2.e+011

0.3

Fig 5.3 : Middle Principal Stress

Fig 5.3: Principal Stress

Fig 5.4: Strain Energy

Fig 5.5: Minimm Principal Elastic Strain

Fig 5.6: Stress Intensity

Fig 5.7: TOTAL Deformation

Fig 5.8: VECTOR Principal Elastic Strain

5.2 THERMAL ANALYSIS

Thermal Analysis is the heat developed in crank shaft.

Units

TABLE 1

Unit System

Metric (m, kg, N, s, V, A) Degrees rad/s Celsius

Angle

Degrees

Rotational Velocity

rad/s

Temperature

Celsius

Model (D4)

Geometry

TABLE 2

Model (D4) > Geometry

Object Name

Geometry

State

Fully Defined

Definition

Source

C:UsersPATRICKDesktopPAPArollcageSUDEEPPart1.CATPart

Type

Catia5

Length Unit

Millimeters

Element Control

Program Controlled

Display Style

Part Color

Bounding Box

Length X

2.e-002 m

Length Y

0.20055 m

Length Z

0.19999 m

Properties

Volume

6.2904e-004 m³

Mass

4.938 kg

Scale Factor Value

1.

Statistics

Bodies

1

Active Bodies

1

Nodes

3258

Elements

556

Mesh Metric

None

Preferences

Import Solid Bodies

Yes

Import Surface Bodies

Yes

Import Line Bodies

No

Parameter Processing

Yes

Personal Parameter Key

DS

CAD Attribute Transfer

No

Named Selection Processing

No

Material Properties Transfer

No

CAD Associativity

Yes

Import Coordinate Systems

No

Reader Save Part File

No

Import Using Instances

Yes

Do Smart Update

No

Attach File Via Temp File

Yes

Temporary Directory

C:UsersPATRICKAppDataLocalTemp

Analysis Type

3-D

Mixed Import Resolution

None

Enclosure and Symmetry Processing

Yes

TABLE 3

Model (D4) > Geometry > Parts

Object Name

Part 1

State

Meshed

Graphics Properties

Visible

Yes

Transparency

1

Definition

Suppressed

No

Stiffness Behavior

Flexible

Coordinate System

Default Coordinate System

Reference Temperature

By Environment

Material

Assignment

Structural Steel

Nonlinear Effects

Yes

Thermal Strain Effects

Yes

Bounding Box

Length X

2.e-002 m

Length Y

0.20055 m

Length Z

0.19999 m

Properties

Volume

6.2904e-004 m³

Mass

4.938 kg

Centroid X

1.e-002 m

Centroid Y

-1.9072e-004 m

Centroid Z

-1.9565e-004 m

Moment of Inertia Ip1

2.4661e-002 kg·m²

Moment of Inertia Ip2

1.2451e-002 kg·m²

Moment of Inertia Ip3

1.2537e-002 kg·m²

Statistics

Nodes

3258

Elements

556

Mesh Metric

None

Coordinate Systems

TABLE 4

Model (D4) > Coordinate Systems > Coordinate System

Object Name

Global Coordinate System

State

Fully Defined

Definition

Type

Cartesian

Ansys System Number

0.

Origin

Origin X

0. m

Origin Y

0. m

Origin Z

0. m

Directional Vectors

X Axis Data

[ 1. 0. 0. ]

Y Axis Data

[ 0. 1. 0. ]

Z Axis Data

[ 0. 0. 1. ]

Mesh

TABLE 5

Model (D4) > Mesh

Object Name

Mesh

State

Solved

Defaults

Physics Preference

Mechanical

Relevance

0

Sizing

Use Advanced Size Function

Off

Relevance Center

Coarse

Element Size

Default

Initial Size Seed

Active Assembly

Smoothing

Medium

Transition

Fast

Span Angle Center

Coarse

Minimum Edge Length

2.e-002 m

Inflation

Use Automatic Tet Inflation

None

Inflation Option

Smooth Transition

Transition Ratio

0.272

Maximum Layers

5

Growth Rate

1.2

Inflation Algorithm

Pre

View Advanced Options

No

Advanced

Shape Checking

Standard Mechanical

Element Midside Nodes

Program Controlled

Straight Sided Elements

No

Number of Retries

Default (4)

Rigid Body Behavior

Dimensionally Reduced

Mesh Morphing

Disabled

Pinch

Pinch Tolerance

Please Define

Generate on Refresh

No

Statistics

Nodes

3258

Elements

556

Mesh Metric

None

Steady-State Thermal (D5)

TABLE 6

Model (D4) > Analysis

Object Name

Steady-State Thermal (D5)

State

Solved

Definition

Physics Type

Thermal

Analysis Type

Steady-State

Solver Target

ANSYS Mechanical

Options

Generate Input Only

No

TABLE 7

Model (D4) > Steady-State Thermal (D5) > Initial C

 

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