chapter 5 - mechanism

8/19/2019 Chapter 5 - Mechanism

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MECHANISM

Mohd Hadri Mohamed Nor


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Topic Learning Outcome

On completion this topic, you should be able to do the

following:

Describe a mechanism

Describe the inversion of mechanism

Define the velocity

Solve the velocity and acceleration point withinmechanism

Use mathematical and graphical method

Construct velocity and acceleration diagram.


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Introduction

When any one link of kinematics chain isfixed, it is called mechanism.

Primary function: transmit or modifymotion.

2 types of mechanism- simple mechanism

- compound mechanism, >4 links


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Example: Crank, connecting rod and pistonmechanism

Angular motion Linear motion

Input torque Force


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Inversion of Mechanism

It is the method of obtaining different

mechanisms by fixing different links of the

same Kinematics chain.

1. Inversion of four bar chain mechanism

2. Inversion of slider crank mechanism

3. Inversions of double slider crank chain


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Four Bar Chain Mechanism

Consist of four links AB, BC, CD, DA Grashof’s Law (if to be continuous relative motion between two links)

∑ shortest and longest link < ∑ remaining 2 links

AB – crank

CD – rocker/follower

BC – connecting rod

AD – frame of m/c


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Some of the inversion of four bar chainmechanism:

• Crank and follower mechanism – Oscillatory motion

• Pantograph – Instrument used to reproduce samemotion exactly in a reduced or enlarged scale.


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Slider Crank Mechanism

1st inversion – Slider crank

link 1 fixed, link 2 rotates, link 4 reciprocates


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2nd

inversion – Oscillating cylinderwhen link 2 rotates piston reciprocates in piston

cylinder cylinder reciprocates at hinge point C


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3rd

inversion – Crank and slotted lever mechanismlink 2 rotates slider O reciprocates link 4 rotate

block N move linearly


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4th

inversion – Hand pumplink 4 fixed link 2 and 3 can be rotate link 1 move

linearly


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Velocities in Mechanism – Relative Velocity Diagram

Velocity of any point on a link wrt t another point on thesame link is always perpendicular to the link joining these

points in the FBD.

Consider point A and B on a link (Fig a). Let velocity A isVA is known in magnitude and direction. Direction ofvelocity point B is VB. The magnitude of point B can be

found by draw the velocity diagram (Fig b)


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Step in drawing velocity diagram

A convenient point O was selected as the starting point.

From O , line Oa was drawn parallel and equal to magnitudeof V A to some suitable scale.

From ‘a’, a line perpendicular to AB represent velocity of Bwrt A. i.e V BA was drawn.

From ‘O ’ a line parallel to V B was drawn, meeting the V BA at‘b’.

Line ‘Ob ’ was measured to give the required velocity ofpoint B to scale.

The velocity of point C on AB link was determine using ratio

Line ‘Oc ’ was joined. The vector Oc now represent thevelocity of point C wrt O . i.e V

C Note that velocity diagram must be drawn according to suitable scale.


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Example 1


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Rubbing velocity at a Pin Joint

If r = radius at pin joint and ω1 and ω2 = angularvelocities of two links, then;

Angular velocities added if link rotates opposite direction

and subtract if rotate in same direction.


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Example 2

The crank and connecting rod of a theoretical

steam engine are 0.5m and 2.0 m respectively.

The crank makes 180rpm in the clockwisedirection. When it has turned 45° from the

inner dead centre position, determine:

a) Velocity of pistonsb) Angular velocity of connecting rod

c) Velocity of point E on the connecting rod 1.5mfrom the gudgeon pin.

d) Velocities of rubbing at all pins of the crankshaft,crank and cross-head, when the diameter of their

pins are 5cm, 6cm and 3cm respectively.


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Acceleration Diagram for a Link

Consider two point of A and B on rigid link. Let point B moves wrtA with velocity ω rad/s and α be the angular acceleration of linkAB. For an acceleration of a particle whose velocity changes withmagnitudes and directions at any instants has two components:

i. Radial or centripetal components which is parallel to AB

ii. Tangential component, which is perpendicular to AB


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Radial component of acceleration of B wrt A

Tangential component of acceleration of B wrt A


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Example 4


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chapter 5 - mechanism

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