ME 202 Mechanical Engineering for Civil Engineers

Kinematics of Simple Machines Asanga Ratnaweera

Dept of Mechanical Engineering

ME 201: Mechanics of Machines I

Kinematics of Simple Machines Asanga Ratnaweera

Dept of Mechanical Engineering

23 October 2006 Asanga Ratnaweera, Department of Mechanical Engineering

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Kinematics of Simple Machines

What is mechanics:

Mechanics

Static Dynamics

Kinematics Kinetics

23 October 2006 Asanga Ratnaweera, Department of Mechanical Engineering

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Kinematics of Simple Machines

What is Kinematics:Kinematics deals with the study of motion without the reference to the forces which cause or are developed by the motion.[Deals with the relative motion between the parts of the machine]

What is Kinetics:Kinetics deals with the forces that produce motion[deals with both motion and the forces]

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Kinematics of Simple MachinesWhat is a machine:

Machines are used to convert energy into different forms and transmit energy. Machines are composed of different types of mechanisms.

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Kinematics of Simple MachinesSimple mechanisms:

A mechanism is a mechanical device used to transfer motion, force and power from a source to an output.

Ex: cams, gears, and pulleys & belts, Linkages.

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Kinematics of Simple MachinesLink:

A rigid body having two or more pairing elements which connect to other bodies for the purpose of transmitting force or motion

Link

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Kinematics of Simple MachinesCommon types of links

Binary link: two nodesTernary link: thee nodes

quaternary link: four nodes

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Kinematics of Simple MachinesKinematic link

A resistant body or an assembly which goes to make a part of a machine connecting other parts which have motion relative to it.

Rigid link

Kinematic link

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Kinematics of Simple MachinesKinematic chain

A combination of links and pairs without a fixed link.

No element is fixed to the ground or frame

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Kinematics of Simple MachinesJoint

In general called a kinematic pair, providing the connection between links that permit constrained relative motion. There are two types of kinematic pairs: Lower pair, Higher pair.

Joints

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Kinematics of Simple MachinesLower pair

Have surface contact between the elemental surfaces.

Revolute (pin) joints prismatic joints

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Kinematics of Simple MachinesLower pair

Helical joints

Cylindrical joint

Universal joint

Spherical joint

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Kinematics of Simple MachinesHigher pair

Have line and point contact between the pairing elements.

CAM Follower Gears

Pin and slot

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Kinematics of Simple MachinesLinkages

Refer to kinematic chains joined by only lower pairs.

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Kinematics of Simple MachinesMechanism

A set of moving parts in a machine that performs a task. Mechanism consists of linkages and joints

Fixed

MechanismsNo fixed link: not a mechanismDoes not perform a task

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LinkagesSome examples

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LinkagesKinematic (skeleton) diagram

It is used to represent the essential skeleton (structure) of a mechanism, (similar to electrical circuit diagram).Basic symbols

Lines or simple shapes are used to represent links, which are labeled by numbers.Circles or blocks are used to represent joints, which are labeled by letters (capital).

The terms such as space diagram and configuration diagram are also used for kinemtaic diagram

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LinkagesKinematic (Skeleton) diagram

Skeleton diagram

A

B

C

1

2

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Fixed

FixedCrank

Connecting rod

Piston

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LinkagesKinematic (Skeleton) diagram

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LinkagesKinematic (Skeleton) diagram

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LinkagesKinematic (Skeleton) diagram

Stewart platform

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LinkagesDegree of Freedom (DOF)

Number of independent movements a rigid body has

In 2D plane

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LinkagesDegree of freedom

Revolute Joint1 DOF(2 DOF restricted)Slider Joint

1 DOF(2 DOF restricted)

Pin in slot2 DOF(1 DOF restricted)

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LinkagesDegree of Freedom (DOF) of a linkage

Gruebler’s Equation

212)1(3 PPnDOF −−−=

wheren : Total number of links (including a fixed or single ground link)P1 : Total number of lower pairsP2 : Total number of higher pairs

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LinkagesDegree of Freedom (DOF) of a linkage

Ex: three bar linkageB

CA

Ex: Four bar linkage

A

B

C

D

Ex: Five bar linkage

A

B

C

D

E

212)1(3 PPnDOF −−−=

n = 3P1 = 3P2 = 0DOF = 0

n = 4P1 = 4P2 = 0DOF = 1

n = 5P1 = 5P2 = 0DOF = 2

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Four bar mechanism

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Four bar linkagesSlider crank mechanism

Skeleton diagramA

B

C

1

2

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Fixed

FixedCrank

Connecting rod

PistonFrame

This is a four bar mechanism

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Four bar linkages

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Four bar linkages

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Four bar linkages

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Four bar linkagesLinkage geometry

Class I : Shortest member can complete a full revolution

Class II :No link can make a full revolution

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Four bar linkagesLinkage geometry

Class I: a – b < c – d

Class II: a – b > c – d

a

cd

b

dcba +>+

ba >dc >

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Kinematic Analysis of Mechanisms

Analytical methodsDifficult when the motion is complicated

Graphical MethodsMajor concern of this course

Computer methodsBeyond the scope