Chapter 02-theory of machines

8/13/2019 Chapter 02-theory of machines

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Chapter 2: KinematicFundamentals

Chapter Outcomes

After covering this chapter, you should beable to: Identify mechanisms and predict their

motion Calculate the degrees of freedom of

mechanisms

2.1: Degrees of Freedom (DoF)

DoF: Number of independent parametersneeded to completely define a systemsposition in space

Marker in 3-D space example (whiteboard) Marker in 2-D space example (whiteboard) Course coverage will be limited to

2-D/planar systems

2.2: Types of Motion

Pure rotation: Object changes angularorientation about fixed axis (whiteboard)

Pure translation: Object changes positionwithout changing angular orientation(whiteboard)

Complex motion = rotation + translation(whiteboard)


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2.3(A): Links Reminder: A mechanism is a collection of links

connected by joints arranged to transmit a specific type

of motion Link: Rigid body which possesses at least 2 nodes

(nodes = points for attachment to other links) Links are classified according to # of nodes

2.3(A): Links

Simplified drawings of links (whiteboard)

Students must be able to identify anddifferentiate types of links

Links do not necessarily need to take theirobvious shapes (links are classifiedaccording to # of nodes, NOT theirshapes)

Example (whiteboard)

2.3(B): Joints

Joint: Connection between 2 or more links(at their nodes) which allows somemotion

Can be classified in several ways. We willfocus on 2: by the DoF allowed at the joint by the number of links joined (order of the

joint)

DoF Classification

Pure roll: 1Pure slide: 1Roll & slide: 2

Rollingcylinder

2 (why?)Pin in slot

2 (why?)Link againstplane

1 (why?)Slider /Translational

1 (why?)Pin /

Rotational

SimplifiedDiagram

DoFDiagramName

Link

LinkJoint

Joint (surface)

Link

Link


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Order Classification

Order = (# of links joined) - 1

2 joints, each

with 1 DoF(whiteboard)

2Multiple

joint

11Single joint

DoFOrder DiagramName

2.3(C): Kinematic Chains

Kinematic chain: An assembly of links and

joints Mechanism: A kinematic chain with at

least one link grounded Example (whiteboard)

2.4: DoF of Planar Mechanisms

Number of inputs needed to fully defineposition of mechanism

Kutzbachs / Modified Grueblers equation:M = 3( L 1) 2 J 1 J 2where: M = DoF

L = # of linksJ 1 = # of 1 DoF jointsJ 2 = # of 2 DoF joints

Example (transparency) Reminder (whiteboard)

2.5: Mechanisms and Structures

If DoF > 0, its a mechanism If DoF = 0, its a structure If DoF < 0. its a preloaded structure (will have

built in stresses with manufacturing error)


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More on DoF Definitions

For a body in free space , it is: The number of independent parameters

needed to completely define a systemsposition in space

For a mechanism , it is: The number of inputs needed to fully define

position of mechanism Are they the same? So what is an input ?

NO!!!

Input Input = Source of Motion The device that introduces/produces motion for

a mechanism Rotary Input Usually provided by a motor

Linear Input Usually provided by a linear

actuator

Simply a piston in a cylindermoved by pneumatic orhydraulic pressure

Computer simulation onnumber of Inputs

Linear Actuator

Piston

Cylinder

SlidingJoint

2.11: Inversion

Act of grounding a different link in akinematic chain

Usually produces different motions fromthe mechanism

Example (computer simulation)

2.12: The Grashof Condition Fourbar link naming conventions:

Ground: Link fixed to the ground Crank: Link which makes a complete revolution Rocker: Link which has oscillatory motion (rocks back

and forth) Coupler: Link connecting input and output links

Ground

Crank

Coupler

Rocker


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2.12: The Grashof Condition Grashof condition: Condition used to predict rotational

behavior/motion of fourbar linkage based on link lengths

Linkage is Grashof if S + L P + Q (whiteboard)where S : length of shortest link

L: length of longest linkP : length of intermediate linkQ : length of another intermediate link

Else linkage is non-Grashof Grashof linkage: At least one link will be able to make a

full revolution Non-Grashof linkage: No link will be able to make a full

revolution

Grashof Classification(Transparency + Computer Simulation) Class 1: S + L < P + Q

Either link attached to the shortest isgrounded Crank-Rocker Shortest link is grounded Double-Crank Link opposite the shortest is grounded

Double Rocker Class 2: S + L > P + Q (non-Grashof)

Tripler Rocker Class 3: S + L = P + Q (special case)

Will have change points when all linksbecome collinear

Output behavior at these points indeterminate

Link Assembly

In order for the four links to be assembledL < (S + P + Q )

If L = S + P + Q , the links can beassembled but will not move (whiteboard)

Course OutcomesIdentify mechanisms and predict their motionCalculate the degrees of freedom of mechanismsDesign mechanisms to fulfill motion generation and quick

return requirementsDetermine the positions, velocities and accelerations of linksand points on mechanismsDerive SVAJ functions to fulfill cam design specificationsCalculate dynamic joint forces of mechanismsBalance simple rotating objects and pin-jointed fourbar linkagesWork in a team to analyze and modify existing mechanisms

Present completed work in oral and written formUse related computer programs to design, model and analyzemechanisms


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End of Chapter 2

Please bring geometrical set +

tracing paper during tutorialsession next week. Thank you.

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Chapter 02-theory of machines