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MAE 342 – Dynamics of Machines

Types of Mechanisms

Classification of Mechanisms by type and mobility

MAE 342 – Dynamics of Machines 2

Planar, Spherical and Spatial Mechanisms

• Planar Mechanisms: all points on each

part move only in .

Images from Tiptop Industry Co., Ltd.Image from Northern Tool + Equipment Catalog Co.

Image from Technische Universität Ilmenau.

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MAE 342 – Dynamics of Machines 3

Planar, Spherical and Spatial Mechanisms

• Spherical Mechanisms: all points on each

part move only in .

Images from the Laboratory for the Analysis and Synthesis of Spatial Movement.

Images from Laboratoire de robotique, Université Laval.

Image from Maarten Steurbaut.

MAE 342 – Dynamics of Machines 4

Planar, Spherical and Spatial Mechanisms

• Spatial Mechanisms: points on each part can move in any direction in 3-dimensional space.

Image from the Kinematic Models for Design Digital Library, Cornell University.

Image from the Special Session on Computer Aided Linkage Synthesis, ASME DETC 2002.

Image from www.robots.com.Image from Slika

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MAE 342 – Dynamics of Machines 5

Mobility

• Degrees of freedom (DOF) is:the number of independent controls needed to position a body. Mathematically it is the number of independent variables needed to specify the position of a body.

� A planar body has ___ DOF.

� A spherical body has ___ DOF.

� A spatial body has ___ DOF.

MAE 342 – Dynamics of Machines 6

Mobility

• Mobility is:the number of degrees of freedom of a mechanism.

� If the number of planar bodies is n (and there are no joints) the mobility is ______ .

� If one of the bodies is fixed, the mobility is ________ .

� If the number of spatial bodies is n (and there are no joints) the mobility is ______ .

� If one of the bodies is fixed, the mobility is ________ .

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MAE 342 – Dynamics of Machines 7

Mobility• Each type of joint imposes a certain number

constraints (i.e., takes away a certain number of DOF

from mechanism):

Type of Joint DOFPlanar Mechanism

DOF removedvariables

Revolute

Prismatic

Cam

Gear

MAE 342 – Dynamics of Machines 8

Mobility

Figure from Unigraphics on-line documentation.

Figure from Uicker et al., Theory of Machines and Mechanisms

a) Revolute joint (R) – Circular motion

b) Prismatic joint (P) – Rectilinear motion

c) Screw joint (S) – Helical motion

d) Cylindrical joint (C) – Cylindrical motion

e) Spherical joint (G) – Spherical motion

f) Flat joint (F) – Planar motion

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MAE 342 – Dynamics of Machines 9

Mobility

Type of Joint DOFSpatial Mechanism

DOF removedvariables

Revolute

Prismatic

Screw

Cylinderical

Spherical

Flat/Planar

MAE 342 – Dynamics of Machines 10

Mobility• “Kutzbach Criteria” for mobility (m) of:

� planar mechanisms:

m = � spatial mechanisms:

m = � where:

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MAE 342 – Dynamics of Machines 11

Mobility• In Kutzbach criteria

a) If m > 0

b) If m = 0

c) if m < 0

MAE 342 – Dynamics of Machines 12

Mobility• What is the mobility in these examples?

a)

b)

c)

d)

Figures from Uicker et al., Theory of Machines and Mechanisms, 2003

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MAE 342 – Dynamics of Machines 13

Mobility• What is the mobility in these examples?

a)

b)

c)

d)

Figures from Uicker et al., Theory of Machines and Mechanisms, 2003

MAE 342 – Dynamics of Machines 14

Mobility• Exceptions to the rule!

� Certain geometric conditions

� Different parts of a linkage can have different mobilities.

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MAE 342 – Dynamics of Machines 15

Torfason’s Classification of Mechanisms• Snap-Action Mechanisms• Linear Actuators• Fine Adjustments• Clamping Mechanisms• Locational Devices• Ratchets and Escapements• Indexing Mechanisms• Swinging or Rocking Mechanisms• Reciprocating Mechanisms• Reversing Mechanisms• Couplings and Connectors• Stop, Pause, and Hesitation Mechanisms• Curve Generators• Straight-Line Generators• …

MAE 342 – Dynamics of Machines 16

Kinematic Inversion

• You can pick different links to be the fixed link – this is “kinematic inversion”

Figures from Uicker et al., Theory of Machines and Mechanisms, 2003

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MAE 342 – Dynamics of Machines 17

Grashof’s Law• In a four bar linkage, if you want to be able

to sit on one link and have some other link rotate 360° relative to you, then:

� where:s is the length of:

l is the length of:

p, q are the lengths of:

MAE 342 – Dynamics of Machines 18

Grashof’s Law

Figures from Uicker et al., Theory of Machines and Mechanisms, 2003