Types of Mechanisms - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE342/Lecture_6...Types...
Transcript of Types of Mechanisms - West Virginia Universitycommunity.wvu.edu/~bpbettig/MAE342/Lecture_6...Types...
MAE 342 – Dynamics of Machines
Types of Mechanisms
Classification of Mechanisms by 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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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.
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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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Mobility
• Degrees of freedom (DOF) is:the number of independent controls needed to position a body. Mathematically it is the number of independent variables 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.
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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 ______ .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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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
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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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Mobility
Type of Joint DOFSpatial Mechanism
DOF removedvariables
Revolute
PrismaticPrismatic
Screw
Cylinderical
Spherical
Flat/Planar
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Mobility• “Kutzbach Criteria” for mobility (m) of:
� planar mechanisms:
m = � spatial mechanisms:
m = � where:
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Mobility• In Kutzbach criteria
a) If m > 0
b) If m = 0
c) if m < 0
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Mobility• What is the mobility in these examples?
a)
b)b)
c)
d)
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003
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Mobility• What is the mobility in these examples?
a)
b)b)
c)
d)
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003
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Mobility• Exceptions to the rule!
� Certain geometric conditions
� Different parts of a linkage can have different mobilities.
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Torfason’s Classification of Mechanisms• Snap-Action Mechanisms• Linear Actuators• Fine Adjustments• Clamping Mechanisms• Locational Devices• Ratchets and Escapements• 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• …
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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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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:
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Grashof’s Law
Figures from Uicker et al., Theory of Machines and Mechanisms, 2003