Kinematics

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Kinematics
Kinematics - the study of relative motion
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Mechanisms

• Mechanism - a mechanical device that transfers or
  transforms motion or energy from an input source
  to an output
• Examples
• Linkages
• Gears
• Cams

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Kinematic Diagrams
Kinematic skeleton diagrams are used to easily
describe mechanism geometry.
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Kinematics Roadmap
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Four-bar Linkage
Four-bar Linkage - simplest close-loop mechanism
has four links and four joints.
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Slider-Crank Linkage
Slider-Crank Linkage - when a link of a four-bar
mechanism is replaced with a slider.

• Examples
• Piston, connecting rod, and crank shaft
• Can crusher

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Linkage Synthesis

• Analysis - analysis is determining motion of a
  mechanism with known geometry
• Synthesis - determining linkage geometry to
  perform a specified task

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Relative Motion

• Relative motion - motion of one point with
  respect to another point.
• Absolute motion - motion of a point with respect
  to ground (the fixed link)
• Reference frames
• Examples
• You
• Coupler curves

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Types of Motion

• Pure Rotation one point is fixed with respect to
  the reference frame
• Pure Translation all points on a body have
  parallel paths
• Complex Motion both rotation translation

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Degrees of Freedom

• Degrees of Freedom (DOF) - the number of
  independent inputs required to define the
  position of all links of a mechanism

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Link Types
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Joint Types
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Kinematic Pairs

• Lower Pairs - joints that allow one degree of
  freedom of relative motion. Pin (revolute)
  joints, sliders (prismatic joints), and screws
  are examples.

• Higher Pairs - allow two degrees of freedom of
  relative motion between mating links. Cams are
  examples

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Degrees of Freedom Cont.
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Grueblers Equation

• Grueblers Equation

F 3(n-1) - 2f1 - f2
Where n number of links f1 number of lower
pairs f2 number of higher pairs
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Degrees of Freedom Examples
n f1 f2 F
n f1 f2 F
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Equivalent Mechanisms
n f1 f2 F
n f1 f2 F
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Degrees of Freedom Cont.
Different values of DOF mean different things. F
0 Structure F lt 0 Statically indeterminate
structure F ? 1 Mobility is allowed
n f1 F
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Exceptions

• Grueblers equation has some exceptions to watch
  for. These usually involve special geometry or
  redundant constraints.

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Six-bar Chains
Watt chain - the ternary links are connected
Stephenson chain - the ternary links are
separated by binary links
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Linkage Transformation
Transformation of a crank-rocker to a slider-crank
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Mechanism Inversions
Mechanism inversions are produced by making
another link the fixed link.
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Grashofs Law

• Grashofs Law - for at least one link to have
  full rotation

Where s - the length of the shortest link l -
the length of the longest link p and q - the
lengths of the other links
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Classifications
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Change-point Mechanisms

• If s l p q, the mechanism has a change
  point where all links are colinear. The mechanism
  may go into another configuration at the change
  point.