kinematics fundamentals
TRANSCRIPT
Kinematics
Fundamentals
Chapter 2
Definitions
• Mechanisms
– A device which transform motion to some
desirable pattern and typically develop
very low forces and transmits little power
• Machine
– Typically contains mechanism which are
design to provide significant forces and
transmit significant power
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Kinematics
Fundamentals
• Degree of Freedom (DOF)
– The system’s DOF equal to the number of
independent parameters(measurement)
which are needed to uniquely define its
position in space at any time
Kinematics
Fundamentals
• Types of Motion
–Pure translation
–Pure rotation
–Complex motion
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– A link is an rigid body which possesses at
least two nodes which are points for
attachment to other links
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– A joints (kinematic pairs) is a connection
between two or more links, which allows some
motion, or potential motion, between the
connected links
– Classification
• Type of contact between the elements, line, point,
or surface
• Number of DOF allowed at the joint
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Classification
• Type of physical closure of the joint
• Number of links joined
– Type of Contact
• Lower pair (full joints)
– Describe joints with surface contact
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Type of Contact
• Lower pair
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Type of Contact
• Higher pair
– Describe joints with point or line contact
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Number of DOF allowed Joint
• One DOF (full joint)
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Number of DOF allowed Joint
• Two DOF (half joint/roll-slide)
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Type of Physical Closure
• Form closed- closed by its geometry
• Force closed- closed by an external force
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Number of links joined
• Order of the joint: the number of links minus one
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Kinematic Chain
• An assemblage of links and joints, interconnected
in a way to provide a controlled output motion in
response to a supplied input motion
– Mechanism
• A kinematic chain in which at least one link has
been “grounded,” or attached, to the frame of
reference
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Machine
• A combination of resistant bodies arranged
to compel the mechanical forces of nature to
do work accompanied by determinate
motions
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Ground
• Any link or links that are fixed with respect to
the reference frame
– Crank
• A link which makes a complete revolution
and is pivoted to ground
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Rocker
• A link which has oscillatory (back and forth)
rotation and pivoted to ground
Kinematics
Fundamentals
• Links, Joints, and Kinematic Chains
– Coupler
• A link which has complex motion and is
pivoted to ground
Kinematics
Fundamentals
• Determining DOF
– DOF or Mobility
• The number of inputs which need to be
provided in order to create a predictable
output
• The number of independent coordinates
required to define its position
– Open or Closed
– Dyads
Kinematics
Fundamentals
• Determining DOF
– DOF in Planar Mechanisms
• Gruebler’s Equation
where
– M = degree of freedom or mobility
– L = number of links
– J = number of joints
– G = number of grounded links
GJLM 323
Kinematics
Fundamentals
• Determining DOF
– DOF in Planar Mechanisms
• Gruebler’s Equation
• If more than one link is grounded, the net
effect will be to create one larger, higher-
order ground link. G is always one, therefore
GJLM 323
JLM 213
Kinematics
Fundamentals
• Determining DOF
– DOF in Planar Mechanisms
• Kutzbach Equation
– Include full and half joints
where
– M = degree of freedom or mobility
– L = number of links
– J1 = number of 1 DOF (full) joints
– J2 = number of 2 DOF (half) joints
21213 JJLM
Kinematics
Fundamentals
Kinematics
Fundamentals
Kinematics
Fundamentals
• Mechanisms and Structures
– The DOF of an assembly of links
completely predicts its character
• If the DOF is positive→ mechanism
• If the DOF is zero→ structure
• If the DOF is negative → preloaded structure
Kinematics
Fundamentals
• Number Synthesis
– The determination of the number and
order of links and joints necessary to
produce motion of a particular DOF
Kinematics
Fundamentals
• Paradoxes
Kinematics
Fundamentals
• Isomers
Kinematics
Fundamentals
• Linkage Transformation– Revolute joints in any loop can be replaced by
prismatic joints with no change in DOF of the
mechanism, provided that at least two revolute
joints remain in the loop
Kinematics
Fundamentals
• Linkage Transformation
– Any full joint can be replaced by a half
joint, but this will increase the DOF by
one
– Removal of a link will reduce the DOF by
one
– The combination of rules 2 and 3 above
will keep the original DOF unchanged
Kinematics
Fundamentals
• Linkage Transformation
Kinematics
Fundamentals
• Linkage Transformation– Any ternary or higher–order link can be partially
shrunk to a lower–order link by coalescing
nodes. This will create a multiple but will not
change the DOF at the mechanism
Kinematics
Fundamentals
• Linkage Transformation– Complete shrinkage of a higher-order link is
equivalent to its removal. A multiple joint will be
created, and the DOF will be reduced
Kinematics
Fundamentals
• Intermittent Motion– Is a sequence of
motions and dwells
• Dwell; is a period in which
the output link remains
stationary while the input
link continues to move
• Geneva Mechanism
Kinematics
Fundamentals
• Inversion
– An inversion is created by grounding a
different link in the kinematic chain
Kinematics
Fundamentals
Kinematics
Fundamentals
• Grashof Condition
– Is a simple relationship that predicts the
rotation behavior or rotatability of a four
linkage’s inversion based only on the link
lengths
• S = length of shorter link
• L=length of longest link
• P=length of one remaining link
• Q=length of the other remaining link
QPLS
Kinematics
Fundamentals
• Grashof Condition
– If the inequality is true, at least one link
will be capable of making a full revolution
with respect to the ground plane(Class I)
– If not true, then the linkage is non-Grashof
and no link will be capable of a complete
revolution relative to any other link (Class
II)
QPLS
Kinematics
Fundamentals
• Grashof Condition
– For the class I case: S+L< P+Q
• Ground either adjacent to the shortest link and
you get a crank-rocker
• Ground the shortest link and you will get a
double-crank
• Ground the link opposite the shortest and you
will get a Grashof double-rocker
Kinematics
Fundamentals
• Grashof Condition
– For the Class II case: S+L> P+Q
• All inversion will be triple-rockers in which no
link can fully rotate
– For Class III: S+L=P+Q
• All inversion will be either double-cranks, or
crank-rocker
Kinematics
Fundamentals
Kinematics
Fundamentals
• Classification of the Four Linkage
– C. Barker developed a classification
scheme that allows prediction of the type
of motion that can be expected from a
fourbar linkage based on the values of its
link lengths
– Link ratio formation
– Letter designation (C), (R) - GCRR
Kinematics
Fundamentals
• Linkages of More Than Four Bars
– Geared Fivebar Linkages
Kinematics
Fundamentals
• Linkages of More Than Four Bars
– Sixbar Linkages
Kinematics
Fundamentals
• Spring as Links
• Compliant Mechanism
• Micro Electro-Mechanical Systems
(MEMS)
Kinematics
Fundamentals
– Problems
Kinematics
Fundamentals
– Problems
Kinematics
Fundamentals