introduction to spatial kinematics
TRANSCRIPT
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Introduction to Spatial
Kinematics
Roger E. Kaufman
2002-2008
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Planar versus Spatial
Mechanisms A body has planar
motion if all of its
particles move in parallelplanes.
In a spatial mechanism,different particles may
move in paths whichdont all always remainin a plane.
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Planar versus Spatial
Mechanisms A body has spherical
motion if all of its particles
move on the surface ofconcentric spheres.
Notice that planar motion isthe limiting case of
spherical motion when theradius of the spheres goesto infinity!
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Planar versus Spatial
Mechanisms For instance, a four-bar linkage is a planar
mechanism, even though it is constructed
in three dimensions This car trunk link mechanism is a rather
elegant example of a planar linkagesystem:
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Planar versus Spatial
Mechanisms With a planar linkage such as
this, you can study the motionby making a two-dimensionalmodel, say out of cardboard.
You can project all the points ofthe different bodies onto one or
more reference planes parallelto the planes traced by theindividual particles.
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Planar versus Spatial
Mechanisms Viewed orthogonally from the side, the
parts of the four-bar linkage on the leftside of the car always are aligned withthose of the linkage on the right side.
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Planar versus Spatial
Mechanisms All the hinge axes are
perpendicular to a commonreference plane which is whythe mechanism remains planar.
The linkage on the right side ofthe car produces the same
motion of the particles as theone on the left, so from akinematics point of view it isredundant.
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Planar versus Spatial
Mechanisms Viewed orthogonally from the
side, the parts of the four-barlinkage on the left side of thecar always are aligned withthose of the linkage on the rightside.
It can be conceptuallycollapsed into a single planarour-bar linkage model.
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Planar versus Spatial
Mechanisms Of course, if this were my car, I would not
propose crushing it into a planar systemcompacted onto that single reference plane.
The added three-dimensional parts addstrength and structural stiffness to themechanism but they dont change the
kinematics. It is a lanar linka e!
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Spatial Mechanisms
Spatial linkages canbe synthesized for
problems such as Function generation
Path generation
Motion generation
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Some Spatial Mechanisms
Even though applications for general spatial
mechanisms are less common than for planar linkages
there are many useful spatial devices, such as folding
baby strollers and cribs.
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Some Spatial Mechanisms
Sometimes things that appear to be planar mechanisms
need to be designed for spatial motions to allow for
flexing in the parts.
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Some Spatial Mechanisms
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A Spherical Four-Bar
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Some Spatial Mechanisms
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Some Spatial Mechanisms
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Some Spatial Mechanisms
Some types of aircraft thrust reverserscome to mind as an important example:
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Some Spatial Mechanisms
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Some Spatial Mechanisms
Here is a shaker laboratory mixer based on a
spatial mechanism:
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Some Spatial Mechanisms
Wobble plate pumps, bent axis pumps, and
swash plate pumps use spatial mechanisms:
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Some Spatial Mechanisms
Simulators for pilot training or for vehicle driving
often use a spatial robot called a Stewart
Platform.
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Some Spatial Mechanisms
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Some Spatial Mechanisms
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Some Spatial Mechanisms
Here are some other useful spatial manipulator
platforms:
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Some Spatial Mechanisms
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Some Spatial Mechanisms
One of the most common spatial mechanisms is the
constant velocity coupling.
Professor Ken Hunt developed a generalized way of
designing all theoretically possible cv joints.
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Some Spatial Mechanisms
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Some Spatial Mechanisms
Here is a spatial mechanism called a Sarrus
Mechanism used in a virtual reality simulator for
close quarter combat training of marines:
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Some Spatial Mechanisms
A few more picts showing additional spatial
mechanisms on different versions of the marine
training simulator:
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Some Spatial Mechanisms
A few more pictures showing additional spatial
mechanisms on different versions of the marine
training simulator:
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Some Spatial Mechanisms
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Some Spatial Mechanisms
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Some Spatial Mechanisms
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A remote center compliance- A
motion generating mechanism(First invented by yours truly at M.I.T.)
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A remote center compliance- A
motion generating mechanism(From Draper Lab at M.I.T.)
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A remote center compliance- A
motion generating mechanism
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A remote center compliance- A
motion generating mechanism
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A remote center compliance- A
motion generating mechanism
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A remote center compliance- A
motion generating mechanism
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A remote center compliance- A
motion generating mechanism
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Helicopter swash plate
A function generating mechanism
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Helicopter swash platecollective linkage
A function generating mechanism
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Helicopter swash plate cycliclinkage
A function generating mechanism
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Helicopter swash plate cycliclinkage
A function generating mechanism