introduction to spatial kinematics

8/3/2019 Introduction to Spatial Kinematics

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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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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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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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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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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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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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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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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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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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A Spherical Four-Bar


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Some types of aircraft thrust reverserscome to mind as an important example:


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Here is a shaker laboratory mixer based on a

spatial mechanism:


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Wobble plate pumps, bent axis pumps, and

swash plate pumps use spatial mechanisms:


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Simulators for pilot training or for vehicle driving

often use a spatial robot called a Stewart

Platform.


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Here are some other useful spatial manipulator

platforms:


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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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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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A few more picts showing additional spatial

mechanisms on different versions of the marine

training simulator:


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A few more pictures showing additional spatial

mechanisms on different versions of the marine

training simulator:


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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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motion generating mechanism(From Draper Lab at M.I.T.)


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motion generating mechanism


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Helicopter swash plate

A function generating mechanism


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Helicopter swash platecollective linkage



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Helicopter swash plate cycliclinkage



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Helicopter swash plate cycliclinkage


introduction to spatial kinematics

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