MECN 4110: Mechanisms Design
Mechanisms Design
MECN 4110
Professor: Dr. Omar E. Meza Castillo
omeza@bayamon.inter.edu
http://facultad.bayamon.inter.edu/omeza
Department of Mechanical Engineering
4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
One thing you learn in science is that there is
no perfect answer, no perfect measure.
A. O. Beckman
Topic 3: Graphical Linkage
Synthesis
Hand on Practice
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
Chapters Objectives
 Up on completion of this chapter, the student will
be able to
 Involve both synthesis and analysis in the engineering
design.
 Explore some simple synthesis techniques to enable you
to create potential linkage design solutions for some
typical kinematic applications.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
QUALITATIVE SYNTHESIS
 The creation of potential solutions in the absence of a welldefined algorithm which configures or predicts the solution
and also judge its quality.
 Several tools and techniques exist to assist you in this
process. The traditional tool is the drafting board, on which
you layout, to scale, multiple orthographic views of the
design, and investigate its motions by drawing arcs,
showing multiple positions, and using transparent, movable
overlays.
 Commercially available programs such as SolidWork and
Working Model allow rapid analysis of a proposed
mechanical design. The process then becomes one of
qualitative design by successive analysis which is really an
iteration between synthesis and analysis.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
TYPE SYNTHESIS
 The definition of the proper type of mechanism
best suited to the problem and is a form of
qualitative synthesis.
 This is perhaps the most difficult task for the
student as it requires some experience and
knowledge of the various types of mechanisms
which exist and which also may be feasible from
a performance and manufacturing standpoint.
 Remember, an engineer can do, with one dollar,
what any fool can do for ten dollars. Cost is
always an important constraint in engineering
design.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
QUALITATIVE SYNTHESIS OR ANALITICAL SYNTHESIS
 The generation of one or more solutions of a
particular type which you know to be suitable to
the problem, and more importantly, one for
which there is a synthesis algorithm defined.
 As the name suggests, this type of solution can
be quantified, as some set of equations exists
which will give a numerical answer.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
DIMENSIONAL SYNTHESIS
 The determination of the proportions (lengths) of
the links necessary to accomplish the desired
motions and can be a form of quantitative
synthesis if an algorithm is defined for the
particular problem, but can also be a form of
qualitative synthesis if there are more variables
than equations.
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4110: Mechanisms
MECN
Design- Bayamón
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MECHANISM SYNTHESIS: TWO APPROACHES
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4110: Mechanisms
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FUNCTION, PATH, AND MOTION GENERATION
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4110: Mechanisms
MECN
Design- Bayamón
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MSP21
LIMITING CONDITIONS
 The manual, graphical, dimensional synthesis techniques
presented in this chapter and the computerizable,
analytical synthesis techniques are reasonably rapid means
to obtain a trial solution to a motion control problem. Once
a potential solution is found, it must be evaluated for its
quality. There are many criteria which may be applied.
However, one does not want to expend a great deal of
time analyzing, in great detail, a design which can be
shown to be inadequate by some simple and quick
evaluations.
 TOGGLE: One important test consist in to check that the
linkage can in fact reach all of the specified design
positions without encountering a limit or toggle position,
also called a stationary configuration.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
LIMITING CONDITIONS
 The toggle positions are determined by the
colinearity of two of the moving links.
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4110: Mechanisms
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Design- Bayamón
Interamericana
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LIMITING CONDITIONS
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4110: Mechanisms
MECN
Design- Bayamón
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MSP21
LIMITING CONDITIONS
 TRANSMISSION ANGLE: The transmission angle μ is defined
as the angle between the output link and the coupler. It is
usually taken as the absolute value of the acute angle of
the pair of angles at the intersection of the two links and
varies continuously from some minimum to some maximum
value as the linkage goes through its range of motion.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
LIMITING CONDITIONS
 The optimum value for the transmission angle is
90°. When it is less than 45° the radial component
will be larger than the tangential component.
Most machine designers try to keep the minimum
transmission angle above about 40° to promote
smooth running and good force transmission.
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FOURBAR LINKAGE
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FOURBAR LINKAGE
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Design- Bayamón
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FOURBAR LINKAGE
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4110: Mechanisms
MECN
Design- Bayamón
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MSP21
DIMENSIONAL SYNTHESIS
Dimensional synthesis of a linkage is the determination of the
proportions (lengths) of the links necessary to accomplish the
desired motions.
 TWO-POSITION SYSNTHESIS: Divided in two categories:
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4110: Mechanisms
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DIMENSIONAL SYNTHESIS - Problem
Example 3-1 Rocker Output – Two Positions with Angular
Displacement. (Function Generation)
 Design a fourbar Grashof crank-rocker to give 45o of rocker
rotation with equal time forward and back, from a constant
speed motor input.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
DIMENSIONAL SYNTHESIS - Solution
1.
2.
3.
4.
5.
6.
7.
8.
Draw the output link O4B in both extreme positions, B1 and B2 in
any convenient location, such that the desired angle of
motion θ4 is subtended.
Draw the chord B1B2 and extend it in either direction.
Select a convenient point O2 on line B1B2 extended.
Bisect line segment B1B2, and draw a circle of that radius
about O2.
Label the two intersections of the circle and B1B2 extended, A1
and A2.
Measure the length of the coupler as A1 to B1 or A2 to B2.
Measure ground length I, crank length 2, and rocker length 4.
Find the Grashof condition. If non-Grashof, redo steps 3 to 8
with O2 further from O4.
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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Design- Bayamón
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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DIMENSIONAL SYNTHESIS
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
DIMENSIONAL SYNTHESIS - Problem
Example 3-2 Rocker Output – Two Positions with Complex
Displacement. (Motion Generation)
 Design a fourbar linkage to move link CD from position C1D1
to C2D2.
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
DIMENSIONAL SYNTHESIS - Solution
1. Draw the link CD in its two desired positions, C1D1
and C2D2, in the plane as shown.
2. Draw construction lines from point C1 to C2 and
from D1 to D2.
3. Bisect line C1C2 and line D1D2 and extend their
perpendicular bisectors to intersect at θ4. Their
intersection is the rotopole.
4. Select a convenient radius and draw an arc
about the rotopole to intersect both lines θ4C1
and θ4C2. Label the intersections B1 and B2.
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4110: Mechanisms
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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DIMENSIONAL SYNTHESIS - Solution
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
DIMENSIONAL SYNTHESIS - Problem
Example 3-3 Coupler Output – Two Positions with Complex
Displacement. (Motion Generation)
 Design a fourbar linkage to move link CD from position C1D1
to C2D2 (with moving pivots at C and D).
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
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DIMENSIONAL SYNTHESIS - Problem
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¿Preguntas?
Comentarios
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4110: Mechanisms
MECN
Design- Bayamón
Interamericana
Universidad
MSP21
GRACIAS
Picture from Robert L. Norton's fifth edition of DESIGN OF MACHINERY
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