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Hand on Practice

Topic: Graphical Linkage Synthesis

One thing you learn in science is thatthere is no perfect answer, no perfectmeasure.

A. O. Beckman

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 designsolutions for some typical kinematicapplications.

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3.1 QUALITATIVE SYNTHESIS

The creation of potential solutions in the absenceof a well-defined algorithm which configures orpredicts the solution and also judge its quality.

Several tools and techniques exist to assist you inthis process. The traditional tool is the draftingboard, on which you layout, to scale, multipleorthographic views of the design, and investigateits motions by drawing arcs, showing multiplepositions, and using transparent, movableoverlays.

Commercially available programs such asSolidWork and Working Model allow rapid analysisof a proposed mechanical design. The process thenbecomes one of qualitative design by successiveanalysis which is really an iteration betweensynthesis and analysis.

3.2 TYPE SYNTHESIS

The definition of the proper type ofmechanism best suited to the problem andis a form of qualitative synthesis.

This is perhaps the most difficult task forthe student as it requires some experienceand knowledge of the various types ofmechanisms which exist and which alsomay be feasible from a performance andmanufacturing standpoint.

Remember, an engineer can do, with onedollar, what any fool can do for tendollars. Cost is always an importantconstraint in engineering design.

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3.3 QUALITATIVE SYNTHESIS OR ANALITICAL SYNTHESIS

The generation of one or more solutions ofa particular type which you know to besuitable to the problem, and moreimportantly, one for which there is asynthesis algorithm defined.

As the name suggests, this type ofsolution can be quantified, as some set ofequations exists which will give anumerical answer.

3.4 DIMENSIONAL SYNTHESIS

The determination of the proportions(lengths) of the links necessary toaccomplish the desired motions and canbe a form of quantitative synthesis if analgorithm is defined for the particularproblem, but can also be a form ofqualitative synthesis if there are morevariables than equations.

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3.5 MECHANISM SYNTHESIS: TWO APPROACHES

3.6 FUNCTION, PATH, AND MOTION GENERATION

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3.7 LIMITING CONDITIONS

The manual, graphical, dimensional synthesistechniques presented in this chapter and thecomputerizable, analytical synthesis techniquesare reasonably rapid means to obtain a trialsolution to a motion control problem. Once apotential solution is found, it must be evaluatedfor its quality. There are many criteria which maybe applied. However, one does not want to expenda great deal of time analyzing, in great detail, adesign which can be shown to be inadequate bysome simple and quick evaluations.

TOGGLE: One important test consist in to checkthat the linkage can in fact reach all of thespecified design positions without encountering alimit or toggle position, also called a stationaryconfiguration.

3.7 LIMITING CONDITIONS

The toggle positions are determined bythe colinearity of two of the moving links.

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3.7 LIMITING CONDITIONS

3.7 LIMITING CONDITIONS

TRANSMISSION ANGLE: The transmission angle μis defined as the angle between the output linkand the coupler. It is usually taken as the absolutevalue of the acute angle of the pair of angles at theintersection of the two links and variescontinuously from some minimum to somemaximum value as the linkage goes through itsrange of motion.

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3.7 LIMITING CONDITIONS

The optimum value for the transmissionangle is 90°. When it is less than 45° theradial component will be larger than thetangential component. Most machinedesigners try to keep the minimumtransmission angle above about 40° topromote smooth running and good forcetransmission.

3.8 FOURBAR LINKAGE

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3.8 FOURBAR LINKAGE

3.8 FOURBAR LINKAGE

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3.9 DIMENSIONAL SYNTHESIS

Dimensional synthesis of a linkage is thedetermination of the proportions (lengths) of the linksnecessary to accomplish the desired motions. TWO-POSITION SYSNTHESIS: Divided in two

categories:

3.9 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 andback, from a constant speed motor input.

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3.9 DIMENSIONAL SYNTHESIS - Solution

1. Draw the output link O4B in both extreme positions,B1 and B2 in any convenient location, such that thedesired angle of motion θ4 is subtended.

2. Draw the chord B1B2 and extend it in either direction.3. Select a convenient point O2 on line B1B2 extended.4. Bisect line segment B1B2, and draw a circle of that

radius about O2.5. Label the two intersections of the circle and B1B2

extended, A1 and A2.6. Measure the length of the coupler as A1 to B1 or A2 to

B2.7. Measure ground length I, crank length 2, and rocker

length 4.8. Find the Grashof condition. If non-Grashof, redo steps

3 to 8 with O2 further from O4.

3.9 DIMENSIONAL SYNTHESIS

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3.9 DIMENSIONAL SYNTHESIS

3.9 DIMENSIONAL SYNTHESIS

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3.9 DIMENSIONAL SYNTHESIS

3.9 DIMENSIONAL SYNTHESIS

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3.9 DIMENSIONAL SYNTHESIS

3.9 DIMENSIONAL SYNTHESIS

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3.9 DIMENSIONAL SYNTHESIS

3.9 DIMENSIONAL SYNTHESIS

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3.9 DIMENSIONAL SYNTHESIS

3.9 DIMENSIONAL SYNTHESIS - Problem

Example 3-2 Rocker Output – Two Positions with Complex Displacement. (Motion Generation)

Design a fourbar linkage to move link CD fromposition C1D1 to C2D2.

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3.9 DIMENSIONAL SYNTHESIS - Solution

1. Draw the link CD in its two desiredpositions, C1D1 and C2D2, in the plane asshown.

2. Draw construction lines from point C1 toC2 and from D1 to D2.

3. Bisect line C1C2 and line D1D2 and extendtheir perpendicular bisectors to intersectat θ4. Their intersection is the rotopole.

4. Select a convenient radius and draw anarc about the rotopole to intersect bothlines θ4C1 and θ4C2. Label the intersectionsB1 and B2.

3.9 DIMENSIONAL SYNTHESIS - Solution

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3.9 DIMENSIONAL SYNTHESIS - Solution

3.9 DIMENSIONAL SYNTHESIS - Solution

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3.9 DIMENSIONAL SYNTHESIS - Solution

3.9 DIMENSIONAL SYNTHESIS - Solution

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3.9 DIMENSIONAL SYNTHESIS - Solution

3.9 DIMENSIONAL SYNTHESIS - Solution

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3.9 DIMENSIONAL SYNTHESIS - Solution

3.9 DIMENSIONAL SYNTHESIS - Problem

Example 3-3 Coupler Output – Two Positions with Complex Displacement. (Motion Generation)

Design a fourbar linkage to move link CD fromposition C1D1 to C2D2 (with moving pivots at C andD).

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3.9 DIMENSIONAL SYNTHESIS - Problem