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**Mechanisms Design MECN 4110**

Professor: Dr. Omar E. Meza Castillo Department of Mechanical Engineering Inter American University of Puerto Rico Bayamon Campus

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**Tentative Lectures Schedule**

Topic Lecture Introduction of Mechanism and Kinematics 1, 2 and 3

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**Topic: Graphical Linkage Synthesis**

One thing you learn in science is that there is no perfect answer, no perfect measure. A. O. Beckman Topic: Graphical Linkage Synthesis Hand on Practice

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**Up on completion of this chapter, the student will be able to**

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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**3.1 QUALITATIVE SYNTHESIS**

The creation of potential solutions in the absence of a well-defined 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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3.2 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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**3.3 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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**3.4 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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**3.5 MECHANISM SYNTHESIS: TWO APPROACHES**

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**3.6 FUNCTION, PATH, AND MOTION GENERATION**

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3.7 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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3.7 LIMITING CONDITIONS The toggle positions are determined by the colinearity of two of the moving links.

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3.7 LIMITING CONDITIONS

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3.7 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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3.7 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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3.8 FOURBAR LINKAGE

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3.8 FOURBAR LINKAGE

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3.8 FOURBAR LINKAGE

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**3.9 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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**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 and back, from a constant speed motor input.

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**3.9 DIMENSIONAL SYNTHESIS**

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**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 from position C1D1 to C2D2.

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

Draw the link CD in its two desired positions, C1D1 and C2D2, in the plane as shown. Draw construction lines from point C1 to C2 and from D1 to D2. Bisect line C1C2 and line D1D2 and extend their perpendicular bisectors to intersect at θ4. Their intersection is the rotopole. 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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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**3.9 DIMENSIONAL SYNTHESIS - Solution**

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**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 from position C1D1 to C2D2 (with moving pivots at C and D).

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**3.9 DIMENSIONAL SYNTHESIS - Problem**

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**Homework3 http://facultad.bayamon.inter.edu/omeza**

Omar E. Meza Castillo Ph.D.

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