mecn 4110 inter - bayamon lecture 3 mechanisms design mecn 4110 professor: dr. omar e. meza castillo...

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LectureLecture

33Mechanisms DesignMechanisms Design

MECN 4110 MECN 4110

Professor: Dr. Omar E. Meza CastilloProfessor: Dr. Omar E. Meza [email protected]

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

Department of Mechanical EngineeringDepartment of Mechanical Engineering

Inter American University of Puerto RicoInter American University of Puerto Rico

Bayamon CampusBayamon Campus

Lecture 3Lecture 3MEC

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Tentative Lectures ScheduleTentative Lectures Schedule

TopicTopic LectureLecture

Introduction of Mechanism and KinematicsIntroduction of Mechanism and Kinematics 1, 2 and 31, 2 and 3


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Hand on PracticeHand on Practice

Topic: Graphical Linkage Topic: Graphical Linkage SynthesisSynthesis

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One thing you learn in science is that One thing you learn in science is that there is no perfect answer, no perfect there is no perfect answer, no perfect measure.measure.

A. O. BeckmanA. O. Beckman


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Chapters ObjectivesChapters Objectives

Up on completion of this chapter, the Up on completion of this chapter, the student will be able tostudent will be able to Involve both synthesis and analysis in the Involve both synthesis and analysis in the

engineering design.engineering design. Explore some simple synthesis techniques to Explore some simple synthesis techniques to

enable you to create potential linkage design enable you to create potential linkage design solutions for some typical kinematic solutions for some typical kinematic applications.applications.

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3.1 QUALITATIVE SYNTHESIS3.1 QUALITATIVE SYNTHESIS

The creation of The creation of potential solutions potential solutions in the in the absenceabsence of a of a well-defined algorithm well-defined algorithm which configures or which configures or predicts the solution and also judge its predicts the solution and also judge its qualityquality..

Several tools Several tools and techniques exist to assist you in and techniques exist to assist you in this process. The traditional tool is the drafting this process. The traditional tool is the drafting board, on which you layout, to scale, multiple board, on which you layout, to scale, multiple orthographic views of the design, and investigate orthographic views of the design, and investigate its motions by drawing arcs, showing multiple its motions by drawing arcs, showing multiple positions, and using transparent, movable positions, and using transparent, movable overlays.overlays.

Commercially available programs such as Commercially available programs such as SolidWork and Working Model allow rapid analysis SolidWork and Working Model allow rapid analysis of a proposed mechanical design. The process of a proposed mechanical design. The process then becomes one of then becomes one of qualitative design qualitative design by by successive successive analysisanalysis which is really an iteration which is really an iteration between synthesis and analysis.between synthesis and analysis.

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3.2 TYPE SYNTHESIS3.2 TYPE SYNTHESIS

The The definitiondefinition of the proper of the proper type of type of mechanism mechanism best suited to the problem and best suited to the problem and is a form of qualitative synthesis.is a form of qualitative synthesis.

This is perhaps the most difficult task for This is perhaps the most difficult task for the student as it requires some experience the student as it requires some experience and knowledge of the various types of and knowledge of the various types of mechanisms which exist and which also mechanisms which exist and which also may be feasible from a performance and may be feasible from a performance and manufacturing standpoint.manufacturing standpoint.

Remember, Remember, an engineer can do, with one an engineer can do, with one dollar, what any fool can do for ten dollarsdollar, what any fool can do for ten dollars. . Cost is always an important constraint in Cost is always an important constraint in engineering design.engineering design.

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3.3 QUALITATIVE SYNTHESIS OR ANALITICAL SYNTHESIS3.3 QUALITATIVE SYNTHESIS OR ANALITICAL SYNTHESIS

The The generation of one or more generation of one or more solutions solutions of a particular type which you know to be of a particular type which you know to be suitablesuitable to the problem, and more to the problem, and more importantly, one for which there is a importantly, one for which there is a synthesis algorithm definedsynthesis algorithm defined..

As the name suggests, this type of As the name suggests, this type of solution can be solution can be quantifiedquantified, as some set of , as some set of equations exists which will give a equations exists which will give a numerical answer.numerical answer.

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3.4 DIMENSIONAL SYNTHESIS3.4 DIMENSIONAL SYNTHESIS

The The determination of the proportions determination of the proportions (lengths) of the links necessary to (lengths) of the links necessary to accomplish the desired motions accomplish the desired motions and can and can be a form of be a form of quantitative synthesis quantitative synthesis if an if an algorithm is defined for the particular algorithm is defined for the particular problem, but can also be a form of problem, but can also be a form of qualitative synthesis qualitative synthesis if there are more if there are more variables than equations.variables than equations.

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3.5 MECHANISM SYNTHESIS: TWO APPROACHES3.5 MECHANISM SYNTHESIS: TWO APPROACHES

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3.6 FUNCTION, PATH, AND MOTION GENERATION3.6 FUNCTION, PATH, AND MOTION GENERATION

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3.7 LIMITING CONDITIONS3.7 LIMITING CONDITIONS

The manual, graphical, dimensional synthesis The manual, graphical, dimensional synthesis techniques presented in this chapter and the techniques presented in this chapter and the computerizable, analytical synthesis techniques computerizable, analytical synthesis techniques are reasonably rapid are reasonably rapid means to obtain a trial means to obtain a trial solution to a motion control problem. solution to a motion control problem. Once a Once a potential solution is found, it must be evaluated potential solution is found, it must be evaluated for its qualityfor its quality. There are many criteria which may . There are many criteria which may be applied. However, one be applied. However, one does not want to expend does not want to expend a great deal of time a great deal of time analyzing, in great detail, a analyzing, in great detail, a design which can be shown to be inadequate by design which can be shown to be inadequate by some simple and quick evaluations.some simple and quick evaluations.

TOGGLE: TOGGLE: One important test consist in to check One important test consist in to check that the linkage can in fact reach all of the that the linkage can in fact reach all of the specified design positions without encountering a specified design positions without encountering a limit or toggle position, also called a stationary limit or toggle position, also called a stationary configuration.configuration.

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

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TRANSMISSION ANGLE: TRANSMISSION ANGLE: The transmission angle The transmission angle μμ is defined as the angle between the output link is defined as the angle between the output link and the coupler. It is usually taken as the absolute and the coupler. It is usually taken as the absolute value of the acute angle of the pair of angles at value of the acute angle of the pair of angles at the intersection of the two links and varies the intersection of the two links and varies continuously from some minimum to some continuously from some minimum to some maximum value as the linkage goes through its maximum value as the linkage goes through its range of motionrange of motion..

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The The optimum value optimum value for the transmission for the transmission angle is angle is 90°90°. When it is less than 45° the . When it is less than 45° the radial component will be larger than the radial component will be larger than the tangential component. Most machine tangential component. Most machine designers try to keep the designers try to keep the minimum minimum transmission angle above about 40° transmission angle above about 40° to to promote smooth running and good force promote smooth running and good force transmission.transmission.

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3.8 FOURBAR LINKAGE3.8 FOURBAR LINKAGE

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Dimensional synthesis of a linkage Dimensional synthesis of a linkage is the is the determination of the proportions (lengths) of the determination of the proportions (lengths) of the links necessary to accomplish the desired motionslinks necessary to accomplish the desired motions..TWO-POSITION SYSNTHESIS: TWO-POSITION SYSNTHESIS: Divided in two Divided in two categories:categories:

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3.9 DIMENSIONAL SYNTHESIS - 3.9 DIMENSIONAL SYNTHESIS - ProblemProblem

Example 3-1 Example 3-1 Rocker Output – Two Positions with Rocker Output – Two Positions with Angular Displacement. (Function Generation)Angular Displacement. (Function Generation)

Design a Design a fourbar Grashof crank-rocker fourbar Grashof crank-rocker to give 45to give 45oo of of rocker rotation with equal time forward and back, rocker rotation with equal time forward and back, from a constant speed motor input.from a constant speed motor input.

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3.9 DIMENSIONAL SYNTHESIS - 3.9 DIMENSIONAL SYNTHESIS - SolutionSolution

1.1. Draw the output link Draw the output link OO44B in both extreme positions, BB in both extreme positions, B11 and Band B22 in any convenient location, in any convenient location, such that the such that the desired angle of motion desired angle of motion θθ44 is subtended. is subtended.

2.2. Draw the chord Draw the chord BB11BB22 and extend it in either direction. and extend it in either direction.

3.3. Select a convenient point OSelect a convenient point O22 on line on line BB11BB22 extended. extended.

4.4. Bisect line segment Bisect line segment BB11BB22, and draw a circle of that , and draw a circle of that radius about radius about OO22..

5.5. Label the two intersections of the circle and Label the two intersections of the circle and BB11BB22 extended, Aextended, A11 and A and A22..

6.6. Measure the length of the coupler as Measure the length of the coupler as AA1 1 to Bto B1 1 or Aor A22 to to BB22..

7.7. Measure ground length I, crank length 2, and rocker Measure ground length I, crank length 2, and rocker length 4.length 4.

8.8. Find the Grashof condition. If non-Grashof, redo steps Find the Grashof condition. If non-Grashof, redo steps 3 to 8 with O3 to 8 with O22 further from O further from O44..

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

Design a Design a fourbar linkagefourbar linkage to move link CD from to move link CD from position Cposition C11DD11 to C to C22DD22..

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1.1. Draw the link CD in its two desired Draw the link CD in its two desired positions, Cpositions, C11DD11 and C and C22DD22, in the plane as , in the plane as shown.shown.

2.2. Draw construction lines from point CDraw construction lines from point C1 1 to to CC2 2 and from Dand from D11 to D to D22..

3.3. Bisect line CBisect line C11CC22 and line D and line D11DD22 and extend and extend their perpendicular bisectors to intersect their perpendicular bisectors to intersect at at θθ44. Their intersection is the rotopole.. Their intersection is the rotopole.

4.4. Select a convenient radius and draw an Select a convenient radius and draw an arc about the rotopole to intersect both arc about the rotopole to intersect both lines lines θθ44CC1 1 and and θθ44CC2.2. Label the intersections Label the intersections BB11 and B and B22..

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

Design a Design a fourbar linkagefourbar linkage to move link CD from to move link CD from position Cposition C11DD11 to C to C22DD22 (with moving pivots at C and (with moving pivots at C and D).D).

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Homework3 Homework3 http://http://facultadfacultad.bayamon.inter.edu/omeza.bayamon.inter.edu/omeza

Omar E. Meza Castillo Ph.D.Omar E. Meza Castillo Ph.D.

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mecn 4110 inter - bayamon lecture 3 mechanisms design mecn 4110 professor: dr. omar e. meza castillo...

Documents

bayamon lecture

type synthesis

synthesis algorithm

dimensional synthesis

analitical synthesis

mechanisms design mecn

form of qualitative

qualitative design