MECN 4110 – Mechanisms Design
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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 4: Position Analysis Fourbar Linkage 2 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 Chapters Objectives Up on completion of this chapter, the student will be able to Present and derive analytical solutions to the position analysis problem for various planar mechanisms. Discuss graphical solutions which are useful for checking analytical results. 3 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 COORDINATE SYSTEMS Global or Absolute system is often taken to be attached to Mother Earth. Local coordinate systems are typically attached to a link at some point of interest. The term inertial reference frame is used to denote a system which itself has no acceleration. All angles in this text will be measured according to the right-hand rule. That is, counterclockwise angles, angular velocities, and angular accelerations are positive in sign. 4 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad COORDINATE SYSTEMS Position Vector in the plane 5 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 POSITION AND DISPLACEMENT POSITION: The position of a point in the plane can be defined by the use of a position vector as shown in previous figure. The choice of reference axes is arbitrary and is selected to suit the observer. The Polar form provides the magnitudes and the angle of the vector. The Cartesian form provides X and Y components of the vector. 6 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 POSITION AND DISPLACEMENT DISPLACEMENT: Displacement of a point is the change in its position and can be defined as the straight line distance between the initial and final position of a point which has moved in the reference frame. 7 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 TRANSLATION, ROTATION, AND COMPLEX MOTION Translation: All points on the body have the same displacement. Rotation: Different points in the body undergo different displacements and thus there is a displacement difference between any two points chosen. 8 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 TRANSLATION, ROTATION, AND COMPLEX MOTION Complex Motion: The general case of complex motion is the sum of the translation and rotation components. 9 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 GRAPHICAL POSITION ANALYSIS OF LINKAGES For any one-DOF linkage, such as a fourbar, only one parameter is needed to completely define the positions of all links. The parameter usually chosen is the angle of the input link. This is shown as θ2 in figure. We want to find θ3 and θ4. The link lengths are known. In this example will consistently number the ground link as 1 and the driver link as 2. Local xy System Global XY System 10 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 GRAPHICAL POSITION ANALYSIS OF LINKAGES The graphical analysis of this problem is trivial and can be done using high school geometry. If we draw the linkage carefully to scale with rule, compass, and protractor in a particular position (given θ2), then it is only necessary to measure the angles of links 3 and with the protractor. The next figure shows the construction of the graphical position solution. The four links a, b, c, d and the angle θ2 of the input link are given. The figure shows two possible solutions, labeled open and crossed. 11 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad GRAPHICAL POSITION ANALYSIS OF LINKAGES 12 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad GRAPHICAL POSITION ANALYSIS OF LINKAGES 13 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad GRAPHICAL POSITION ANALYSIS OF LINKAGES 14 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad GRAPHICAL POSITION ANALYSIS OF LINKAGES 15 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad GRAPHICAL POSITION ANALYSIS OF LINKAGES 16 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 17 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 18 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 19 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 20 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 21 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 22 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 23 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 24 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 25 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 26 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 27 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 28 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 29 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 30 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES 31 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 32 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 33 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 34 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 35 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 36 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 37 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 38 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 39 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 40 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 41 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional 42 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 ALGEBRAIC POSITION ANALYSIS OF LINKAGES -Additional Excel or other program 43 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION 44 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION 45 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION 46 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 47 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 48 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 49 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 50 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 51 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 52 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad THE FOURBAR SLIDER-CRANK POSITION SOLUTION-Add 53 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad AN INVERTED SLIDER-CRANK POSITION SOLUTION 54 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad AN INVERTED SLIDER-CRANK POSITION SOLUTION 55 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad AN INVERTED SLIDER-CRANK POSITION SOLUTION 56 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad LINKAGES OF MORE THAN FOUR BARS 57 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad LINKAGES OF MORE THAN FOUR BARS 58 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad LINKAGES OF MORE THAN FOUR BARS 59 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad LINKAGES OF MORE THAN FOUR BARS 60 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad LINKAGES OF MORE THAN FOUR BARS 61 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ¿Preguntas? Comentarios 62 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 GRACIAS Pictures from Robert L. Norton's fifth edition of DESIGN OF MACHINERY 63
