MENG 372 Chapter 7 Acceleration Analysis All figures

Acceleration Analysis Linear acceleration Angular acceleration Acceleration of a point Acceleration has 2 components:

Acceleration Analysis Magnitudes of acceleration components Magnitude of normal acceleration Magnitude of tangential acceleration

Acceleration Analysis If point A is moving Graphically: 4

Graphical Acceleration Analysis (a 3&a 4) • Given linkage configuration, a 2. Find a

Acceleration of point C • Now we know a 3 from previous step •

Analytical Acceleration Analysis (4 bar) Given a 2. Find a 3 and a 4

Analytical Acceleration Analysis (4 bar) Write vector loop equation: Take two derivatives: 8

Analytical Acceleration Analysis (4 bar) Separate knowns and unknowns Take conjugate Put in matrix

Coriolis Acceleration Position of slider . Velocity of slider Transmission Slip velocity Acceleration: Use

Inverted Crank Slider • Given a 2. Find , a 3 and a 4

Inverted Crank Slider • Write vector loop equation and take two derivatives b varies

Inverted Crank Slider • Group into knowns and unknowns, a 3=a 4 • Take

Acceleration of any point on the mechanism • Write the vector for RP •

Inverted Crank Slider. . • Given a 2. Find a 3 and d 15

Common Values of Accelerations • A ‘g’ is the acceleration of gravity =9. 81

Human Tolerance for Acceleration • Humans are limited in the level of acceleration they

Jerk • Jerk is the derivative of acceleration linear jerk angular jerk • High

Jerk Analysis of 4 -bar Linkage • Recall • Taking another derivative 19

Slides: 19

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MENG 372 Chapter 7 Acceleration Analysis All figures taken from Design of Machinery, 3 rd ed. Robert Norton 2003 1

Acceleration Analysis Linear acceleration Angular acceleration Acceleration of a point Acceleration has 2 components: normal & tangential 2

Acceleration Analysis Magnitudes of acceleration components Magnitude of normal acceleration Magnitude of tangential acceleration 3

Acceleration Analysis If point A is moving Graphically: 4

Graphical Acceleration Analysis (a 3&a 4) • Given linkage configuration, a 2. Find a 3 and a 4 • Know An. A, At. A, An. B, and direction of At. BA, At. B • AB=AA+ABA An. B+At. B= An. A+At. A+An. BA+At. BA A n. B At. BA At. B line An. BA At. BA line 5

Acceleration of point C • Now we know a 3 from previous step • AC=AA+AC/A=An. A+At. A+An. C/A+At. C/A Enlarged scale A n. A AC At A At C/A An. C/A 6

Analytical Acceleration Analysis (4 bar) Given a 2. Find a 3 and a 4 7

Analytical Acceleration Analysis (4 bar) Write vector loop equation: Take two derivatives: 8

Analytical Acceleration Analysis (4 bar) Separate knowns and unknowns Take conjugate Put in matrix form Solve 9

Coriolis Acceleration Position of slider . Velocity of slider Transmission Slip velocity Acceleration: Use the product rule Combining terms: Slip Normal Tangential Coriolis acc. cccurs when a body has vslip and w Coriolis 10

Inverted Crank Slider • Given a 2. Find , a 3 and a 4 11

Inverted Crank Slider • Write vector loop equation and take two derivatives b varies with time • Recall • so 12

Inverted Crank Slider • Group into knowns and unknowns, a 3=a 4 • Take conjugate • Put in matrix form • Solve 13

Acceleration of any point on the mechanism • Write the vector for RP • Take derivative twice • Similarly RP 14

Inverted Crank Slider. . • Given a 2. Find a 3 and d 15

Common Values of Accelerations • A ‘g’ is the acceleration of gravity =9. 81 m/s 2 • Common values of acceleration: 16

Human Tolerance for Acceleration • Humans are limited in the level of acceleration they can tolerate • Machines are limited by the stresses in the parts, e. g. automobile piston 40 g’s at idle, 700 g’s at highway 2000 g’s peak 17

Jerk • Jerk is the derivative of acceleration linear jerk angular jerk • High value of jerk causes stomach to go funny in roller coaster or elevator starting to descend High acceleration High jerk 18

Jerk Analysis of 4 -bar Linkage • Recall • Taking another derivative 19