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All figures taken from Design of Machinery , 3 rd ed. Robert Norton 2003

MENG 372 Chapter 7 Acceleration Analysis. All figures taken from Design of Machinery , 3 rd ed. Robert Norton 2003. Acceleration Analysis. Linear acceleration Angular acceleration. Acceleration of a point. Acceleration has 2 components: normal & tangential. Acceleration Analysis.

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All figures taken from Design of Machinery , 3 rd ed. Robert Norton 2003

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

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

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

  4. Acceleration Analysis If point A is moving Graphically:

  5. Graphical Acceleration Analysis (a3&a4) AnA AnB AtB AtA AtB line AtBA AnBA AtBA line • Given linkage configuration, a2. Find a3 and a4 • Know AnA,AtA,AnBA,AnB, and direction of AtBA,AtB • AB=AA+ABA AnB+AtB= AnA+AtA+AnBA+AtBA

  6. Acceleration of point C AnA AC AtA AnC/A AtC/A • Now we know a3 from previous step • AC=AA+AC/A=AnA+AtA+AnC/A+AtC/A Enlarged scale

  7. Analytical Acceleration Analysis (4bar) Given a2. Find a3 and a4

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

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

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

  11. Inverted Crank Slider • Given a2. Find , a3 and a4

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

  13. Inverted Crank Slider • Group into knowns and unknowns, a3=a4 • Take conjugate • Put in matrix form • Solve

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

  15. Inverted Crank Slider .. • Given a2. Find a3 and d

  16. Common Values of Accelerations • A ‘g’ is the acceleration of gravity =9.81m/s2 • Common values of acceleration:

  17. 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 40g’s at idle, 700g’s at highway 2000g’s peak

  18. 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

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

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