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

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

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

4 If point A is moving Acceleration Analysis Graphically:

5 Graphical Acceleration Analysis (  3 &  4 ) Given linkage configuration,  2. Find  3 and  4 Know A n A,A t A,A n BA,A n B, and direction of A t BA,A t B A B =A A +A BA A n B +A t B = A n A +A t A +A n BA +A t BA AnBAnB A t B line AtAAtA AnAAnA A n BA A t BA line A t BA AtBAtB

6 Acceleration of point C Now we know  3 from previous step A C =A A +A C/A =A n A +A t A +A n C/A +A t C/A A n C/A AtAAtA AnAAnA ACAC A t C/A Enlarged scale

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

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: SlipNormalTangentialCoriolis Coriolis acc. cccurs when a body has v slip and w

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

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

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

14 Acceleration of any point on the mechanism Write the vector for R P Take derivative twice Similarly RPRP

15 Inverted Crank Slider Given  2. Find  3 and d..

16 Common Values of Accelerations A ‘g’ is the acceleration of gravity =9.81m/s 2 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 highway2000g’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 jerk High acceleration

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