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Unformatted text preview: 14:440:222 Dynamics (Lecture Note #17) Instructor: Prof. Peng Song Rutgers University Todays Lecture Relative motion analysis: acceleration In the mechanism for a window, link AC rotates about a fixed axis through C, and AB undergoes general plane motion. Since point A moves along a curved path, it has two components of acceleration while point B, sliding in a straight track, has only one. The components of acceleration of these points can be inferred since their motions are known. How can we determine the accelerations of the links in the mechanism? Applications In an automotive engine, the forces delivered to the crankshaft, and the angular acceleration of the crankshaft, depend on the speed and acceleration of the piston. How can we relate the accelerations of the piston, connection rod, and crankshaft to each other? Applications (contd) The equation relating the accelerations of two points on the body is determined by differentiating the velocity equation with respect to time. The result is a B = a A + ( a B/A ) t + ( a B/A ) n These are absolute accelerations of points A and B. They are measured from a set of fixed x,y axes . This term is the acceleration of B with respect to A and includes both tangential and normal components. / + dt d v A B dt d v A dt d v B = Relative Motion Analysis: Acceleration The relative normal acceleration component ( a B/A ) n is ( 2 r B/A ) and the direction is always from B towards A . Graphically: a B = a A + ( a B/A ) t + ( a B/A ) n The relative tangential acceleration component ( a B/A ) t is ( r B/A ) and perpendicular to r B/A ....
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This document was uploaded on 10/31/2011 for the course ENG MECH 232 at Rutgers.
 Fall '11
 R.C.Hibbeler

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