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lecture+notes+14 - 14:440:222 Dynamics (Lecture Note #14)...

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Unformatted text preview: 14:440:222 Dynamics (Lecture Note #14) Instructor: Prof. Peng Song Rutgers University Today’s Lecture • Planar rigid body motion: translation and rotation • Absolute motion analysis Does each passenger experience the same velocity and acceleration? Applications To do this design, we need to relate the angular motions of contacting bodies that rotate about different fixed axes. How is this different than the analyses we did in earlier chapters? We will now start to study rigid body motion. The analysis will be limited to planar motion. For example, in the design of gears, cams, and links in machinery or mechanisms, rotation of the body is an important aspect in the analysis of motion. There are cases where an object cannot be treated as a particle. In these cases the size or shape of the body must be considered. Rotation of the body about its center of mass requires a different approach. A body is said to undergo planar motion when all parts of the body move along paths equidistant from a fixed plane. Rigid Body Motion There are three types of planar rigid body motion. Planar Rigid Body Motion Translation: Translation occurs if every line segment on the body remains parallel to its original direction during the motion. When all points move along straight lines, the motion is called rectilinear translation. When the paths of motion are curved lines, the motion is called curvilinear translation. Planar Rigid Body Motion (cont’d) Rotation about a fixed axis: In this case, all the particles of the body, except those on the axis of rotation, move along circular paths in planes perpendicular to the axis of rotation. General plane motion: In this case, the body undergoes both translation and rotation. Translation occurs within a plane and rotation occurs about an axis perpendicular to this plane. Planar Rigid Body Motion (cont’d) The piston undergoes rectilinear translation since it is constrained to slide in a straight line. The connecting rod undergoes curvilinear translation, since it will remain horizontal as it moves along a circular path. The wheel and crank undergo rotation about a fixed axis. In this case, both axes of rotation are at the location of the pins and perpendicular to the plane of the figure. An example of bodies undergoing the three types of motion is shown in this mechanism. The connecting rod undergoes general plane motion, as it will both translate and rotate. Planar Rigid Body Motion (cont’d) The positions of two points A and B on a translating body can be related by r B = r A + r B/A where r A & r B are the absolute position vectors defined from the fixed x-y coordinate system, and r B/A is the relative-position vector between B and A....
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This document was uploaded on 10/31/2011 for the course ENG MECH 232 at Rutgers.

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lecture+notes+14 - 14:440:222 Dynamics (Lecture Note #14)...

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