EME 6303 MACHINE DYNAMCSLECTURE NOTES (4)March 2015-June 2015Dr. J.B. Byiringiro (Ph.D, R. Eng)20 151CHAP.4 KINEMATIC ANALYSIS OF MECHANISMS4.1 OverviewThere are various methods of performing kinematic analysis of mechanisms,including: Graphical Analytical NumericalThe choice of a method depends on the problem at hand and on availablecomputational means. In this chapter the emphasis is placed on studyingmechanisms rather than methods of analysis.Thus, the presentation is limited to one method, which is sufficient for simpleand for many compound mechanisms. This method is known as the Loop-closureequation method and it is presented here in vector notation.Coordinate SystemsOne should differentiate between the global (inertial, absolute) and local(moving) coordinate systems. Fig.1 shows a point P on a body referenced in global(x, y) and local (x1, y1) coordinate systems. The local coordinate system isembedded in the body and thus moves with it in a global system.For consistency, the right-hand coordinate system is used throughout thischapter for both local and global coordinate systems. Recall that the coordinatesystem is called right-hand if the rotation of the x-axis toward the y-axis iscounterclockwise when viewed from the tip of the z-axis.2Fig.1 Global (x, y) and local (x1, y1) coordinate systemsThus, in Fig.1 the z-axis is directed toward the reader. A vector r has twocomponents in the (x, y) plane: rx and r ...

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