chapter4-a-pictures_1-5

# chapter4-a-pictures_1-5 - MEEG439 MACHINE DYNAMICS SPRING,...

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MEEG439 MACHINE DYNAMICS SPRING, 2006 Chapter 4 Position Analysis 4.0 Introduction We need to analyze the mechanisms synthesized in Chapter 3 Eventually we need stresses in all members to assure no parts fail Need force, and acceleration o Force: both static and dynamic o Acceleration: can be found by differentiating velocity, velocity by differentiating position We can look at position graphically, algebraically, or computationally o Graphically: need to redraw mechanism at many positions Lots of work but very easy o Algebraically: derive the equations for position as functions of time or the input angle θ o Computationally: use a program like Working Model, Mechanica, DADS, Adams, etc. to look at position To find velocity and acceleration from position, we can do o A graphical approach (tedious) o Algebraic approach: convenient and relatively straightforward o Computational approach: very easy 4.1 Coordinate Systems Define a ground coordinate system XY , inertial for the problem being looked at Positive angle is counterclockwise (assuming rotation is about the z -axis) We will add various rotating and nonrotating coordinate systems later 4.2 Position and Displacement Position of a point is defined by a position vector X A Y r A θ r y r x cos sin A x y r r r r θ = + = + r i j i j 1 5ba486973ccc6d82f90d6f545ca73e6b02646934.doc

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MEEG439 MACHINE DYNAMICS SPRING, 2006 Displacement is defined as the change in position and is measured in a line from initial point to final point o
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## This note was uploaded on 02/06/2012 for the course MEEG 439 taught by Professor Scf during the Spring '11 term at The Petroleum Institute.

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chapter4-a-pictures_1-5 - MEEG439 MACHINE DYNAMICS SPRING,...

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