162A 2 - Position and Displacement

162A 2 - Position and Displacement - 162A. Position and...

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162A. Position and Displacement in Mechanisms Chapter 2: Position & Displacement
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Chapter 2 s Position and Displacement
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Notation s Consider a fixed reference coordinate system O xyz or simply O xy if we have a 2-d reference system. O is the origin from which positions are measured s The position of a point P in the coordinate system is represented as R PO which is a vector verbalized as “R P to O”. Remember: tip-to-tail. This R PO vector is sometimes simply written as R P , when it is w.r.t. the origin. s Vector R P is written with R in bold (or with a line above or below the letter) to connote it is a vector. Without bold (or a line), it connotes just the magnitude
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Terms s Absolute Position of a point is its position with respect to the origin of the coordinate system s Relative Position between two points P and Q can be expressed as position ifference between those difference between those two points R PQ = R PO - R QO s Apparent Position of a point P is the position of the point P relative to the observer s Absolute and Relative Positions are related as : R PO = R QO + R PQ
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We’ll employ two methods for position analysis s Graphical Method b Intuitive b Inexact s Complex Algebra Method b Analytic b Exact
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Before that…. The Loop Closure Equation s Loop Closure Equation: A vector equation representing all or part of mechanism formulated according to the fact: The vector sum of a closed polygon equals zero. s That is, the sum of vectors to close the loop is 0 , or,
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Loop-Closure Equation s Applying the loop closure equation to the hand-operated clamp A B C D R BA + R CB + R DC + R AD = 0
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This note was uploaded on 08/08/2011 for the course MAE 162A taught by Professor Glenn during the Spring '08 term at UCLA.

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162A 2 - Position and Displacement - 162A. Position and...

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