PositionAnalysis

# PositionAnalysis - Analytic Approach to Mechanism Design...

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Position synthesis 1 Analytic Approach to Mechanism Design MEEG439 SPRING 2006

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Position synthesis 2 Analytic Approach Would like to solve for: Position Velocity Acceleration Forces and torques at each position Can be done graphically Our approach will be analytic for generality
Position synthesis 3 Chapter 4 - Analytic Position Analysis Focus on fourbar only Will use vector-loop technique and complex number notation Equations can often be written by inspection Sections 4.1 - 4.6 for position Sections 4.9 - 4.11 for toggle positions / transmission angles

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Position synthesis 4 Chapter 5 - Analytical Linkage Synthesis Skip Chapter 5 Solution technique esoteric Graphical techniques useful and intuitive for synthesis Simulation and modeling packages used if graphical technique unsuitable
Position synthesis 5 Chapter 6 - Velocity Analysis Graphical velocity analysis - sections 6.0 - 6.2 Instantaneous centers of velocity - sections 6.3 - 6.4 Analytic solution for velocity - sections 6.7 - 6.9

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Position synthesis 6 Chapter 7 - Acceleration Analysis Graphical acceleration analysis - sections 7.0 - 7.2 Analytic acceleration analysis - sections 7.3 and 7.5
Position synthesis 7 Chapter 11 - Dynamic Force Analysis Review 10.0 - 10.8 independently Introduce matrix solution techniques in Chapter 11 Apply to single link in 11.0 - 11.2 Apply to fourbar in 11.4 Discuss kinetostatic vs. dynamic analysis Develop solution for dynamic analysis

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Position synthesis 8 Chapter 4 - Analytic Position Analysis A vector can be represented by a complex number Real part is x-axis Imaginary part is y- axis Useful when we begin to take derivatives Real Axis Imaginary Axis Point A R A θ R  cos  θ jR  sin  θ
Position synthesis 9 Derivatives, Vector Rotations in the Complex Plane Taking a derivative of a complex number will result in multiplication by j Each multiplication by j rotates a vector 90° CCW in the complex plane Real Imaginary R A R B = j R R C = j 2 R = -R R D = j 3 R = - j R A B C D

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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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PositionAnalysis - Analytic Approach to Mechanism Design...

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