HW2_10_solns

HW2_10_solns - ME 563 HOMEWORK # 2 SOLUTIONS Fall 2010...

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ME 563 HOMEWORK # 2 SOLUTIONS Fall 2010 PROBLEM 1: (40%) Derive the equations of motion for the dual micromirror system shown below using both Newton-Euler techniques and Lagrange’s equations. Assume that the two racks, M r , experience only translational motion. The two mirrors, I cm , are free to swing about the pins that connect them to the two racks. Give all relevant information you need to solve the problem using the procedure developed in class. cm cm
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2 FBD Assumptions No slip between gears, racks and pinions. Gravity ignored. Gear contacts have zero normal force. Friction modeled as viscous damping. Racks have one degree of motion. Newton – Euler method For M 1 For M r2 : For I cm5 : For J 3 : For J 1 : For J 2 : For M r3 :
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For I cm4 : No slip constraints: Require 2 more equations since there are 14 unknowns and 12 equations. For M m5 : For M m4 : where There are now 14 equations and 14 unknowns, and x 1 , θ 1 , θ 4 and θ 5 can be found. Lagrange’s equations
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HW2_10_solns - ME 563 HOMEWORK # 2 SOLUTIONS Fall 2010...

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