Computer Assignment 1 Solution

Computer Assignment 1 Solution - 1 ሶ ሷ ൌ 0 ሺݐሻ...

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Unformatted text preview: 1 ሶ ሷ ൌ 0 ሺݐሻ ൌ ߠ ሶ ݐ ൅ ߠሺ0ሻ ൌ ݐ ௥ ௥ ൌ ݎሷ െ ݎߠ ሶ ଶ Since it is given that ܽ ௥ ൌ െܿݐ ଶ , we have, ܽ ௥ ൌ െܿݐ ଶ ൌ ݎሷ െ ݎߠ ሶ ଶ (4) ݎሷ ൌ െܿݐ ଶ ൅ ݎߠ ሶ ଶ (5) rom (2) and (5) we have, ݎሷ ൌ െܿߠ ଶ ൅ ݎߠ ሶ ଶ (6) erical simu ݔ ଵ ൌ ߠ ݔ ଶ ൌ ߠ ሶ ݔ ଷ ൌ ݎ ݔ ସ ൌ ݎሶ (7) ME 240: Introduction to Dynamics and Vibrations Mechanical Engineering Department The University of Michigan Fall 2008 Computer Assignment #1 Solution October 13, 2008 Question 1: The follower rotates with constant angular velocity ߠ = 1 rad/s , therefore we have, ߠ (1) ߠ (2) In polar co-ordinates, the radial acceleration ܽ , of the follower is given by: ܽ (3) Then, F Use the following state variables for num lation. Therefore the state equations can be written as follows: 2 ݔሶ ଶ ൌ 0 ݔሶ ଷ ൌ ݔ ସ ݔሶ ସ ൌ െܿݔ ଵ ଶ ൅ ݔ ଷ ݔ ଶ ଶ (8) The initial conditions for the state variables are as follows: ݔ ଵ,଴ ൌ 0 ݔ ଷ,଴ ൌ 0.3 ݔ ସ,଴ ൌ 0 (9) The MATLAB code to find the cam profile for c = 0.5 is as shown below: %-------------------------------------------------------------------------- %This program is ODE Solver for Computer Assignment #1 for ME 240. The %problem consists of cam-follower mechanism with certain initial conditions: %Created by: Vivek Vichare, GSI ME 240 - Fall 08--------------------------------------------- time interval. This means that we integrate the om t = 0 to pi/2. n,y0,options… ,parameter1,…,parameterN)--- ݔ ଵ ሶ ൌ 1 ݔ ଶ,଴ ൌ 1 File – main.m %-------------------------------------------------------------------------- % main.m clear all ; clc; ------------------------- %------------------------------------------------- % Define parameters m = 1; c = 0.5; %-------------------------------------------------------------------------- itions. % Define initial cond ; r0 = 0.3 rdot0 = 0; th0 = 0; thdot0 = 1; ------------------- %---------- % Define the fr %equation t_start=0; t_end=pi/2; ------------- %-------------------------------------------------------------...
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This note was uploaded on 04/08/2010 for the course MECHENG 240 taught by Professor Perkins during the Fall '09 term at University of Michigan.

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Computer Assignment 1 Solution - 1 ሶ ሷ ൌ 0 ሺݐሻ...

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