mws_ind_inp_txt_spline_examples

mws_ind_inp_txt_spline_examples - 05.05.1 Chapter 05.05...

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Unformatted text preview: 05.05.1 Chapter 05.05 Spline Method of Interpolation – More Examples Industrial Engineering Example 1 The geometry of a cam is given in Figure 1. A curve needs to be fit through the seven points given in Table 1 to fabricate the cam. Figure 1 Schematic of cam profile. Table 1 Geometry of the cam. Point x   in. y   in. 1 2.20 0.00 2 1.28 0.88 3 0.66 1.14 4 0.00 1.20 5 –0.60 1.04 6 –1.04 0.60 7 –1.20 0.00 a) If the cam follows a straight line profile from 28 . 1  x to 66 .  x , what is the value of y at 10 . 1  x using linear splines. b) Find the cam profile using linear splines. 1 2 3 5 6 7 x y 4 05.05.2 Chapter 05.05 Solution a) Since we want to find the value of y at 10 . 1  x , and we are using linear splines, we need to choose the two data points that are closest to 10 . 1  x that also bracket 10 . 1  x to evaluate it. The two point are 28 . 1  x and . 66 . 1  x Then , 28 . 1  x 88 . ) (  x y , 66 . 1  x 14 . 1 ) ( 1  x y gives ) ( ) ( ) ( ) ( ) ( 1 1 x x x x x y x y x y x y      ) 28 . 1 ( 28 . 1 66 . 88 . 14 . 1 88 .      x Hence 28 . 1 66 . ), 28 . 1 ( 41935 . 88 . ) (      x x x y At , 10 . 1  x ) 28 . 1 10 . 1 ( 41935 . 88 . ) 10 . 1 (    y . in 95548 .  b) Going in increasing order of x-values, the first linear spline connects 20 . 1   x and 04 . 1   x . ) 20 . 1 ( 20 . 1 04 . 1 00 . 60 . 00 . ) (       x x y ), 20 . 1 ( 75 . 3   x 04 . 1 20 . 1     x (1) The rest of the splines are as follows....
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_ind_inp_txt_spline_examples - 05.05.1 Chapter 05.05...

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