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pset_III-06-2 - MMAE 350 D Rempfer Problem Set III Page 1...

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MMAE 350 D. Rempfer Problem Set III Page 1 of 2 Due Date: September 27, 2006 1. We want to write a M ATLAB function crankangle that can give us the crank an- gle α of the crank drive shown on the right, given the vertical position s of the piston. The function should take as its input parameters the radius r of the crank, the length l of the con- necting rod, and the piston position s measured as shown in the figure. Thus the function will roughly have the following structure: function alpha=crankangle(r,l,s) ... alpha=...; a. What is the equation describing the piston position s as a function of r , l , and α ? b. If the ratio of connecting rod length over crank radius becomes very large, l/r 1, then the above equation can be approximated by a much simpler relation. What is the equation for the approximate piston position in this case? α c. Write a M ATLAB function, spiston(r,l,alpha) that takes r , l , and α as its input, and provides the piston position s as the output, plus a function dspiston(r,l,alpha) which provides the derivative of the piston position with respect to the crank angle. d. With these preparations out of the way, you can now code the M ATLAB function crankangle .
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