For the problems listed below, print out a shaded isometric view (3D view) and a view of the part in the xy plane before you extrude or revolve it (show a few dimensions on this 2D plot):
2. Problem 1 of chapter 2 of the Parametric Modeling workbook.

3. Problem 4 of chapter 2 of the Parametric Modeling workbook.

1. Implement the parametric equation of a line in Mathcad using the points (1,5) and (8,20). Present your Mathcad worksheet and the resulting Mathcad plot for your homework.

2. Implement the parametric equation of a circle in Mathcad with a radius of 10. Present your Mathcad worksheet and the resulting Mathcad plot for your homework. Show plots for 12 and 80 line segments that work to build the circle.

3. Write your first or last name using the Bezier Mathcad file passed around in class. Show how you arrived at your control points by turning in a hand written copy of each letter on a piece of graph paper with the control points indicated (as on the class handout). You can reference the Mathcad file handed out in class, but do not copy an electronic version of the file as you implement your solution. Turn in all of the required Mathcad worksheets and the plot of your name.

2. Consider a square (in the x-y plane) that is defined by the points (1,1), (2,1), (2,2) and (1,2). Make a Mathcad worksheet to complete the following:
(a) Print out a plot of the square without any transformations.
(b) Reflect your square about the y axis.
(c) Scale your square so that it is 1/3 as large in x and 2 times as large in the y. 
(d) Translate your square -4 in the x direction.
(e) Rotate your square 45 degrees counterclockwise.
(f) Translate your square to the origin (so that the original point (1,1) is moved to the origin), rotate by 45 degrees clockwise, then translate your square back to the original position (undo the first translation). This should result in a 45 degree clockwise rotation about point (1,1).

Start at the original position for (b) through (f), and print out plots for each transformation.  Make sure the plots are big enough to take up about 1/2 of a page and that the dimensions in the x and y directions are clearly showing.  Write each transformation matrix by hand on the printout of (a) through (f) so that I can clearly see the transformation matrix applied.

Print out your entire Mathcad file for (f).

3. Go through chapter 5 of your I-DEAS 10 workbook entitled "Parametric Constraints Fundamentals." Using the techniques presented in this chapter, draw part 3 on the handout given in class. Create and establish three parametric relations for the part, and identify these features on your part (you can annotate your part by hand). Print out a 2D drawing with all the dimensions possible as well as a 3D drawing.

2. Rotate the bowl in problem 1 by 30 degrees counterclockwise about the x axis (counterclockwise when looking down the x-axis toward the origin). Print out a 3D plot of the rotated bowl and show your transformation matrix  (by hand or in Mathcad).

3. Translate the rotated bowl in problem 2 away from the origin. The x, y and z translation distances should be equal to the radius of the bowl (NOTE: This is different from what I said in class, since translating the bowl by xmean, ymean, and zmean would lead to no translation at all if the bowl in problem 1 was truly centered at the origin. I won't count off if you have already done it this way). Print out your entire Mathcad worksheet for this problem. The worksheet should include the transformation matrices in problems 2 and 3 as well as the 3D plot of the final translated and rotated bowl.

1. Optimize a kingpost truss for minimum weight as in class for a span of 60 inches, an applied load of 1000 lbs, a yield strength of 40,000 psi, and a specific weight of the steel members of 0.284 lbs per cubic inch. However, include the additional influence of the potential buckling of members in compression (assume that the modulus of elasticity is 30,000,000 psi). Annotate your Mathcad worksheet to explain your work.  

a. Print out a plot containing four lines: one composite objective function that includes the influence of all members considering yielding and buckling failure, one for member AB in compression, one for member AD in tension, one for member BD in tension, and one for member AB considering buckling.
b. Give the optimum weight of the truss.
c. Give the diameter of the members at this optimum weight.

2. Find a public domain computer program or subroutine (such as CONMIN) on the web that can be used for constrained optimization problems.  Write a couple of paragraphs detailing what the program does and how it can be utilized to solve an optimization problem.  Give the  link(s) to the web page(s) where you found this information.

3. From http://www.ae.su.oz.au/wwwdocs/note1.html, define give some applications of shape optimization to continuum structures.

1. Complete the chapter in the I-DEAS workbook entitled "Assembly Modeling – Putting It All Together." This is Chapter 12 in the I-DEAS 10 workbook. Print out 3D views of each part as well as a 3D view of the final assembly. This will also require that you draw the bracket which is described in Chapter 11.
 
 2. On your own, draw an assembly that has at least three parts (you pick what you want to draw). Print out 3D views of each part and a 3D view of the assembly.

The homework solution is given here.