Mathcad Tips

PTC Mathcad Community Challenge is a bimonthly event where we pose a math problem for you to collaborate and solve using Mathcad Prime.

This month’s challenge is related to electrical engineering. We have a simple circuit with an electrical potential of 220 Volts. Initially we have a single 10 Ohm resistor. Then we add a second resistor in parallel, with 10% higher resistance. Then we add a third resistor in parallel, with 10% higher resistance than the previous resistor. And so on. Calculate the current in the circuit for the single resistor case. Calculate the resistance of each additional resistor and current through each resistor for 2, 3, 4, 5, and 10 resistors in parallel. Can you write a function or program that calculates the resistance of each resistor and current through each resistor for n resistors in parallel? These calculations are fairly straightforward, so it will be interesting to see what tools – vectors, matrices, loops, plots, charts, etc. – that you use to solve the problem. As always, how you document your calculations is important as your worksheet will be visible to the community. Here is an example of three resistors in parallel, as drawn in Creo Schematics:   Find the Mathcad Community Challenge Guidelines here!

This month's challenge is another geometry-based challenge - but it's non-Euclidean geometry. Given the following three points on a circle of radius 10 units, calculate the area of the spherical triangle: (5.339, 6.948, 4.819) (-4.018, -3.703, 8.375) (6.455, -6.679, -3.705) (Note that the point coordinates are rounded to three decimal places.)   Optional: Can you write a program or function that calculates the area for any three points on the surface? Is there a symbolic evaluation for three generic points (a,b,c), (d,e,f), and (g,h,k)?   Here is a 3D model in Creo 9 of the sphere and points:   Find the Mathcad Community Challenge Guidelines here!   Edit: the coordinates of the second point were incorrect. Wildly incorrect. I have no idea how I wrote down the wrong numbers.

The first two challenges were biased towards mechanical engineering. May’s challenge pertains to geometry. Create a worksheet in which you calculate (1) the diameter of a circle and (2) the length of a side of a square that yields the minimum combined area for a combined perimeter of 1 meter. This is an optimization problem. What tools within Mathcad can provide you with a result? Optional: How can you depict the results? Can you use a 2D plot or Chart Component to visualize the answer? Find the Mathcad Community Challenge Guidelines here!  

Let’s face it, planetary gears are cool. They are used in all kinds of mechanisms, including transmissions, motors, and turbines. Your challenge, should you choose to accept it, is to use Mathcad to build a worksheet that calculates the gear ratios and output speeds of a planetary gear under different configurations. The math behind the gear ratios is straightforward. But users should be able to select: The sun or planet carrier as the input; The planet carrier or ring as the output; and, The ring, sun, or planet carrier as the stationary component. How can the user select the desired component? How can you add intelligence to the worksheet to prevent an incorrect combination of input, output, and stationary? What inputs do you want for your calculator? You will have to make some choices. Your choices could include: Number of planets Number of teeth Component diameters Module / pitch Tools that you might consider include Combo boxes, programs, and functions involving strings. Here are some technical references to get you started: KHK Gears Instructables How Stuff Works Once again, this is a great project for students to work on in teams. Make the worksheet as simple or as complicated as you want. Others can build on your work, and you can build on others. Let’s see what the community can create! Good luck!   Find the Mathcad Community Challenge Guidelines here!

Mathcad Contest Idea - January 2022 Plane Truss Mechanics Can you use Mathcad to solve this problem?   This comes from page 88 of “An Introduction to the Mechanics of Solids,” by Stephen H. Crandall, Norman C. Dahl, and Thomas J. Lardner. This was the text for the first mechanical engineering class (2.01 Mechanics) that I took my sophomore year at MIT way back in 1989. You can find the book for as little as $5 on Amazon. It shows three different solutions for the problem, including: closed-form solutions involving equilibrium of forces and the beam-deflection equation a computer program called IBM STRESS Castigliano’s theorem which solves via elastic energy. Any introductory mechanics text or a Schaum’s Outline should guide you to a solution. As with the other contests that will follow this one, the point is not the answer to the problem, but your execution of the solution. Some ideas you may consider including in your worksheet: Allowing the user to change the material via a Combo Box Input Controls. Depicting the results with a Chart Component, such as the truss in the deformed shape, or the deflection at D due to changing input loads. Making the problem more open-ended, such as using matrices and programming for different geometry and loading. Note that these are just ideas; I have not tried any of these. Maybe you can explore different approaches. The problem is simply a starting point. This is an excellent problem for a team to solve, especially for civil and mechanical engineering students. How would you tackle this problem in Mathcad?   Find the Mathcad Community Challenge Guidelines here!  

There's more to this Easter egg than meets the eye.  This Easter Egg was created with a Mathcad Prime 6.0 Surface Plot, all within PTC Mathcad.   Download the attached Mathcad Prime file (EE.mcdx), manipulate the surface plot display, and see if you can find the hidden message.    h/t Anji Seberino!