Computational Methods for FIRST Engineers: Mathcad Webinar 3
With the school year in full swing, Robotalk Webinar 3 focused on computer algebra symbolics (CAS) and numerical solve blocks. The preparation of future engineers typically involves years of symbolic work in algebra, calculus, linear algebra and differential equations. Later, engineering students learn (and engineers employ) numerical methods to solve many of the problems that they face. For FIRST participants, Mathcad Prime provides a platform where both symbolic and numeric solutions can be used, sometimes interchangably. As a result, students can gain experience and confidence in using these methods while solving real problems for their FIRST teams.
All of the Mathcad files used in the webinar are available for download at the link below. If you have problems with the video or the files, please email -.
The first half of tonight's webinar focused on Computer Algebra Symbolics or CAS. Most high school students are familiar with CAS through phone apps, graphing calculators, or websites that offer CAS capabilities. Mathcad Prime's CAS tools are available directly within the worksheet. Because of this, students may find Mathcad Prime to be a good platform for completing or checking homework in mathematics classes. The CAS examples that were used in tonight's webinar were:
Symbolic Derivation of the Quadratic Formula.mcdx
This worksheet derives the quadratic formula using Mathcad's solve command. A function is defined that accepts the coefficients of a polynomial in standard form and calculates the roots of a parabola. CAS tools are also used to find the vertex of the parabola.
Safe Load on a Beam.mcdx
This worksheet demonstrates the use of CAS to solve engineering problems from a common course of study, such as engineering statics.
Curve Driving Generator.mcdx
Based on post to Chief Delphi, this worksheet demonstrates the use of a Mathcad to derive a path for a robot passing from one point to another on an FTC field. A model is created by solving a system of equations using matrices.
After demonstrating Mathcad's CAS capabilities, Mathcad's Solve Block was used to show how numerical methods can be used to derive exact solutions to problems where constraints can be expressed as a system of equations. A solve block is a powerful capability when used correctly. Three examples were used to introduce the Solve Block structure and to demonstrate its power.
Cubic Polynomial Intersection Solve Block.mcdx
This file demonstrates how the Solve Block can be used to find the exact point of intersection between two curves, if the equations for each curve are known. In this example cubic polyniomials are used. Guess values for the numerical method are taken from a plot of the curves. The numerical solver find is employed to derive the x- and y-coordinates of the intersection point.
Angle Solve Block.mcdx
Based on a suggestion from a team in last year's FRC competition, this worksheet demonstrates how to use a Solve Block to find the launch angle for a basketball based on the known exit velocity from the launcher. The worksheet begins with the derivation of the formula to use as a constraint in the solve block. Thus, the worksheet is a self-documenting reference for FIRST teams to use to learn about both the physics of projectile motion and the use of Mathcad solve blocks.
Trapezoidal Prism Volume with Design Change.mcdx
This example extends an earlier worksheet by adding a design change to a worksheet documenting an initial concept design. The design change encourages the use of Mathcad's maximize function within a Solve Block to generate input parameters that lead to an optimal design.
All of the files mentioned above are in the folder Webinar 3 Mathcad Files.zip that is attached to this blog post. Next week's Webinar will highlight the use of Matrices to manage data. We will also talk about how Mathcad's built-in programming capabilities enable users to work with data in a worksheet. In order to register for this and other upcoming Robotalk Webinars, please visit our FIRST Program page.