Overview

The object of this project is to demonstrate your understanding of the analytical tools we have been studying in class, as well as your mastery of the Matlab techniques. To do so, your goal is to develop and simulate the equations of motion of a system of your choosing. Your system should be unique to you, be made of one or more rigid objects (i.e.  not particles nor non-rigid objects) and you should strive to include some more complex features, such as;

•  3-D rotations

•  Holonomic Constraints (links, slots, surfaces, wire tracks)

•  Non-holonomic Constraints (friction, damping, skates, rolling)

•  Sclerenomic and/or Rheonomic Constraints

• Applied Forces

•  Elastic Collisions  (done simply with events;  changes of direction can create interesting interactions)

Don’t try to include all of these (unless you are super ambitious), but your system should include some of these.  You should also make sure that you can solve for the equations of motion using at least two approaches (DAE and Euler-Lagrange).  If you choose to model a real system, try to recreate some existing footage (You don’t need to recreate anything exactly, just make general approximations to dimensions and masses). Finally, you should draw some conclusion based on the insight you have gained from modelling the system; perhaps a limitation on range of motion, or a plot of reaction force you could use to design a loading.

The length of the report is limited. Use this, and the grading scheme, as a guide to how much detail you include. Your work should be new (don’t resubmit something you have done in another course) and don’t include any feedback/active control systems (i.e. only use concepts we have explored in this course specifically).

Options for Choosing a System

You have 3 basic options.  The first is to select a real system, like the ideas discussed in class. Secondly, you can invent a system,such as a combination of skates and pendulums.  Thirdly, you have can choose the default project (no limit to how many people choose this); a double compound pendulum in 3-D. If you choose this, your discussion should consider the energy in the pendulum system to show that your equations preserve the conservation of energy.

Senior 4730 vs Masters 5730 and Executed Difficulty Criteria

This project is where the Masters students should distinguish themselves. Your investigation should include multiple initial conditions or constraints.   Each project will be scored on the difficulty attempted and ultimately executed. For instance, choosing the default system above will be worth 6 out of 10 for a student in 4730, and 4 out of 10 for a student in 5730.  To bring this score up to 10, you should extend the analysis of the pendulum to 3-bar, and n-bar respectively (though animations can be capped at some computationally reasonable length).

Submission

There are 3 parts to the submission. The Report is the main submission, which will be supported by a full copy of your Matlab code and a presentation of your animations.

1.  Report. Typed, or neatly handwritten, and submitted to Gradescope including;

(a)  Description of chosen system This should include an image/diagram, an explanation

of what the system is used for, and either; a description of the motion you intend to model from the reference video, or a prediction of the action if the chosen system doesn’t have a reference video. No more than 1 page

(b)  Setup of the Analytical Models This section should include the overall Free Body

Diagram of your system, and a description of any simplifying assumptions that you make.  If you have invented your own system, or chosen the default, then this section and the previous will overlap significantly and should be combined.  (Any individual FBDs of components should be kept for the next section.) No more than 1 page

(c)  Equations of Motion - Developed 2 Ways You should solve for the motion of the system with both the DAE and Euler-Lagrange approach.  In your DAE method, be sure to include your individual FBDs for each component as required. The object here is to layout the development of the solution, including constraint equations, reactions, collisions etc. You only need to develop the equations to the point that they are ready for Matlab.  Each section should be completed with a statement of the final equations such that they can be readily compared  Try  to  summarize  and  keep  under 4  pages, approx.  2 per method

(d)  Animation Still Frames Two images from your animation:  (i) at the start and (ii) at some later time.  The point here is to prepare the reader for what to expect in the animation, such that any buggy animation is understood.   The initial figure should be well annotated and show the system setup.  Annotation can be done via Matlab, Inkscape or Powerpoint etc.  The second image should show the trajectory after some time, capturing motion of interest.  If you are modelling a single rigid object, show the trajectories of multiple edges.  These figures should serve as introduction to your animation. 1 page

(e)  Discussion A brief discussion about the results, including any comparisons between

your animation and the reference video, potential problems and how you might address them, and any engineering insights that you got from conducting the analysis. This can include plots of reaction forces, internal tensions, or total energy etc.  1 page

2.  Matlab code. Submit to Canvas one zip file called YourName4730.zip or YourName5730.zip. It should be a compressed version of a single folder of Matlab files. It should be easy for graders to use the files for simple demonstrations.

3.  Presentation.  Demonstrate your working code and talk through the animations. You can expect the graders to have at least reviewed your report. You should be ready to show FBDs, your reference footage, and animations using both approaches.  The point is to complement your report, you don’t need to setup the entire problem again. (Roughly 5- 8 min)