High speed camera fixture analysis
Computers have the ability to crunch large amounts of information and solve multiple equations much faster than any person can do. Modeling real objects and situations in math is a common practice. Such variables and relationships can be understood and optimized for a particular application. This project analyzes a linkage device within high speed film cameras. This is used to feed film very quickly. Given were closed loop equations for a specific linkage length.
The linkage lengths a1, a2 and a3 were given for this application. The idea was to predict the motion of the linkage at the end of the hook. This will produce a path for which the apparatus will travel for each rotation.
I first modeled the linkage with the given parameters in SolidWorks to provide a visualization of the system. In SW, the user can manipulate the parts, which provided me an idea of what the path would look like.
Also provided were the relationships for the position of the hook. However, in order to map out the path, there are three unknowns that need to be solved. The equations are not straightforward, but can be solved using Mathematica. A good deal of coding needs to be done to solve these equations. I produced the following code to determine the three different angles.
I had the program print out the solutions for a range of angles from 0 to 2pi.
With this information, I can then plug the angles into the coordinate equations to plot the path of the hook.
As a result, this is the predicted path that the linkage assembly will produce at the hook.
To confirm the model, I superposed the image produced by Mathematica into my SolidWorks model. As it turns out, my coding was correct and predicted the exact path. With these tools, we can then manipulate the linkage lengths and understand how the path changes. The system can then be designed for different applications without having to build a single product.
