Overview

This is just a random though dump as I dig into the design and math of the lynchpin configuration.

Design

To start, the Lynchpin frame was designed Terrence Howard as a novel airframe with the abillty to sustain flight in all 6 axes. His Website can be found here: https://www.terryslynchpins.com/pages

The Lynchpin frame is built around the collapsed tetrahedron. Let’s dive into the design! If we take a Tetrahedron with a vertex radius of 1 unit, the resulting collapsed triangle has the sides lengths of \[x, \; x \sqrt{10}, \; \frac{1}{3} x\] with \(x\) being both the radius of the sphere and the hypotenuse. More math here… However, if we look at the lines connecting the motors to the origin, things look a lot more simple. Each of the six lines are tangent to each other, so we can simplify the design to just \(x \pm , y \pm , z \pm \) vectors. Notice the motors are positioned tangentially to the inverted pair. Now the Kinamatic model becomes much more simple.