During my senior year at yale I was an undergraduate research assistant in the Yale Biomechanics and Controls lab. While there I designed & conducted an experiment to produce a geometric theory that models limb movement using joint surface features.

The final experimental set up is shown here. The three key principles are incorporated in this experimental set-up. The translation stage applies a translation shown by the red arrow. The load cell measures a force. Then, the rotation stage can be used to accurately rotate the joint substitute. Additionally, five free degrees of freedom are produced through the use of the XY planar stage, and the 2D rotation stage. It is important to note in the bottom left hand corner there is a new coordinate axis. This coordinate axis comes from the readings that the load cell takes, which will be important in the experimental results.

Abstract – When recreating species that no longer exist, paleontologists aim to put together bone structures to try to determine how that species may have moved. We aim to quantify their work by producing a geometric theory that can determine how a limb moves based on the surface geometry at its joint. Previous work has concluded that the movement in joints is determined by the surface geometry of adjoining bones and the attachment pattern of surrounding ligaments. However, we believe by producing a predictive geometric model we can determine joint displacement purely based on the principal curvatures of the articular surfaces of the joint. We aim to design an experiment that will allow us to predict movement capabilities at a joint based purely on the principal curvatures of the articular surfaces. To do this we have designed an experiment that will be used on a chicken knee bone. The experiment incorporates three key principles. First, we will apply a known displacement to one end of the bone. Second, we will measure a force at the other end. Third, we will rotate the joint about its neutral axis, and repeat displacement and measurements until we have data about all 360 degrees of the joint. With these three key principles, we can use Hooke’s Law to determine stiffness at a given orientation, and ultimately determine which directions are the soft and stiff directions of the bone. Afterwards, this data can be compared to CT scans of the joint, which will be used to create a geometrical relationship between surface curvature and displacement.

Below you can find a video of an example experiment:

Below is a video recording of a presentation of my work:

The powerpoint slides used in the above presentation are presented below:

A detailed report is also found below: