Discrete Frenet Frame with Application to Structural Biology and Kinematics

The classical Frenet frame is a moving frame on a smooth curve. Connecting a sequence of points in space by line segments makes a discrete curve. The reference frame consisting of tangent, normal and binormal vectors at each point is defined as discrete Frenet frame (DFF). The DFF is useful in studying shapes of long molecules such as proteins. In this dissertation, we provide a solid mathematics foundation for DFF by showing the limit of the Frenet formula for DFF is the classical Frenet formula. As part of a survey of various ways to compute rigid body motion, we show the Denavit-Hartenberg (D-H) conventions in robotics are a special case of the DFFs. Finally, we apply DFF to solve the kink angle problem in protein alpha helical structure using data from NMR experiments.