Projective geometry for human motion, with an application to injury risk

We give an exposition of Plucker vectors for a system of joint axes in projective 3-space. We use Plucker vectors to analyse dependencies among joint axes, and in particular show that two rotational joints rigidly joined by a bar and each with 3 degrees of freedom always forms a 5-dimensional system. We introduce the concept of reduced redundancy in a dependent set of projective Lines, and argue that reduced redundancy in the axes of a body position increases injury risk. We apply this to a simple two-joint model of bowling in cricket, and show by analysis of some experimental data that reduced redundancy around ball release is observed in some cases.