Projective Geometry of Human Motion, with an Application to Injury Risk

We give an exposition of Plücker vectors for a system of joint axes in projective 3-space. We use Plücker vectors to analyze dependencies among joint axes and in particular to show that two rotational joints rigidly joined by a bar and each with 3 degrees of freedom always form 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.