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

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

2004-06-11

arxiv.org/abs/q-bio/0406024v1

Biology

Quantitative Biology

Quantitative Methods

19 pp, 4 figs. To be published in SIAM Journal on Applied Mathematics

Scientific paper

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.

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