Instant center of rotation estimation using the Reuleaux technique and a Lateral Extrapolation technique

A mathematical model of a rolling wheel was used to investigate the errors encountered when the Reuleaux technique is employed to estimate planar instant centers of rotation (ICRs). The investigation showed that large errors can result when this pole measurement technique is applied to objects rotating more than 12°. The investigation also showed that these errors can be substantially reduced by applying a new Lateral Extrapolation technique to the pole data. When the Reuleaux technique is applied to marks on a 10 cm radius wheel, the resulting offset errors from the ICR are 3.96 cm for a 45° roll and 1 cm for a 12° roll. Following lateral extrapolation, these offset errors reduce to 0.52 cm for the 45° roll and less than 0.04 cm for the 12° roll. Thus, the extrapolation technique is over seven times more accurate for a 45° roll, and over 25 times more accurate for a 12° roll. The extrapolation technique has been validated with the model for joints that exhibit both slip and roll, such as the knee. As joint ICR pathway measurement can be used to detect pathology, these accuracy improvements offer potential benefits for clinical applications.