Factorization of Dual Quaternion Polynomials Without Study's Condition.

In this paper we investigate factorizations of polynomials over the ring of dual quaternions into linear factors. While earlier results assume that the norm polynomial is real ("motion polynomials"), we only require the absence of real polynomial factors in the primal part and factorizability of the norm polynomial over the dual numbers into monic quadratic factors. This obviously necessary condition is also sufficient for existence of factorizations. We present an algorithm to compute factorizations of these polynomials and use it for new constructions of mechanisms which cannot be obtained by existing factorization algorithms for motion polynomials. While they produce mechanisms with rotational or translational joints, our approach yields mechanisms consisting of "vertical Darboux joints". They exhibit mechanical deficiencies so that we explore ways to replace them by cylindrical joints while keeping the overall mechanism sufficiently constrained.

Poor accuracy of plain radiographic measurements of prosthetic migration and alignment in total ankle replacement.

BACKGROUND: The rotational position of the leg substantially influences measurements in ankle radiographs after total ankle replacement (TAR). The aim of our study was to further specify the influence of different projections on radiographic parameters used to assess component position after TAR. METHODS: The effect of varying degrees of internal rotation, flexion, and ab-/adduction on reference lines in anteroposterior and lateral ankle radiographs was investigated in a cadaveric TAR model. Observed variations were then compared with those found in 34 consecutive patients that received a HINTEGRA total ankle prosthesis in our department. RESULTS: A change of rotation of 20° resulted in a variation of measured reference lines of more than 1.3 cm in anteroposterior radiographs and more than 1 cm in lateral radiographs in our experimental setting. Even higher intraindividual changes of up to 1.4 cm were observed in our in vivo series. CONCLUSIONS: The findings suggest that rotational position of the leg highly influences measurements in ankle radiographs after TAR. It further raises the question, if previously described radiographic parameters do provide accurate information for the outcome after TAR in clinical routine as suggested in literature.