Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves

A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of $n$-copies of a rigid body joined together by hinges to form a ring. Each hinge joint has its own axis of revolution and rigid bodies joined to it can be freely rotated around the axis. The family includes the famous threefold symmetric Bricard6R linkage also known as the Kaleidocycle, which exhibits a characteristic "turning over" motion. We can model such a linkage as a discrete closed curve in $\mathbb{R}^3$ with a constant torsion up to sign. Then, its motion is described as the deformation of the curve preserving torsion and arc length. We describe certain motions of this object that are governed by the semi-discrete mKdV equations, where infinitesimally the motion of each vertex is confined in the osculating plane

指尖部再建術後における患者満足度とハンドパフォーマンスについての後ろ向き検討

Introduction: Hand performance tests that evaluate hand dexterity and use in daily living have been frequently used to evaluate outcomes in patients with various hand disorders but not in patients with fingertip injuries. The present study aimed to evaluate patient satisfaction and hand performance following digital artery flap reconstruction for fingertip injury and identify factors associated with these outcomes. Methods: This retrospective cohort study included 25 patients with amputation injuries at our institution between 2003 and 2013. Patients with amputations at the Tamai 1 or 2 zone of their index (14 patients) or middle finger (11 patients) who underwent digital artery flap surgery and were followed up for > 1 year were included. Follow-up evaluations were conducted at an average of 44 months postoperatively (range, 12–105 months). The primary outcomes were patient satisfaction and hand performance determined by a 4-grade Likert scale and the Purdue Pegboard test, respectively. Secondary outcomes were recovery of sensitivity measured by Semmes–Weinstein monofilaments, total active finger motion (TAM), and tip pinch strength. Results: There were no postoperative complications. Patient satisfaction was rated as fair, good, and excellent, in 1, 15, and 9 patients, respectively. The average hand performance test scores were significantly lower in the affected finger than the adjacent finger (22 vs. 30, respectively; p < 0.05). The mean ± standard deviation (SD) sensitivity test score was 3.5 ± 1.6 (range, 2.4–4.0). The average percentage TAM and tip pinch strength compared with the contralateral hand were 82 (range, 45–100%) and 82% (range, 60–112%), respectively. The hand performance score significantly correlated with the recovery of sensitivity and age (r = – 0.42 and 0.43, respectively; both p < 0.05). Patient satisfaction was significantly correlated with TAM (r = 0.42, p < 0.05) and tended to correlate with the recovery of sensitivity (r = – 0.395, p = 0.051). Conclusion: Although reconstructed fingers had a lower performance score than the adjacent fingers, patient satisfaction with flap surgery was relatively high. Recovery of finger sensitivity contributed to patient satisfaction and enhanced dexterity of motor skill activities following fingertip reconstruction.博士（医学）・乙第1410号・平成29年11月24日Copyright © 2017 by Thieme Medical Publishers, Inc.This journal is published under the Creative Commons license CC BY-NC-ND (Attribution-NonCommercial-NoDerivatives : https://creativecommons.org/licenses/by-nc-nd/4.0/)The definitive version is available at " http://dx.doi.org/10.1055/s-0037-1604157