論文摘要

動態單側骨外固定器已廣泛地使用於治療長骨骨折或是骨頭之不正常癒合，在治療過程中使得骨折部位整復(reduction)讓骨骼得到完全的復位，加上利用骨外固定器充分的穩定性和結構之靈敏度，能提高在手術過程當中的效率，使得骨折斷端部分得以快速癒合，同時能夠讓骨頭增長。骨外固定器在調整過程中，由於具有三個自由度之球關節不易控制，而過多絞接關節會增加結構複雜度。

因此，本文研究目的主要參考兩組商品化骨外固定器Orthofix與Dynafix之機構設計與關節排序，並根據文獻提出之概念性骨外固定器結構加以簡化，並設計出新型單側骨外固定器。本文運用機器人學空間座標之齊次轉換矩陣建立運動鏈方程式，以計算出Orthofix、Dynafix以及新型骨外固定器之各個關節的調整範圍。

調整範圍分析結果得知，Orthofix、Dynafix與新型三種骨外固定器調整範圍可藉由齊次轉換矩陣運動鏈分析求出，再經由電腦模擬方式驗證數值解的正確性。透過電腦模擬的方式可得知，在不同數值解之結果會有不同的復位路徑，同時骨外固定器各個關節調整角度和方向也會有所不同，此外本文也針對不同初始條件下模擬斷骨復位路徑，其結果透過電腦模擬也符合數值解之正確性。最後本文也針對三種骨外固定器之機構設計概念、關節排序、自由度與調整範圍進行探討與分析。

Abstract

The dynamic unilateral external fixators have been widely used to treat long bone fractures, non-union, and malunion. They can easily correct the residual fracture deformity and achieve the fracture reduction. However, the past designs of external fixators had disadvantages of difficult to control the directions of ball-and-socket joints and complicated structure of hinge joints. The purpose of this study was to design a new external fixator based on the designs of two commercial external fixators (Orthofix & Dynafix) and the structure of a conceptual fixator from the related work.

The numerical models were developed as rigid linkage systems with use of the 4×4 homogeneous transformation matrices and the kinematic chain theory. The rotations and translations at each joint of three kinds of fixators (Orthofix, Dynafix, and New external fixator) were calculated to correct bone deformities at the fracture site. The kinematic equations of each external fixator were solved by the least square optimization method, and the numerical solutions were validated by computational simulations.

The results showed that the fracture reduction paths of three kinds of fixators can be successfully acquired, and the correctness of the numerical solutions of them is confirmed. In conclusion, the new external fixator had similar adjustability and simpler structure as compared with Orthofix. The result of this study can help the designers to improve external fixators and give the selection information to the surgeons.

參考文獻
[1]A. F. T. Mak and T. K. K. Koo, “A knowledge-based computer-aided system for closed diaphyseal fracture reduction,” Clinical Biomechanics, Vol. 22, pp. 884-893 (2007)
[2]E. Y. S. Chao, T. K. K. Koo and A. F. T. Mak, “Development and validation of a new approach for computer-aided long bone fracture reduction using unilateral external fixator,” Journal of Biomechanics, Vol. 39, pp. 2104-2112 (2006)
[3]Austin T. Fragomen, Daniel O. Kendoff, Andrew D., Pearle, Mustafa Citak, and S. Robert Rozbruch, “Computer Navigation and Fixator-Assisted Femoral Osteotomy for Correction of Malunion After Periprosthetic Femur Fracture,” Journal of Arthroplasty, Vol. 25, pp. 1-7 (2009)
[4]Soon-Geul Lee and Yoon-Hyuk Kim, “Computer and Robotic Model of External Fixation System for Fracture Treatment,” ICCS, pp. 1081-1087 (2004)
[5]Simon Winkelbach, Ralf Westphal, Thomas Gösling, Markus Oszwald , Tobias üfner, Christian Krettek and Friedrich M. Wahl, “Automated Robot Assisted Fracture Reduction,” Advances in Robotics Research, pp. 251-262 (2009)
[6]Markus Oszwald, Ralf Westphal1, Jan Bredow, Daniel Klepzig, Simon Winkelbach, Tobias Hüfner, Christian Krettek, and Friedrich Wahl, “Robot Assisted Fracture Reduction,” Experimental Robotics, pp. 153-163 (2008)
[7]Yeong-Jeong Ou, “Kinematic adjustability of unilateral external fixators for fracture reduction and alignment of axial dynamization,” Journal of Biomechanics, Vol. 42, pp. 1974-1980 (2009)
[8]Yoon H. Kim, Raymond W. Liu, David C. Lee, Nozomu Inoue, Terry K. Koo, Edmund Y. S. Chao, “Computational simulation of axial dynamization on long bone fractures,” Clinical Biomechanics, Vol. 20 pp. 83-90 (2005)
[9]宋晏仁、游祥明、古宏海、傅毓秀和林光華，解剖學，華杏圖書出版社，第152-153頁 (2004)
[10]黃啟仲、陳偉淦等，大體解剖學，義軒圖書出版社，第601-604頁 (1988)
[11]麥麗敏、王錫崗等，簡明解剖生理學，匯華圖書出版有限公司，第 117-121頁 (2003)
[12]R. J. Minns, G. R. Bremble and J. Campbell, “The geometrical properties of the human tibia,” Journal of Biomechanics, Vol. 8, pp. 253-255 (1975)
[13]許文賢, 「脛骨骨隨內釘之有限元素分析」，碩士論文，國立台灣科技大學，台北 (2002)
[14]C.B. Howard, A. Simkin, Y. Tiran, S. Porat, D. Segal and T. Mattan, “Do axial dynamic fixators really produce axial dynamization?,” Injury, Int. J. Care Injured, Vol. 30, pp. 25-30 (1999)
[15]F. Behrens and K. Searls, “External fixation of the tibia. Basic concepts and prospective evaluation,” Journal of Bone and Joint Surgery, Vol. 68, pp. 246-254 (1986)
[16]Thakur A. J., “External fixators. In: Thakur, A.J. (Eds), The Elements of Fracture Fixation,” Churchill Livingstone, New York, pp. 147-176 (1997)
[17]Yoon Hyuk Kim, Nozomu Inoue and Edmund Y. S. Chao, “Kinematic simulation of fracture reduction and bone deformity correction under unilateral external fixation,” Journal of Biomechanics, Vol. 35, pp. 1047-1058 (2002)
[18]溫志杰，「骨外固定器及肩關節活動之運動學分析」，碩士論文， 國立台灣大學，台北 (2003)
[19]宋長耀，「利用齊次轉換矩陣分析骨外固定器之調整範圍與肱骨骨內固定器之固定姿勢」，碩士論文，國立台灣大學，台北 (2002)
[20]Kavin Karunratanakul, Jan Schrooten and Hans Van Oosterwyck, “Finite element modelling of a unilateral fixator for bone reconstruction: Importance of contact settings,” Medical Engineering & Physics, Vol. 32, pp. 461-467 (2010)
[21]M. Viceconti, A. Sudanese, A. Toni, and A. Giunti, “A software simulation of tibial fracture reduction with external fixator,” Computer Methods and Programs in Biomedicine, vol. 40, pp. 89-94 (1993)
[22]Agrawal S. K., and Sun, L., “Regional structures of free-floating robots: a comparative study of the workspace,” International Journal of Robotics and Automation, Vol. 12, pp. 58-64 (1997)
[23]Bonev I. A., and Ryu, J., “A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators,” Mechanism and Machine Theory, pp. 1-13 (2001)
[24]Marco Ceccarelli and Sorli M., “The effect of design parameters on the workspace of a Turin parallel robot,” International Journal of Robotics Research, Vol. 17, pp. 886-902 (1998)