為了手動器具的研發並預估其操作時的效果，許多人致力發展一套更準確而可靠的上肢肌肉骨骼分析模型。但在許多研究中的肌肉骨骼模型與肌力分析模式，常僅針對於上肢的單一關節之活動或是特定的動作。因此，本研究嘗試建立一S-SUCr-U肌肉骨骼模型，以期能分析上肢在操作各式器具時的各肌肉之出力和各關節負荷等。
本文首先分別簡介上肢的骨骼、關節及肌肉。而以Obstacle-set方法分別建立上肢驅動輪椅及上肢驅動復健機械手時之肌肉路徑與長度之分析模式。再針對肌肉繞經球、單圓柱及雙圓柱等三種障礙物時，其路徑與長度的演算法，分別提出一套最佳化模式以驗證其分析所得之結果的正確性。
接著將各個關節的負荷及肌肉之激發程度作為待求之未知數，並加入適當之限制條件讓肌力的作用能使關節結合，再配合Hill肌力模型建立可分析上肢肌力與關節負荷之靜力分析模式，且所建立者為二次規劃模式，故所得之結果應為全域最佳解。最後分別將此模式應用於上肢驅動復健機械手與上肢驅動輪椅的實例分析並討論其分析所得之結果。
本文所提出的模型及所建立的各種分析模式，應有助於進一步建立更完整的上肢肌肉骨骼模型；對於評估機器人輔助(Robot-assisted)之復健療程以及手動器具之設計亦應有其參考價值。

For the development of hand-tools and investigating their effects, there are many researchers attempting to construct a more precise and reliable musculoskeletal model of the upper limb. However, many of them focus on a particular joint of the upper limb or a specified motion to develop their musculoskeletal models and those for the muscular force analysis. The purpose of this study is to propose an S-SUCr-U musculoskeletal model, which can be applied on the analysis of muscular force and joint loads during operating various devices with upper limb.
Firstly the skeleton, joints and muscles of the upper limb are introduced. Then the obstacle-set method is adopted to build the analysis models of muscle paths and its lengths for propelling a wheelchair and driving a rehabilitation robot, and three models, based on the optimization techniques, are proposed to verify the single sphere, single cylinder and double cylinder obstacle-set algorithms.
Based on Hill-type muscular model and the static equilibrium of bones, the models for the muscle force and joint load analysis, of using an upper limb to operate a rehabilitation robot and to propel a wheelchair, are developed. These models are built as quadratic programming problems with considering joint-engagement constraints, and using muscle activations and joint forces as unknown variables. Furthermore, operating a rehabilitation robot and propelling a wheelchair are used as examples to show the usage of the models developed and to display the analysis results.
The musculoskeletal models and the analysis methodologies proposed in this study may aid on further design and development of hand-tools, and on the evaluation of robot-assisted rehabilitation treatments.

Angel, G.-A., Antonio, D. A.-E., Enrique, P.-R., Soraya, P.-N., and Luis P. R.-R., 2010, "Upper Limb Joint Kinetics During Manual Wheelchair Propulsion in Patients with Different Levels of Spinal Cord Injury," Journal of Biomechanics, Vol. 43, No. 13, pp. 2508-2515.
Argosy Publishing, 2010, http://www.visiblebody.com, 31st May.
Audenaert, A., and Audenaert, E., 2008, "Global Optimization Method for Combined Spherical–Cylindrical Wrapping in Musculoskeletal Upper Limb Modeling," Computer Methods and Programs in Biomedicine, Vol. 92, pp. 8-19.
Barhorst, A., and Schovanec, L., 2002, "Effects of Control Strategies on Stress Development in Skeletal Structures," Proceedings of the American Control Conference.
Blajer, W., Czaplicki, A., Dziewiecki, K., and Mazur, Z., 2010, "Influence of Selected Modeling and Computational Issues on Muscle Force Estimates," Multibody System Dynamics, Vol. 24, No. 4, pp. 473-492.
Blemker, S. S., and Delp S. L., 2006, "Rectus Femoris and Vastus Intermedius Fiber Excursions Predicted by Three-Dimensional Muscle Models," Journal of Biomechanics, Vol. 39, pp. 1383-1391.
Burgar, C. G., Lum, P. S., Erika S., Garber, S. L., van der Loos, M., Kenney, D., and Shor, P., 2011, "Robot-assisted Upper-limb Therapy in Acute Rehabilitation Setting Following Stroke: Department of Veterans Affairs Multisite Clinical Trial," Journal of Rehabilitation Research and Development, Vol. 48, No 4, pp. 445-458.
Chao, E., Y., S., 2003, "Graphic-based Musculoskeletal Model for Biomechanical Analyses and Animation," Medical Engineering & Physics, Vol. 25, pp. 201-212.
Charlton, I. W., and Johnson, G. R., 2001, "Application of Spherical and Cylindrical Wrapping Algorithms in a Musculoskeletal Model of the Upper Limb," Journal of Biomechanics, Vol. 34, pp. 1209-1216.
Cheng, E. J., Brown, I. E., and Loeb, G. E., 2000, "Virtual Muscle: A Computational Approach to Understanding the Effects of Muscle Properties on Motor Control,” Journal of Neuroscience Methods, Vol. 101, pp. 117-130.
Chumanov, E. S., Heiderscheit, B. C., and Thelen, D. C., 2007, "The Effect of Speed and Influence of Individual Muscles on Hamstring Mechanics during the Swing Phase of Sprinting," Journal of Biomechanics, Vol. 40 pp. 3555–3562.
Colombo, R., Pisano, F., Micera, S., Mazzone, A., Delconte, C., Carrozza, M. C., Dario, P., and Minuco, G., 2005, "Robotic Techniques for Upper Limb Evaluation and Rehabilitation of Stroke Patients," IEEE Transactions on Neural Systems and Rehabilitation Engineering, Vol. 13, No. 3, pp. 311-324.
Cooper, A., and Straker, L., 1998, "Mouse Versus Keyboard Use: A Comparison of Shoulder Muscle Load," International Journal of Industrial Ergonomics, Vol. 22, pp. 351-357.
Crowninshield, R. D., and Brand, R. A., 1981, "A Physiologically Based Criterion of Muscle Force Prediction in Locomotion," Journal of Biomechanics, Vol. 14, No. 11, pp. 793-801.
Damsgaard, M., Rasmussen, J., Visser, B., Christensen, S. T., Surma, E., and Zee, M. D., 2006, "Analysis of Musculoskeletal Systems in the AnyBody Modeling System," Simulation Modeling Practice and Theory, Vol. 14, pp. 1100-1111.
Dariush, B., Parnianpour, M., and Hemami, H., 1998, "Stability and a Control Strategy of a Multilink Musculoskeletal Model with Applications in FES," IEEE Transaction on Biomedical Engineering, Vol.45, pp. 3-14.
Davoodi, R., Brown, I. E., and Loeb, G. E., 2003, "Advanced Modeling Environment for Developing and Testing FES Control Systems," Medical Engineering & Physics, Vol. 25, pp. 3-9.
Desailly, E., Sardain, P., Khouri, N., Yepremian, D., and Lacouture, P., 2010, "The Convex Wrapping Algorithm: A Method for Identifying Muscle Paths Using the Underlying Bone Mesh," Journal of Biomechanics, Vol. 43, No. 13, pp. 2601-2607.
Desroches, G., Dumas, R., Pradon, D., Vaslin, P., Lepoutre, F.-X., and Chèze, L., 2010, " Upper Limb Joint Dynamics during Manual Wheelchair Propulsion," Clinical Biomechanics, Vol. 25, No. 4, pp. 299-306.
Dubowsky, S. R., Rasmussen, J., Sisto, S. A, and Langrana, N. A, 2008, "Validation of a Musculoskeletal Model of Wheelchair Propulsion and Its Application to Minimizing Shoulder Joint Forces," Journal of Biomechanics, Vol. 41, pp. 2981-2988.
Erol, D., and Sarkar, N., 2008, "Coordinated Control of Assistive Robotic Devices for Activities of Daily Living Tasks," IEEE Transactions on Neural Systems and Rehabilitation Engineering, Vol. 16, No. 3, pp. 278-285.
Formica, D., Zollo1, L., Guglielmelli, E., and Rodgers, M. M., 2006, "Torque-Dependent Compliance Control in the Joint Space for Robot-Mediated Motor Therapy," Journal of Dynamic Systems, Measurements and Control, Vol. 128, pp. 152-158.
Gao, F., Damsgaard, M., Rasmussen, J., and Christensen, S. T., 2002, "Computational Method for Muscle-Path Representation in Musculoskeletal Models," Biological Cybernetics, Vol. 87, pp. 199-210.
Garner, B. A., and Pandy, M. G., 1999, "A Kinematic Model of the Upper Limb Based on the Visible Human Project (VHP) Image Dataset," Computer Methods in Biomechanics and Biomedical Engineering, Vol. 2, No. 2, pp. 107-124.
Garner, B. A., and Pandy, M. G., 2000a, "The Obstacle-Set Method for Representing Muscle Paths in Musculoskeletal Models," Computer Methods in Biomechanics and Biomedical Engineering, Vol. 3, pp. 1-30.
Garner, B. A., and Pandy, M. G., 2000b, "Musculoskeletal Model of the Upper Limb Based on the Visible Human Male Dataset," Computer Methods in Biomechanics and Biomedical Engineering, Vol. 4, No. 2, pp. 93-126.
Garner, B. A., and Pandy, M. G., 2003, "Estimation of Musculotendon Properties in the Human Upper Limb," Annals of Biomedical Engineering, Vol. 31, No. 2, pp. 207-220.
Gatti C. J., and Hughes, R. E, 2009, "Optimization of Muscle Wrapping Objects Using Simulated Annealing," Annals of Biomedical Engineering, Vol. 37, No. 7, pp. 1342-1347.
Heintz, S., and Gutierrez-Farewik, E. M., 2007, "Static Optimization of Muscle Forces during Gait in Comparison to EMG-to-Force Processing Approach,” Gait & Posture, Vol. 26, pp. 279-288.
Holzbaur, K. R. S., Murray, W. M., and Delp, S. L., 2005, "A Model of the Upper Extremity for Simulating Musculoskeletal Surgery and Analyzing Neuromuscular Control," Annals of Biomedical Engineering, Vol. 33, No. 6, pp. 829-840.
Howarth, S. J., Pronovost, L. M., Polgar, J. M., Dickerson, C. R., and Callaghan, J. P., 2010, "Use of a Geared Wheelchair Wheel to Reduce Propulsive Muscular Demand During Ramp Ascent: Analysis of Muscle Activation and Kinematics," Clinical Biomechanics, Vol. 25, No. 1, pp. 21-28.
Hughes, A., Freeman, C., Burridge, J., Chappell, P., Lewin, P., and Rogers, E., 2009, "Upper Limb Rehabilitation of Stroke Participants Using Electrical Stimulation: Changes in Tracking and EMG Timing," IEEE 11th International Conference on Rehabilitation Robotics.
Kikuuwe, R., Yamamoto, T., and Fujimoto, H., 2008, "A Guideline for Low-force Robotic Guidance for Enhancing Human Performance of Positioning and Trajectory Tracking: It Should Be Stiff and Appropriately Slow," IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, Vol. 38, No. 4, pp. 945-957.
Kirihara, K., Saga, N., and Saito, N., 2010, " Design and Control of an Upper Limb Rehabilitation Support Device for Disabled People Using a Pneumatic Cylinder," Industrial Robot, Vol. 37, No. 4, pp. 354-363.
Kung, P.-C., Lin, C.-C. K., and Ju, M.-S., 2010, "Neuro-rehabilitation Robot-assisted Assessments of Synergy Patterns of Forearm, Elbow and Shoulder Joints in Chronic Stroke Patients," Clinical Biomechanics, Vol. 25, No. 7, pp. 647-654.
Langenderfer, J., LaScalza, S., Mell, A., Carpenter, J. E., Kuhn, J. E., and Hughes, R. E., 2005, "An EMG-Driven Model of the Upper Extremity and Estimation of Long Head Biceps Force," Computers in Biology and Medicine, Vol. 35, pp. 25–39.
Laurence, R., and Agnes, R.-B., 2006, "Shoulder Movements during the Initial Phase of Learning Manual Wheelchair Propulsion in Able-Bodied Subjects," Clinical Biomechanics, Vol. 21, pp. S45-S51.
Laursen. B., Sogaard, K., and Sjogaard, G., 2003, "Biomechanical Model Predicting Electromyographic Activity in Three Shoulder Muscles from 3D Kinematics and External Forces during Cleaning Work,” Clinical Biomechanics, Vol. 18 pp. 287-295.
Li, L., Tong, K., Song, R., and Koo, T. K. K., 2007, "Is Maximum Isometric Muscle Stress the Same among Prime Elbow Flexors, " Clinical Biomechanics, Vol. 22, pp. 874-883.
Louis, N., and Gorce, P., 2009, "Upper Limb Muscle Forces during a Simple Reach-to-Grasp Movement: A Comparative Study," Medical and Biological Engineering, Vol. 47, pp. 1173-1179.
Louis, N., and Gorce, P., 2010, "Surface Electromyography Activity of Upper Limb Muscle during Wheelchair Propulsion: Influence of Wheelchair Configuration," Clinical Biomechanics, Vol. 25, No. 9, pp. 879-885.
Mahoney, R. M., Van der Loos, H. F. M., Lum, P. S., and Burgar, C., 2003, "Robotic Stroke Therapy Assistant," Robotica, Vol. 21, No. 1, pp. 33-44.
Masia, L., Krebs, H. I., Cappa, P., and Hogan, N., 2007, "Design and Characterization of Hand Module for Whole-Arm Rehabilitation Following Stroke," IEEE/ASME Transactions on Mechatronics, Vol. 12, No. 4, pp. 399-407.
Menegaldo, L. L., Fleury, A. T., and Weber, H. I., 2003, "Biomechanical Modeling and Optimal Control of Human Posture," Journal of Biomechanics, Vol. 36, pp. 1701–1712.
Menegaldo, L. L., Fleury, A. de T., and Weber, H. I., 2004, "Moment arms and Musculotendon Lengths Estimation for a Three-Dimensional Lower-Limb Model," Journal of Biomechanics, Vol. 37, pp. 1447-1453.
Menegaldo, L. L., Fleury, A. T., and Weber, H. I., 2006, "A 'Cheap' Optimal Control Approach to Estimate Muscle Forces in Musculoskeletal Systems," Journal of Biomechanics, Vol. 39, pp. 1787-1795.
Mercer, J. L., Boninger, M., Koontz, A., Ren, D., Dyson-Hudson, T., and Cooper, R., 2006, "Shoulder Joint Kinetics and Pathology in Manual Wheelchair Users," Clinical Biomechanics, Vol. 21, No. 8, pp. 781-789.
Moody, C. B., Barhorst, A. A., and Schovanec, L., 2009, "A Neuro-Muscular Elasto-Dynamic Model of the Human Arm Part 2: Musculotendon Dynamics and Related Stress Effects," Journal of Bionic Engineering, Vol. 6, pp. 108-119.
Morrow, M. M. B., Hurd, W. J., Kaufman, K. R., and An, K. N., 2010, "Shoulder Demands in Manual Wheelchair Users Across a Spectrum of Activities," Journal of Electromyography and Kinesiology, Vol. 20, pp. 61-67.
Murray, I. A., and Johnson, G. R., 2004, "A Study of the External Forces and Moments at the Shoulder and Elbow while Performing Every Day Tasks," Clinical Biomechanics, Vol. 19, No. 6, pp. 586-594.
Ogihara, N., and Yamazaki, N., 1999, "Generation of Human Reaching Movement Using a Recurrent Neural Network Model," Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Vol. 2, pp. 692-697.
Ozawa, T., Furusho, J., Kikuchi, T., Akai, H., Fukushima, K., Fukuda, T., Tanida, S., Fujikawa, T., and Kano, S., 2010, "Development of Rehabilitation System for Upper Limbs, PLEMO-P3 System for Hemiplegic Subject (Motor Function Test for Assessment and Training, and Research for Development of Practical Type)," Transactions of the Japan Society of Mechanical Engineers, Part C, Vol. 76, No. 762, pp. 323-330.
Pal, S., Langenderfer , J. E., Stowe, J. Q., Laz, P. J., Petrella, A. J., and Rullkoetter, P. J., 2007, "Probabilistic Modeling of Knee Muscle Moment arms: Effects of Methods, Origin–Insertion, and Kinematic Variability," Annals of Biomedical Engineering, Vol. 35, No. 9, pp. 1632-1642.
Pigeon, P., Yahia, L., and Feldman, A. G., 1996, "Moment arms and Lengths of Human Upper Limb Muscles as Functions of Joint Angles," Journal of Biomechanics, Vol. 29, No. 10, pp. 1365-1370.
Rengifo, C., Aoustin, Y., Plestan, F., and Chevallereau, C., 2010, "Distribution of Forces Between Synergistics and Antagonistics Muscles Using an Optimization Criterion Depending on Muscle Contraction Behavior," Journal of Biomechanical Engineering, Vol. 132, No. 4, pp.1-10.
Rosen, J., and Perry, J. C., 2007, "Upper Limb Powered Exoskeleton," International Journal of Humanoid Robotics, Vol. 4, No. 3, pp. 529-548.
Rosati, G., Gallina, P., and Masiero, S., 2007, "Design, Implementation and Clinical Tests of a Wire-Based Robot for Neurorehabilitation," IEEE Transactions on Neural Systems and Rehabilitation Engineering, Vol. 15, No. 4, pp. 560-569.
Seth, A., and Pandy, M. G., 2007, "A Neuromusculoskeletal Tracking Method for Estimating Individual Muscle Forces in Human Movement," Journal of Biomechanics, Vol. 40, pp. 356-366.
Soetanto, D.,and Kuo, C-Y., 2002, "Improved Dynamics Model for Human Standing Posture Control Using Functional Neuromuscular Stimulation," International Journal of Systems Science, Vol. 33, No. 2, pp. 129-140.
Tang, G., and Wang, C.-T., 2010, "A Muscle-path-plane Method for Representing Muscle Contraction During Joint Movement," Computer Methods in Biomechanics and Biomedical Engineering, Vol. 13, No. 6, pp. 723-729.
Terrier, A., Vogel, A., Capezzali, M., and Farron, A., 2008, "An Algorithm to Allow Humerus Translation in the Indeterminate Problem of Shoulder Abduction," Medical Engineering and Physics, Vol. 30, No. 6, pp. 710-716.
Veeger, H. E. J., Rozendaal, L. A., and Van der Helm, F. C. T., 2002, "Load on the Shoulder in Low Intensity Wheelchair Propulsion," Clinical Biomechanics, Vol. 17, No. 3, pp. 211-218.
Wei, S.-H., Huang, S.-L., Jiang, C.-J., and Chiu, J.-C., 2003, "Wrist Kinematic Characterization of Wheelchair Propulsion in Various Seating Positions: Implication to Wrist Pain," Clinical Biomechanics, Vol. 18, No. 6, pp. S46-S52.
Wojcik L. A., 2003, "Modeling of Musculoskeletal Structure and Function Using a Modular Bond Graph Approach," Journal of the Franklin Institute, Vol. 304, No. 1, pp. 63-76.
Wu, H., van der Helm, Frans, C. T., Veeger, H. E. J. (DirkJan), Makhsouse, M., Roy, P. V., Angling, C., Nagelsh, J., Kardunai, A. K., McQuadej, K., Wangk, X., Wernerl, F. W., and Buchholzm, B., 2005, "ISB Recommendation on Definitions of Joint Coordinate Systems of Various Joints for the Reporting of Human Joint Motion—Part II: Shoulder, Elbow, Wrist and Hand," Journal of Biomechanics, Vol. 38, pp. 981-992.
Yanagawa, T., Goodwin, C. J., Shelburne, K. B., Giphart, J. E., Torry, M. R., and Pandy, M. G., 2008, "Contributions of the Individual Muscles of the Shoulder to Glenohumeral Joint Stability during Abduction," Journal of Biomechanical Engineering, Vol. 130, No. 2, pp. 021024
Zajac, F. E., 1989, "Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control," Biomedical Engineering, Vol. 17, No. 4, pp. 359-411.
Zhang, L.-L., Zhou, J., Zhang, X.-A., and Wang, C.-T., 2011, "Upper Limb Musculo-skeletal Model for Biomechanical Investigation of Elbow Flexion Movement," Journal of Shanghai Jiaotong University (Science), Vol. 16, No. 1, pp. 61-64.
江迦拿，2005，"降低相對於不舒適度、關節負荷及驅動扭矩之輪椅尺寸最佳設計"，碩士論文，國立成功大學機械工程研究所，台南，台灣。
沈柏宇，2010，"一SSCP-S肩部肌肉骨骼模型及其於手臂外展動作之運動及肌力分析的應用"，碩士論文，國立成功大學機械工程研究所，台南，台灣。
吳思穎，2003，"上肢復健機器臨床試驗與改良"，碩士論文，國立成功大學機械工程學系，台南，台灣。
范宏竹，2003，"設計發展機械手臂輔助系統於中風病人的上肢治療訓練"，碩士論文，國立成功大學機械工程學系，台南，台灣。
徐玉珍，2003，"輪椅設計系統之研發"，碩士論文，國立台北科技大學機電整合研究所，台北，台灣。
陳宜成，2010，"使用SUU為基礎之模型於上肢驅動輪椅及復健機械手之運動及靜力分析"，碩士論文，國立成功大學機械工程研究所，台南，台灣。
陳秋旺，2000，"肘關節神經復健用機器人之研究"，碩士論文，國立成功大學機械工程學系，台南，台灣。
陳健行與陳柏松編譯， 2003，彩色解剖學圖譜，合計圖書出版社，台北，台灣。(原著：Putz, R., and Pabst, R., 2000, Atlas of Human Anatomy, Urban & Fischer, Munchen Jena.)
郭藍遠，2003，"推力最佳化輪椅研究"，博士論文，國立成功大學醫學工程研究所，台南，台灣。
張豐榮與郭玉梅 編譯，1990，人體的地圖，暢文出版社，台北，台灣。(原著：高橋長雄，1898，からだの地図帳，講談社，音羽，文京區，東京都，日本)
許世昌，2001，解剖生理學，永大書局有限公司，台北，台灣。
楊書菱與許怡婷 編譯，2007，認識關節：關節的功能與構造，合記圖書出版社，台北，台灣。(原著：Bernard, K., 2000, Understanding Joints: A Practical Guide to Their Structure and Function, Nelson Thornes Limited, Cheltenham, UK)
楊境睿，2000，"脊椎損傷患者輪椅驅動之上肢生物力學分析"，碩士論文，國立成功大學醫學工程研究所，台南，台灣。
鄭博文，2010，"一SUU上肢肌肉骨骼模型及其於驅動輪椅與一復健機械手之肌力分析的應用"，碩士論文，國立成功大學機械工程研究所，台南，台灣。
劉豪哲，2011，"一S-SUCr-U上肢骨骼模型及其於上肢驅動輪椅與復健機械手的運動及負荷分析"，碩士論文，國立成功大學機械工程研究所，台南，台灣。
蕭學隆，1997，"復健用機器人研究"，碩士論文，國立成功大學機械工程學系，台南，台灣。