本研究以Hung & Kuo提出之Cardan重力平衡器為基礎[1, 2]，簡化並改良其設計，保持相同的功能及優點。同樣使用Cardan齒輪機構，其中安裝真實彈簧來達成重力補償，不使用零自由長度彈簧，且彈簧沒有被安裝在移動桿和固定桿間，以避免使用時干涉。
　　Cardan齒輪機構是一種齒輪傳動直線機構(straight-line mechanism)，能夠將旋轉運動轉換為直線運動，可將掛有配重的桿件旋轉運動，轉換為彈簧的直線拉伸運動。本研究所提出之改良型單自由度Cardan重力平衡器有以下優勢：

(1) 構型更簡單，將行星齒輪系及Cardan齒輪機構簡化合併為Cardan齒輪機構；
(2) 桿件數量從5個簡化為3個；
(3) 對稱設計無側向力，降低齒輪嚙合摩擦力；
(4) 考慮真實彈簧初張力，提出挑選拉伸彈簧的最佳化方法，達成近似重力平衡；
(5) 安裝壓縮彈簧時，可達成理論上的完美重力平衡(perfectly gravity balanced)；
(6) 評估齒輪嚙合之摩擦力能量。

　　根據此構想，本研究亦進一步提出改良型雙自由度Cardan重力平衡器的概念，並使用機構模擬軟體Adams驗證其正確性。
　　為了使改良型單自由度Cardan重力平衡器，在現實中能完美的達成重力平衡，並符合預期的設定。不同於先前的研究，本研究考慮到真實彈簧之初張力，設計出一套流程，實際挑選市售可用之拉伸彈簧與壓縮彈簧，並且評估理論上齒輪嚙合之摩擦力能量。最後，製作原型機實際量測並驗證摩擦力之能量，並且計算其機械效率可達86.6 %。

This thesis proposes an improved Cardan-gear-based gravity balancer which is based on the gravity balancer proposed by Hung & Kuo [1, 2]. We improve their design and maintain the same features. The improved 1-DoF Cardan-gear-based gravity balancer has the following advantages:

(1) The configuration is simpler. We only use Cardan gear mechanisms instead of planetary gear trains;
(2) The number of links is reduced from 5 to 3;
(3) We use the symmetrical design without lateral force to reduce the friction;
(4) Considering the initial tension of the real spring, we propose an optimization method for selecting the tension spring to achieve an approximate gravity compensation;
(5) When the compression spring is installed, a theoretical perfectly gravity balancing can be achieved;
(6) We evaluate the gear loss energy from the dynamic friction.

　　　This thesis further proposes the concept of an improved 2-DoF Cardan-gear-based gravity balancer. We use the mechanism simulation software Adams to verify it. Different from the previous research, this thesis considers the initial tension of the real spring. We propose a set of process to select the tension springs or the compression springs. Next, we evaluate the energy of the dynamic friction force and built an experiment platform to measure the energy consumed by the friction. Last, we calculate the mechanical efficiency which can reach to 86.6%.

[1] Hung, Y. C., Kuo, C. H., 2017, “A Novel One-Dof Gravity Balancer Based on Cardan Gear Mechanism,” Mechanisms and Machine Science, 43, pp. 261-268.
[2] Hung, Y. C., 2016, “Design of a Novel Gravity Balancer Based on Cardan Gear Mechanism, ” Mechanical Engineering, National Taiwan University of Science and Technology, Master Thesis, Taipei, Taiwan.
[3] Agrawal, S., Fattah, A., Banala, S., 2006, Gravity Balanced Orthosis Apparatus, US Patent No. US 20060241539.
[4] Lin, P.-Y., Shieh, W.-B., Chen, D.-Z., 2013, “A Theoretical Study of Weight-Balanced Mechanisms for Design of Spring Assistive Mobile Arm Support (MAS),” Mechanism and Machine Theory, 61, pp. 156-167.
[5] Smith, R. L., Lobo-Prat, J., Van Der Kooij, H., Stienen, A. H. A., 2013, “Design of a Perfect Balance System for Active Upper-Extremity Exoskeletons,” 2013 IEEE 13th International Conference on Rehabilitation Robotics, ICORR 2013, Seattle, WA.
[6] Kuo, C. H., Lai, S. J., 2016, “Design of a Novel Statically Balanced Mechanism for Laparoscope Holders with Decoupled Positioning and Orientating Manipulation,” Journal of Mechanisms and Robotics, 8(1)
[7] Ahn, K. H., Lee, W. B., Song, J. B., 2016, “Reduction in Gravitational Torques of an Industrial Robot Equipped with 2 Dof Passive Counterbalance Mechanisms,” 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 9-14 Oct. 2016, pp. 4344-4349.
[8] Arakelian, V., 2015, “Gravity Compensation in Robotics,” Advanced Robotics, 30(2), pp. 79-96.
[9] Kim, H. S., Min, J. K., Song, J. B., 2016, “Multiple-Degree-of-Freedom Counterbalance Robot Arm Based on Slider-Crank Mechanism and Bevel Gear Units,” IEEE Transactions on Robotics, 32(1), pp. 230-235.
[10] Lin, P.-Y., Shieh, W.-B., Chen, D.-Z., 2010, “Design of a Gravity-Balanced General Spatial Serial-Type Manipulator,” ASME Journal of Mechanisms and Robotics, 2(3), p. 031003.
[11] Song, J.-B., Kim, H.-S., 2014, “Multi-Dof Counterbalance Mechanism for a Service Robot Arm,” IEEE/ASME Transactions on Mechatronics, 19(6), pp. 1756-1763.
[12] Lee, D., Seo, T., 2017, “Lightweight Multi-Dof Manipulator with Wire-Driven Gravity Compensation Mechanism,” IEEE/ASME Transactions on Mechatronics, 22(3), pp. 1308-1314.
[13] Ma, O., Wang, J., 2012, Apparatus and Method for Reduced-Gravity Simulation, US Patent No. US8152699.
[14] Xiu, W., Ruble, K., Ma, O., 2014, “A Reduced-Gravity Simulator for Physically Simulating Human Walking in Microgravity or Reduced-Gravity Environment,” IEEE International Conference on Robotics and Automation (ICRA), Hong Kong, China, 31 May-7 June, pp. 4837-4843.
[15] Hand, J. A., Pelton, C. R., 1927, Dental Light, US Patent No. US1642367.
[16] George, C., 1937, Equipoising Mechanism, US Patent No. US2076446.
[17] Mendelsohn, W. A., 1951, Jointed Bracket, US Patent No. US2547532.
[18] Riis, J. B., 1967, Equipoise Mechanism Particularly for Supporting Lamps and Small Television Sets, US Patent No. US3311340.
[19] Bouhuijs, M. C., 2002, Force Compensator, US Patent No. US6464183.
[20] Timothy, M., James, D., Stephen, A., David, P., 2018, Enclosure Assembly and Monitor Device Including Same, US Patent No. US20180116058.
[21] Herder, J. L., 2001, Energy-Free Systems: Theory, Conception and Design of Statically Balanced Spring Mechanisms, PhD. Dissertation, Department of Mechanical Engineering, Delft University of Technology, Delft, The Netherlands.
[22] Alling, E. D., 1879, Improvement in Dental Brackets, US Patent No. US218210.
[23] Hain, K., 1961, “Spring Mechanisms-Point Balancing and Spring Mchanism-Continuous Balancing,” in Chironis, N. P., Ed., Spring Design and Application, New York, McGraw-Hill, pp. 268-275.
[24] Streit, D. A., Gilmore, B. J., 1989, “‘Perfect’ Spring Equilibrators for Rotatable Bodies,” ASME Journal of Mechanical Design, 111(4), pp. 451-458.
[25] Ou, Y.-H., Chen, D.-Z., 2017, “Compact Arrangements of Cable-Pulley Type Zero-Free-Length Springs,” Journal of Mechanisms and Robotics, 9(4), pp. 044502-044502-7.
[26] Rahman, T., Ramanathan, R., SeUktar, R., Harwin, W., 1995, “A Simple Technique Gravity-Balance Passive Mechanisms ” Journal of Mechanical Design, Transactions of the ASME, 117, pp. 655-658.
[27] Morita, T., Kuribara, F., Shiozawa, Y., Sugano, S., 2003, “A Novel Mechanism Design for Gravity Compensation in Three Dimensional Space,” IEEE International Conference on Advenced Intelligent Mechatronics, Kobe, Japan, pp. 163-168.
[28] Endo, G., Yamada, H., Yajima, A., Ogata, M., Hirose, S., 2010, “A Passive Weight Compensation Mechanism with a Non-Circular Pulley and a Spring,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, Alaska, USA, 3-8 May, pp. 3843-3848.
[29] Koser, K., 2009, “A Cam Mechanism for Gravity-Balancing,” Mechanics Research Communications, 36(4), pp. 523-530.
[30] Nakayama, T., Araki, Y., Fujimoto, H., 2009, “A New Gravity Compensation Mechanism for Lower Limb Rehabilitation,” IEEE International Conference on Mechatronics and Automation, Changchun, China, 9-12 August, pp. 943-948.
[31] Shieh, W.-B., Chou, B.-S., 2015, “A Novel Spring Balancing Device on the Basis of a Scotch York Mechanism,” The 14th IFToMM World Congress Taipei, Taiwan, Oct. 25-30.
[32] Takesue, N., Ikematsu, T., Murayama, H., Fujimoto, H., 2011, “Design and Prototype of Variable Gravity Compensation Mechanism (VGCM),” Journal of Robotics and Mechatronics, 23(2), pp. 249-257.
[33] MISUMI, 2016-2017, Fa Mechanical Standard Components, 1 ed., Taipei, Taiwan.
[34] York, D., 1966, “Least-Squares Fitting of a Straight Line,” Canadian Journal of Physics, 44(5), pp. 1079-1086.
[35] Ohlendorf, H., 1958, Verlustleistung Und Erwärmung Von Stirnrädern, Ph. D Thesis, TH München.
[36] Höhn, B.-R., 2010, “Improvements on Noise Reduction and Efficiency of Gears,” Meccanica, 45(3), pp. 425-437.
[37] Fernandes, C. M. C. G., Martins, R. C., Seabra, J. H. O., 2013, “Friction Torque of Cylindrical Roller Thrust Bearings Lubricated with Wind Turbine Gear Oils,” Tribology International, 59, pp. 121-128.
[38] Fernandes, C. M. C. G., Marques, P. M. T., Martins, R. C., Seabra, J. H. O., 2015, “Gearbox Power Loss. Part Ii: Friction Losses in Gears,” Tribology International, 88, pp. 309-316.
[39] Jurkschat, T., Lohner, T., Stahl, K., 2017, “Improved Calculation Method for Load-Dependent Gear Losses,” Forschung im Ingenieurwesen, 81(2-3), pp. 109-115.
[40] Diez-Ibarbia, A., Fernandez-del-Rincon, A., de-Juan, A., Iglesias, M., Garcia, P., Viadero, F., 2018, “Frictional Power Losses on Spur Gears with Tip Reliefs. The Friction Coefficient Role,” Mechanism and Machine Theory, 121, pp. 15-27.
[41] Diab, Y., Ville, F., Velex, P., 2006, “Prediction of Power Losses Due to Tooth Friction in Gears,” Tribology Transactions, 49(2), pp. 260-270.
[42] Diez-Ibarbia, A., Fernandez-Del-Rincon, A., Garcia, P., De-Juan, A., Iglesias, M., Viadero, F., 2018, “Assessment of Load Dependent Friction Coefficients and Their Influence on Spur Gears Efficiency,” Meccanica, 53(1), pp. 425-445.
[43] Schlenk, L., 1995, Untersuchungen Zur Freßtragfähigkeit Von Großzahnrädern, Ph. D Thesis, TU München.