本研究之動機在於基本機構以不同方式進行組合時，往往可以導致多種新奇結果的產生，而這些結果對於從事機構的設計或再設計，提供了更多的概念與想法。因此，本研究針對函數機構概念設計領域，發展一套機構系統定性功能解的具體導向合成方法，其中機構系統是由一個給定的動力源與數個基本機構所組成。

　　首先，根據機構之輸入/輸出運動特性與轉換關係，歸納其定性功能特徵，並定義、列舉出36個單輸入單輸出基本機構；藉由圖畫的表示，系統之構成單元間的組合關係可以明確地表示成外向樹；並且利用物元概念，以定性化方式將機構表示成十維物元，如此可以系統化分析基本機構的內在功能性質與外在組合特徵。接著，以兩個階段發展出本研究提出之具體導向方法；第一階段根據圖形理論，提出一個以矩陣運算為基礎的方法，用於合成出組成單元間的所有組合構型；第二階段則是藉由建立物元運算的性質與規則，提出一個以符號運算為基礎的方法，用以計算出前一階段產生構型之可能實現的功能解。最後，依照給定基本機構是否完全相異，舉出兩個完整的例子驗證該方法的可行性；以滑件曲柄機構、正齒輪組、直動型從動件楔形凸輪、以及直動型從動件圓柱形凸輪等四個相異的基本機構組合為例，若機構系統是由一般的旋轉或直線動力源驅動，則可分別求得28種與20種機構系統之功能解；以三個滑件曲柄機構（一個以曲柄為輸入、兩個以滑件為輸入）與兩個日內瓦輪的組合為例，可分別求出108種與60種功能解。

　　本研究所提出的系統化方法，可合成出多種具有不同功能特性之組合機構，有助於函數機構之概念設計。

　　The motivation of this study is that various amazing results can be obtained by combining the primitive mechanisms or kinematic building blocks in different ways and which may provide more alternatives in the design or re-design of mechanisms. With aiming at the function generation issue, this work is devoted to develop a physical oriented methodology for synthesizing the qualitative functional alternatives of mechanism systems that are constructed with a designated power source and a given number of building blocks.

　　In accordance with the input/output kinematic natures and transformations of mechanisms, the study begins with concluding the qualitative functional characteristics, defining and listing 36 building blocks for reference. With the aid of graph representation, the combination relationships among the building blocks are revealed explicitly by representing the system as an arborescence. By adopting the matter-element concept, mechanisms are characterized as 10-dimensional matter-elements and such representations facilitate exploring and analyzing the inner functional natures and outer combinatorial characteristics of building blocks. Then, the physical oriented methodology consisted of two phases is proposed. In the first phase, based on graph theory, a matrix-based method is presented to enumerate all possible and feasible combined configurations of the given building blocks. In the second phase, through establishing the matter-element properties and operation rules, a rules-based method for symbolic manipulation is developed to generate the functional alternatives for the configurations obtained in the first phase. Ultimately, according to whether the building blocks are all distinct or not, two complete examples are illustrated to validate the presented methodology. Four distinct building blocks, namely, a slider-crank mechanism, a spur-gear pair, a wedge cam with a translating follower, and a cylindrical cam with a translating follower, are taken as the first example. And, supposing the mechanism systems are driven by either a rotary power source or a translational one, the results show that 28 and 20 functional alternatives of mechanism systems are obtained respectively. The other combinatorial example is taken by three slider-crank mechanisms (one is driven by the crank and two are driven by the slider) and two Geneva wheel mechanisms, and the results reveal that 108 and 60 functional alternatives are generated respectively.

　　In this work, since various combined mechanisms with different functionality can be synthesized systematically by the proposed approach, the result is beneficial to the conceptual design of mechanisms for function generation.

[1]　Yan, H. S., Hwang, W. M., Chen, F. C., Huang, P., and Fan, Y. S., “Automatic tool changing apparatus,” U.S. Patent, No. 5,749,819, 1998.

[2]　Erdman, A. G., Sandor, G. N., and Kota, S., Mechanism Design: Analysis and Synthesis, Vol. 1, 4th ed., Prentice-Hall, Inc., New Jersey, 2001.

[3]　Erdman, A. G. edited, Modern Kinematics: Developments in the Last Forty Years, John Wiley & Sons, Inc., New York, 1993.

[4]　Artobolevskii, I. I., Mechanisms in Modern Engineering Design, MIR Publishers, Moscow, 1986.

[5]　Chironis, N., Mechanisms, Linkages and Mechanical Controls, McGraw Hill, New York, 1978.

[6]　Jensen, P. W., Classical and Modern Mechanisms for Engineers and Inventors, Marcel-Dekker, New York, 1991.

[7]　Jones, F. D., Horton, H. L., and Newell, J. A., Ingenious Mechanisms for Designers and Inventors, Industrial Press, New York, 1930.

[8]　Crossley, F. R. E., “The permutations of kinematic chains of eight member or less from the graph-theoretic viewpoint,” Developments in Theoretical and Applied Mechanisms, Vol.2, Shaw, W. A. edited, Pergamon Press, Oxford, pp. 467-486, 1965.

[9]　Dobrjanskyj, L. and Freudenstein, F., “Some applications of graph theory to the structural analysis of mechanisms,” ASME Transactions, Journal of Engineering for Industry, pp. 153-158, 1967.

[10]　Freudenstein, F. and Dobrjanskyj, L., “On a theory for the type synthesis of mechanisms,” Proceedings of the 11th International Congress of Applied Mechanics, Springer, Berlin, pp. 420-428, 1964.

[11]　Woo, L. S., “Type synthesis of plane linkages,” ASME Transactions, Journal of Engineering for Industry, pp. 159-172, 1967.

[12]　Johnson, R. C. and Towfigh, K., “Application of number synthesis to practical problems in creative design,” ASME Paper, NO. 65-WA-MD9, 1965.

[13]　Chen, J. J., Type synthesis of planar mechanisms, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1982.

[14]　Yan, H. S. and Chen, J. J., “Creative design of a wheel damping mechanism,” Mechanism and Machine Theory, Vol.20, No.6, pp. 597-600, 1985.

[15]　Yan, H. S. and Hsu, C. H., “A method for the type synthesis of new mechanism (in Chinese),” Journal of the Chinese Society of Mechanical Engineers (TAIWAN), Vol. 4, No.1, pp.11-23, 1983.

[16]　Yan, H. S. and Hwang, Y. W., “The generalization of mechanical devices,” Journal of the Chinese Society of Mechanical Engineers (TAIWAN), Vol. 9, No.3, pp. 191-198, 1988.

[17]　Yan, H. S. and Hwang, Y. W., “The specialization of mechanisms,” Mechanism and Machine Theory, Vol. 26, No. 6, pp. 541-551, 1991.

[18]　Hwang, Y. W., An expert system for creative mechanism design, Ph. D. Dissertation, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1990.

[19]　Yan, H. S., “A methodology for creative mechanism design,” Mechanism and Machine Theory, Vol. 27, No. 3, pp. 235-242, 1992.

[20]　Chang, W. L., Conceptual design of step-climbing wheelchair linkages, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2000.

[21]　Liao, J. Y., On the design of step-climbing wheelchair linkages, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2001.

[22]　Chang, M. Y., On the design of anti-dive front suspension mechanisms for bicycles, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2000.

[23]　Chen, P. H., On the mechanism design of 4-link and 6-link types wooden horse carriages, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1998.

[24]　Chiu, C. P., On the design of a wave gait walking horse, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1996.

[25]　Hung, C. C., On the mechanism design of a hybrid 8-link type walking horse, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2002.

[26]　Hwang, K., On the design of an optimal 8-link type walking horse, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1997.

[27]　Shen, H. W., On the mechanism design of 8-link type walking horses, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1999.

[28]　Lin, T. Y., A systematic reconstruction design of ancient Chinese escapement regulators, Ph. D. Dissertation, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2001.

[29]　Wang, Y. X. and Yan, H. S., “Computerized rules-based regeneration method for conceptual Design of mechanisms,” Mechanism and Machine Theory, Vol. 37, pp. 833-849, 2002.

[30]　Wang, Y. X., Wang, L. J., and Duan, L. Q., “Computerized creative design method for mechanical system under 3D environment (in Chinese),” Machine Design and Research, supplement, Shanghai, pp. 32-34, 2002.

[31]　Chen, F. C., Mechanism configuration synthesis of machining centers, Ph. D. Dissertation, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1997.

[32]　Chen, F. C. and Yan, H. S., “A methodology for the configuration synthesis of machining centers with automatic tool changer,” ASME Transactions, Journal of Mechanical Design, Vol. 121, pp. 359-367, 1999.

[33]　Yan, H. S. and Chen, F. C., “Configuration synthesis of machining centers without tool change arms,” Mechanism and Machine Theory, Vol. 33, pp. 197-212, 1998.

[34]　Liu, N. T., Configuration synthesis of mechanisms with variable chains, Ph. D. Dissertation, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2001.

[35]　Yan, H. S. and Liu, N. T., “Configuration synthesis of one step push-button stopper lock with variable passwords,” Proceedings of 10th World Congress on the Theory of Machine and Mechanisms, Oulu, Finland, June 20-24, pp. 622-629, 1999.

[36]　Yan, H. S. and Liu, N. T., “Joint-codes representations for mechanisms and chains with variable topologies,” Transactions of the Canadian Society for Mechanical Engineering, Vol. 27, No. 1&2, pp. 131-143, 2003.

[37]　Freudenstein, F. and Maki, E. R., “The creation of mechanisms according to kinematic structure and function,” Environment and Planning B, Vol. 6, pp. 375-391, 1979.

[38]　Erdman, A. G. and Bowen, J., “Type and dimensional synthesis of casement window mechanisms,” ASME, Mechanical Engineering, Vol. 103, pp. 46-55, 1981.

[39]　Freudenstein, F. and Maki, E. R., “Development of an optimum variable-stroke internal combustion engine from the viewpoint of kinematic structure,” ASME Transactions, Journal of Mechanisms, Transmission, and Automation in Design, Vol. 105, No.2, pp. 259-266, 1983.

[40]　Freudenstein, F. and Maki, E. R., “Kinematic structure of mechanisms for fixed and variable stroke axial-piston reciprocating machines,” ASME Transactions, Journal of Mechanisms, Transmission, and Automation in Design, Vol. 106, pp. 355-364, 1984.

[41]　Yu, Z. and Lee, T. W., “Kinematic structural and functional analysis of wobble-plate engines,” ASME Transactions, Journal of Mechanisms, Transmission, and Automation in Design, Vol. 108, pp. 226-236, 1986.

[42]　Jobes, C. C., Palmer, G. M., and Means, K. H., “Synthesis of a controllable circuit breaker mechanism,” ASME Transactions, Journal of Mechanical Design, Vol. 112, pp. 324-330, 1990.

[43]　Chew, M., Shen, S. N. T., and Issa, G.. F., “Kinematic structural synthesis of mechanism using knowledge based systems,” ASME Transactions, Journal of Mechanical Design, Vol. 117, pp. 96-103, 1995.

[44]　Yang, B., Dasteris, P., Datta, U., and Kowalski, J., “An integrated system for design of mechanisms by an expert system - DOMES: Theory,” ASME Transactions, Journal of Mechanical Design, Vol. 112, pp. 488-493, 1990.

[45]　Yang, B., Dasteris, P., Datta, U., and Kowalski, J., “An integrated system for design of mechanisms by an expert system - DOMES: Applications,” ASME Transactions, Journal of Mechanical Design, Vol. 113, pp. 25-31, 1991.

[46]　Chiou, S. J., Conceptual design of mechanisms using kinematic building blocks - A computational approach, Ph. D. Dissertation, Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, 1994.

[47]　Chiou, S. J. and Kota, S., “Automated conceptual design of mechanisms,” Mechanism and Machine Theory, Vol. 34, pp. 467-495, 1999.

[48]　Kota, S., “A qualitative matrix representation scheme for conceptual design of mechanisms,” Proceedings of the 1990 ASME Mechanisms Conference, Chicago, pp. 217-230, September, 1990.

[49]　Kota, S. and Chiou, S. J., “Conceptual design of mechanisms based on computational synthesis and simulation of kinematic building blocks,” Research in Engineering Design, Vol. 4, pp. 75-87, 1992.

[50]　Moon, Y. M. and Kota, S., “Automated synthesis of mechanisms using dual-vector algebra,” Mechanism and Machine Theory, Vol. 37, pp. 143-166, 2002.

[51]　Subramanian, D. and Wang, C. S., “Kinematic synthesis with configuration spaces,” Research in Engineering Design, Vol. 7, pp. 193-213, 1995.

[52]　Li, C. L., Tan, S. T., and Chan, K. W., “A qualitative and heuristic approach to the conceptual design of mechanisms,” Engineering Applications of Artificial Intelligence, Vol. 9, No. 1, pp. 17-31, 1996.

[53]　Chakrabarti, A. and Bligh, T. P., “An approach to functional synthesis of solutions in mechanical conceptual design. Part II: Kind synthesis,” Research in Engineering Design, Vol. 8, pp. 52-62, 1996.

[54]　Kong, F. G., “Research on multilevel case searches of the two-grade case based reasoning for conceptual design (in Chinese),” Machine Design and Research, Vol. 15, No. 3, Shanghai, pp. 20-22, 1999.

[55]　Kong, F. G. and Zou, H. J., “Research on the process model of mechanical conceptual innovative design (in Chinese),” Machine Design and Research, Vol. 15, No. 1, Shanghai, pp. 15-17, 1999.

[56]　Liang, Q. H., Zou, H. J., and He, Y. J., “A modeling method of conceptual design process on the basis of function component (in Chinese),” Machine Design and Research, Vol. 15, No. 4, Shanghai, pp. 14-16, 1999.

[57]　Lin, S. L., A qualitative method for the conceptual design of mechanisms, Master Thesis, Department of Mechanical Engineering, National Taiwan University, Taipei, TAIWAN, 1992.

[58]　Ou, F. M., Design methodology of the modularization of mechanisms,
Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 2000.

[59]　Xie, J., Ding, J.F., and Cheng, Y., “Conceptual mechanism design based on functions, constrains and structures (in Chinese),” Machine Design and Research, Vol. 15, No. 2, Shanghai, pp.33-35, 1999.

[60]　Ye, Z. G., Zou, H. J., Guo, W. Z., Hu, S., and Tian, Y. L., “The establishment of knowledge base management system and the types synthesis of mechanism for mechanism motion scheme (in Chinese),” Machine Design and Research, Vol. 19, No. 2, Shanghai, pp. 11-14, 2003.

[61]　Zou, H. J. and Gu. M. M., “An expert system for the scheme design of mechanical system (1) – the establishment of knowledge base management system (in Chinese),” Journal of Machine Design, No. 5, Tianjin, pp. 26-28, 1996.

[62]　Zou, H. J. and Gu. M. M., “An expert system for the scheme design of mechanical system (2) – the establishment and application of reasoning system (in Chinese),” Journal of Machine Design, No. 6, Tianjin, pp. 12-14, 1996.

[63]　Chiang, I. H., A study on the combinations of simple mechanism modules, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1996.

[64]　Tang, M. F., A study on the combinations of serial and parallel mechanism modules, Master Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, TAIWAN, 1997.

[65]　Chang, Y. N., A study for applying the agile design in equipment research and development process – Example for IC singlation mechanism, Master Thesis, Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung, TAIWAN, 2003.

[66]　Yan, H. S., Mechanisms (in Chinese), 2nd ed., Tung Hua Books, Taipei, TAIWAN, 1999.

[67]　Yan, H. S., Creative Design of Mechanical Devices, Springer-Verlag, Singapore, 1998.

[68]　Chen, F. Y., “Gripping mechanisms for industrial robots – An overview,” Mechanism and Machine Theory, Vol. 17, pp. 299-311, 1982.

[69]　Christofides, N., Graph Theory – An Algorithm Approach, Academic Press, New York, 1975.

[70]　Deo, N., Graph Theory with Application to Engineering and Computer Science, Prentice-Hall, Inc., New Jersey, 1974.

[71]　Harary, F., Graph Theory, Addison-Wesley, Massachusetts, 1969.

[72]　Cai, W., “The extension set and non-compatible problems,” Science Exploration, Vol. 3, No. 1, pp. 83-97, 1983.

[73]　Cai, W., Yang, C. Y., and Lin, W. C., Extension Engineering Methods, Science Press, Beijing, 2003.

[74]　Cai, W., Matter-element model and its applications (in Chinese), Publisher of Scientific and Technologic Literature, Beijing, 1994.

[75]　Cai, W. edited, From Analysis of Matter-Elements to Extension Sets (in Chinese), Publisher of Scientific and Technologic Literature, Beijing, 1995.

[76]　Bott, R. and Mayberry, J. P., “Matrices and trees,” Economic Activity Analysis, Morgenstern, O. edited, John Wiley & Sons, Inc., New York, pp. 391-400, 1954.

[77]　Tutte, W. T., “The dissection of equilateral triangles into equilateral triangles,” Proceedings of Cambridge Philosophy Society, Vol. 44, pp. 463-482, 1948.