當機構之輸入桿與輸出桿的運動關係成一定之函數關係者，即稱之為函數產生機構。本論文研究合成函數產生四桿機構在位置及速度的問題。並研究輸入及輸出接頭旋轉角有相同角位移的特殊函數產生4C機構之桿件長度及扭角的關係式。
本論文所有的函數產生機構問題皆利用運動倒置的方法，首先將原先的固定輸出接頭變為運動接頭，輸入接頭進行反向運動，此時問題變為合成雙接頭對連桿問題。接著再利用有限螺旋位移推導出的螺旋三角形合成空間雙圓柱連桿對位置合成問題，最後在利用瞬時螺旋運動推導出的瞬時螺旋三角形合成雙圓柱連桿速度合成的問題。當設計不同型式的輸入接頭空間函數產生四桿機構時，可由螺旋三角形理論，用一螺旋運動描述C-C、H-C及R-C合成位置及指定速度問題，並用此螺旋運動合成雙圓柱對連桿，結合成4C、HCCC及RCCC函數產生機構。
本研究於合成函數四桿機構配合4對旋轉角問題最多有6組解。而當指定的2個位置無窮接近時，其斜率即為通過指定位置時的速度。此外本文利用電腦輔助繪圖軟體SolidWorks建立三維模型，並利用動畫模擬驗證函數產生機構數值例的正確性。
經由本論文的証明，成功的將雙圓柱對連桿位置合成應用在合成函數產生四桿機構之設計，並進一步將問題延伸至指定速度的合成。並設計HCCC、RCCC及4C空間函數產生機構。

The function generation problem involves designing mechanisms of which output motions are specified functions of input motions. In this thesis, we are concerned with synthesizing spatial four-bar function generators, with position and velocity specifications. This thesis also investigates the relationship between link lengths and twist angles of the 4-cylindrical function generator that has identical input and output motions.
The method of synthesis used in thesis is similar to that used for the design of rigid body guidance mechanisms. The function generation synthesis problem is converted to an equivalent rigid body guidance problem by employing the idea of kinematic inversion. Then the screw triangle formulation is applied to the position and velocity synthesis of CC dyad for the design of different driving joints, including H, C, and R joints, of spatial function-generation mechanisms.
The CC dyad 5-position synthesis and the 4-bar function generator mechanism give at most 6 solutions. When only two finitely separated positions are specified, the slopes of the input/output function curve can also be specified. The slopes of the specified function represent the velocities of the specified positions. Several numerical examples are provided in this thesis, and the numerical results are verified by using SolidWorks.
This dissertation has successfully demonstrated the technique of applying the position and velocity synthesis of CC dyad to the design of spatial function-generation mechanisms. The designs of three different linkages, HCCC, RCCC, and 4C have been presented.

Angeles, J., Spatial Kinematic Chains, Analysis, Synthesis and Optimization, Springer-Verlag, Berlin, 1982.
Ball R. S., A Treatise on the Theory of Screws, The University Press, Cambridge, England, 1900.
Burmester, L., “Gerafuhrung durch das Kurbelgetriebe,” Civilingenieru, Vol. 22, pp. 597-606, 1876.
Burmester, L., “Gerafuhrung durch das Kurbelgetriebe,” Civilingenieru, Vol. 23, pp. 227-250, 1877.
Chasles M., “Note sur les propriétés générales du système de deux corps semblables entre eux, placés d’une manière quelconque dans l’espace ; et sur le déplacement fini, ou infiniment petit d’un corps solide libre,” Bulletin des Sciences Mathématiques de Férussac, XIV, pp. 321-336, 1831.
Chen, P. and Roth, B., “Design Equations for the Finitely and Infinitesimally Separated Position Synthesis of Binary Links and Combined Link Chains,” Journal of Engineering for Industry, Trans. ASME, Vol. 91, No. 1, pp. 208-218, 1969.
Dhall, S., and Kramer, S., “Design and Analysis of the HCCC, RCCC, and PCCC Spatial Mechanism for Function Generation,” Journal of Mechanical Design, Trans. ASME, Vol. 112, pp. 74-78, 1990.
Duffy, J., and Crane, C., “A Displacement Analysis of the General Spatial 7-Link, 7 R Mechanism,” Mechanism and Machine Theory, Trans. ASME, Vol. 15, pp. 153-169, 1980.
García-Ríos, I., Palacios-Montufar, C., Flores-Campo, J. A., Osorio-Saucedo R. Osorio-Saucedo, “Synthesis of 4C Mechanism for Generation of a Dual Mathematic Function,”Applied Mechanics and Materials, Trans Tech Publications, Vol. 15, pp. 67-72, 2009.
Grassmann, H., Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik, Leipzig: Wiegand. English translation, 1995, by Lloyd Kannenberg, A new branch of mathematics, 1844.
Mavroidis, C., and Roth, B., “Analysis of Over Constrained Mechanisms , ”Journal of Mechanical Design, Trans. ASME, Vol. 117, pp. 69-74, 1995.
Murray, A. P., and McCarthy, J. M., “Five Position Synthesis of Spatial CC Dyad,” In Proc. ASME DETC Mechanism Conf., Minneapolis, Minnesota, September 1997.
Plücker J., “On a New Geometry of Space,” Philosophical Transactions of the Royal Society of London, Vol. 155, pp. 725-791, 1865.
Roth, B., “On the Screw Axes and other Special Lines Associated with Spatial Displacements of a Rigid Body,” Journal of Engineering for Industry, Trans. ASME, Ser. B, pp. 102-110, 1967.
Suh C., “Design of Space Mechanisms for Function Generation,” Journal of Engineering for Industry, Trans. ASME, Vol. 90, Series B, No. 3, pp. 507-512, 1968.
Suh C., “Design of Space Mechanisms for Rigid Body Guidance,” Journal of Engineering for Industry, Trans. ASME, Vol. 90, Series B, No. 3, pp. 499-506, 1968.
Suh, C. H., “Design of Space Mechanism for Rigid-Body Guidance,” Journal of Engineering for Industry, Trans. ASME, Series B, Vol. 87, No. 1, pp. 215-222, 1967.
Suh, C. H., “On the Duality in the Existence of R-R Links for Three Positions,” Journal of Engineering for Industry, Trans. ASME, 91B(1), pp. 129-134, 1969.
Suh, C. H., and Radcliffe, C. W., Kinematics and Mechanisms Design, Wiley, New York, 1978.
Tsai, L. W., Robot Analysis, John Wiley and Sons, 1999.
The MathWorks Inc., 2007, Matlab® Getting Started Guide, R2007b, Natick, MA, USA.
Tsai, L. W. and Roth, B., “Design of Dyads with Helical, Cylindrical, Spherical, Revolute, and Prismatic Joints,” Mechanism and Machine Theory, Trans. ASME, Vol. 7, pp. 85-102, 1972a.
Tsai, L. W. and Roth, B., “A Note on the Design of Revolute-Revolute Cranks,” Mechanism and Machine Theory, Trans. ASME, Vol. 8, pp. 23-31, 1972b.
Tsai, L. W., Design of Open Loop Chains for Rigid Body Guidance, Ph.D. Dissertation, Mechanical Engineering Department, Stanford University, Stanford, CA, USA.
Tsai, L. W. and Roth, B., “Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis,” Journal of Engineering for Industry, Trans. ASME, Vol. 95(B), pp. 603-611, 1973.
Veldkamp, G., R., “Canonical System and Instantaneous Invariants in Spatial Kinematics,” J. Mechanism, Trans. ASME, Vol. 2, pp. 329-388, 1967.
Wampler, C. W., Morgan, A. P., and Sommese, A. J., “Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics,” J. Mechanical Design, Trans. ASME, Vol. 112, pp. 59-68, 1990.
張育叡，雙圓柱對連桿位置合成方程式之解，國立成功大學機械工程學系碩士班碩士論文，1999。
田昆明，空間雙接頭連桿尺寸合成問題的一些數值解，國立成功大學機械工程學系碩士班碩士論文，2001。
黃秉融，合成具雙圓柱對連桿之空間四桿機構於直線導引問題，國立成功大學機械工程學系碩士班碩士論文，2009。