當一剛體由一個位置運動至另一個位置進行有限位移時，平面上對於此兩位置間之移動必有相對之一點不會移動，此點即所謂的極心。而當此物體固定由某位置不斷進行有限位移運動至其他位置，則其所得之所有極心所形成之曲線即所謂的有限位移極心曲線。因此，當假若僅知若干極心之位置時，將可藉由此曲線來分析與極心相對應之物體位置；反之，若知物體所移動之位置，則可合成此極心曲線，進而得知此物體所有可能之位移。
就一般最常使用之四連桿運動而言，其耦桿上一點之運動曲線－耦桿曲線之相關研究已臻成熟，但四連桿機構的有限位移極心曲線相關探討之研究非常少見。因此，在本論文中，將依作圖法的作圖原理來進行極心位置之分析，並建立有限位移極心曲線之數學程式，進而探討此曲線之特性。由於極心曲線推導相當複雜，一般四連桿有限位移極心曲線僅能以數值方法獲得，而無法求得其代數式，對於具有滑件之特殊四連桿機構，本文則已推導出其有限位移之極心曲線代數式。

When a rigid body undergoes a planar finite displacement from one position to another, there exists a point that does not move. This point is called pole. When a body undergoes infinite displacements from a certain position, the curve traced by all the poles is called the pole curve. Given the locations of poles, we can find the corresponding positions of the body. Conversely, if we know the displacements of the body, we can obtain the pole curve.
This thesis studies the pole curves of the finite displacements of planar four-bar linkages. There have been a lot of research reports on the paths traced by coupler points of a four-bar mechanism, called coupler curves. However, the research about the pole curves in the finite displacements of planar four-bar linkages was seldom seen. Building on the principle of the graphical synthesis technique, this thesis analyzes the locations of poles and derives the mathematical formula of the pole curves. The characteristics of the pole curves are then investigated. Due to the complex of the pole-curves, we can obtain the pole curve of a general four-bar linkage only by using numerical methods. For the special four-bar linkages that contain sliders, the analytic expressions of their pole curves have been derived.

1. Baker, J. E., 1979, “The Bennett, Goldberg and Myard Linkages in
Perspective,” Mechanism and Machine Theory, Vol. 14, pp. 239-253.
2. Baker, J. E., 1988, “The Bennett Linkage and Its Associated Quadric
Surfaces,” Mechanism and Machine Theory, Vol. 23, pp. 147-156.
3. Bennett, G. T., 1903, “A New Mechanism,” Engineering, Vol. 76, pp.
777-888.
4. Bennett, G. T., 1914, “The Skew Isogram Mechanism,” Proceedings of
London Mathematical Society, Series 2, Vol. 13, pp. 151-173.
5. Beyer, R., 1953, Kinematische Getriebesynthese, Springer, Berlin.
6. Dijksman, E. A., 1976, Motion Geometry of Mechanisms, Cambridge University
Press.
7. Erdman, A. G., and Sandor, G. N., 1984, Advanced Mechanism Design:
Analysis and Synthesis, Vol. 2, Prentice-Hall, New Jersey.
8. Eschenbach, P. W. and Tesar, D., 1971, “Link Length Bounds on the Four-Bar
Chain,” Trans. ASME 93B.
9. Hall, A. S., Jr., 1986, Kinematics and Linkage Design, Waveland Press
Inc., USA.
10.Huang, C., 1994, “On the Finite Screw System of the Third Order
Associated with a Revolute-Revolute Chain,” Journal of Mechanical Design,
Trans. ASME, Vol. 116, pp. 875-883.
11.Huang, C., 1997, “The Cylindroid Associated with Finite Motions of the
Bennett Mechanism,” Journal of Mechanical Design, Trans. ASME, Vol. 119, pp.
521-524.
12.Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press,
Oxford.
13.Martin, G. H., 1994, Kinematics and Dynamics of Machines, Vol. 2,
McGraw-Hill Inc., New York.
14.McCarthy, J. M., 2000, Geometric Design of Linkages, Springer-Verlag
New York Inc., New York.
15.Parkin, I. A., 1992, “A Third Conformation with the Screw Systems：Finite
Twist Displacements of a Directed Line and Point,” Mechanism and Machine
Theory, Vol.27, pp. 177-188.
16.Prentis, J. M., 1970, Dynamics of Mechanical Systems, Longman, London.
17.Wilson, C. E., and Sadler, J. P., 1993, Kinematics and Dynamics of
Machinery, 2nd ed., HarperCollins College Publishers, New York.
18.Yu, H. C., 1981, “The Bennett Linkage, Its Associated Tetrahedron and the
Hyperboloid of Its Axes,” Mechanism and Machine Theory, Vol. 16, No. 4, pp. 105-114.