滾子凸輪機構（Roller Gear Cam；文中簡稱RGC）已廣泛被使用於自動化生產線與各式工具機定位機構中。近來為因應製程高速化之發展趨勢，加上凸輪機構之間歇運動特性，往往使高速運轉下之轉子在作動瞬間，因扭矩之瞬間上升，導致馬達驅動轉速之瞬間異常下降，除易衍生系統殘振外，更可能造成分割定位精度之喪失。本文中將結合馬達驅動及滾子凸輪兩不同特性之子系統，藉由拉格朗日方程式（Lagrange’s equation）推導整體機、電整合系統之運轉模式。文中並將針對可能之轉速補償機構：如增加平板凸輪力矩補償機構或傳統惰輪機構，對高速滾子凸輪系統於作動瞬間之速度變化進行補償，文中將分就此各種補償機構參數，其對高轉速下對直流馬達運轉速變異情況、滾子凸輪 輸入軸扭矩變動，進行數值模擬與實驗之分析，並探討、分析兩種設計其可能達成之補償效應。

數值分析主要藉由六階藍日卡達法（Runge-Kutta method），配合滾子凸輪在作動與間歇階段之雙剛度假設，進行此非線性系統之時域動態響應解析；實驗驗證方面量測重點置於平板式凸輪力矩補償裝置與簡單惰輪力矩補償裝置兩不同補償機構，對直流馬達轉速、輸入軸扭矩變動之抑制成效、及系統輸出端殘振資料之分析，及其與數值結果之比對。

經由實驗量測與數值模擬結果顯示，文中所提之整體機、電整合系統之運轉模式，具頗佳之準確性。另在補償裝置效應方面，結果顯示，平板式凸輪力矩補償裝置在特定設計之運轉速度下，輸出端定位精度可獲得較佳的改善，但此精度對運轉速度甚敏感，換言之，若非在其原先設計轉速下，此精度改善效應可能喪失。反之惰輪補償裝置在特定轉速下，其補償效果不若平板式凸輪力矩補償裝置有效，但其補償效應之適用轉速範圍較寬，兩者各有其特色。

Roller Gear Cam mechanism（RGC）has been used widely in different automation mechanisms and all kinds of orientation mechanism. High speed and high accuracy of the RGC system is a tendency in high production automation. The interaction between the driving speed and torque of a high speed RGC system is investigated in this work. The effect of adding a torque compensation cam（TCC）on the improving of indexing precision of a RGC system is investigated in this thesis.

The dynamic responses of a RGC system driven by a DC motor are conducted. Dynamic equations of the intermittent- motion of a RGC driven system are derived by using the Lagrange’s equation with the assumption of dual-stiffness. Furthermore, the effect of adding a torque compensation mechanism（TCM） such as torque compensation cam（TCC） or idle wheel on the improving of indexing precision of a RGC system is investigated in this work. The sixth order Runge-Kutta iteration method is employed in the system’s responses simulation. Variations of the driving torque, driving speed and residual vibration of a RGC system with different torque compensation devices are analyzed in this research.

The simulated and measured results indicate that a RGC system attached with a TCC can improve its speed and torque fluctuation at the designed speed significantly. However, this compensation effect is quite sensitive to the driving speed. On the contrary, the compensation effect introduced by using an idle wheel is not so sensitive to the speed as the TCC does. The low cost and easy design are also the favorable factors for using an idle wheel to instead of an expensive TCC device.

Contents
Abstract i
Contents v
List of Figures vii
List of Tables x
Nomenclature xi
Chapter 1 Introduction 1
1-1 Background 1
1-2 Literature review 4
1-3 Structure of the thesis 6
Chapter 2 Mathematical Model of a Roller Gear Cam System 8
2-1 Cam profile curves for a RGC mechanism 8
2-2 Equations of motion of a RGC system 12
2-3 Mathematical modeling of DC motors 19
2-4 Torque compensation mechanism 25
2-5 Numerical simulation of the dynamic responses of a RGC system 34
Chapter 3 Experimental Verification and Numerical Simulation 37
3-1 Layout of the RGC measurement system 37
3-2 System parameters extraction 43
3-3 Comparison between the numerical and measured results 51
Chapter 4 Conclusion and Discussion 82
Appendix A 84
Appendix B 88
Appendix C 91
References 101

Chen, C.H. 1979, “Boundary Curves, Singular Solutions, Complementary Conjugate Surfaces and Conjugate Analysis in Theory of Conjugate Surfaces,” Proc. of 5th World Congress on Theory of Machines and Mechanisms, Montreal, Canada, pp.1478-1481.

Chen, F.Y., 1982, “Mechanics and Design of Cam Mechanisms, ” Pergamon Press, New York.

Churchill, F. T. and Hanson, D. R. S., 1962, “Theory of Envelope Provides New Cam Design Equation,” Product Engineering, Aug. 20, pp. 45-55.

Hilderbrand F.B., 1972, “Methods of Applied Mathematics, ” Englewood Cliffs, N.J., pp339-343.

Ho T.Y., Hu C.C., Kuang J.H., 1999, “Dynamic Responses of the Roller Gear Cam System with a Torque Compensation Mechanism, ” Proc. of 2th National Conference on the Design of Mechanisms and Machines, pp209-216.

Hsieh, W.H., 1991, “Improving the State of Motion of Followers by Controlling Cam Speed,” M.S. Thesis, National Cheng Kung University, Tainan, TAIWAN.

Huang, S. P., 1997, “A Study on the Dynamic Characteristics of Roller Gear Cam System,” M.S. Thesis, National Sun Yat-sen University, Kaohsiung, TAIWAN.

Kuang, J. H., Chen, C. J., and Huang, S. P., 1996, “Determination of Couplings Stiffness via Series and Parallel Arrangement of Accelerometers,” Proc. of 20th National Conference on Theoretical and Applied Mechanics, Taipei, Taiwn, R.O.C., pp. 32-39.

Kuang, J. H., Huang, S. P., and Ho, T. Y., 1999, “Dynamic Responses of a Roller Gear Cam System,” Proc. of 10th World Congress on the Theory of Machines and Mechanisms, Finland , Vol.4, pp. 1465-1470.

Kuang, J. H. and Lin, J. F., 1994, “Accelerometer Pair Measurements for Shaft Dynamic Parameters Analysis,” Proc. of 12th International Modal Analysis Conference, Honolulu, Hawaii, U.S.A., pp.1649-1655.

Neklutin, C. N., 1952, “Designing Cams,” Machine Design, June, pp. 143-160.

Nishioka, M. 1977, “Indexing drives without the twist vibration on the input shaft,” Proc. of JSME/JSPEN, No. 771-1, pp. 103-105.

Nishioka, M., 1983, “Study of flywheel cam mechanisms,” JSME, Vol. 49, No. 446C, pp. 1781-1788.

Nishioka, M. 1994, “Compensation of Input Shaft Torque on Indexing Cam Mechanisms(2nd Report, Verification of the Theory),” JSME, Vol. 60, No. 569, pp. 338-342.

Nishioka, M., 1999, “Design of Torque Compensation Cam Using Measured Torque Distribution,” Proc. of 10th World Congress on the Theory of Machines and Mechanisms, Finland, Vol.4, pp. 1471-1476.

Nishioka, M. and Uchino, M., 1993, “Compensation of Input Shaft Torque on Indexing Cam Mechanisms(II),” JSME, Vol. 59, No. 562, pp. 311-317.

Rothbart, H. A., 1956, “Cams-Design, Dynamics and Accuracy, ” John Willey &Sons New York.

Sanchez, M. N. and Jalon, J. G., 1980, “Application of B-spline Function to the Motion Specification of Cams,”ASME Design Engineering Technical Conference, 80-DET-28.

Teasar, D. and Matthew, G. K., 1976, “The Dynamics Synthesis, Analysis, and Design of Modeled Cam System,” Lwxington Books.

Tsay, D. M., Ho, H. C. and Wang K. C., 2000, “Design of Torque Balancing Cams for Globoidal Cam Indexing Mechanisms,” ASME Journal of Mechanical Design （submitted）.

Tsay, D. M. and Huey, C. O., 1993, “Application of Rational B-Splines to the Synthesis of Cam-follower Motion programs,” ASME Journal of Mechanical Design, Vol.115, pp.621-626.

Tsay, D. M. and Hwang, G. S., 1994, “Application of Theory of Envelop to the Determination of Camoid Profiles with Translation Followers, ” ASME Journal of Mechanical Design, Vol.116, No. 1, pp.321-325.

Tsay, D. M. and Lin, B. J., 1996, “Improving the Geometry Design of Cylindrical Cams Using Nonparametric Rational B-splines,” Computer-Aided Design, Vol.28, No.1, pp.5-15.

Tsay, D. M. and Lin, B. J., 1996, “Profile Determination of Planar and Spatial Cams with Cylindrical Roller-Followers,” IMecE Journal of Mechanical Engineering Science, Vol.210, pp.565-574.

Yu, C.M., 1994, “Servo Controller Design for a Variable Speed Cam-Follower System,” M.S. Thesis, National Cheng Kung University, Tainan, TAIWAN.