[M], [C], [K] are the mass matrix, damper matrix and stiffness matrix, all of these are 33×33matrix. Analysis  Solved the equation at Matlab, result can be shown in figure 9-a, it can be seen, the natural frequency not concentrate at one stable frequency, but varying with the turning angle, that’s because the exist  of eccentricity, the connection position will changing with the turning of crankshaft, caused one of the stiffness varying, which resulted the varying of natural frequency.From the figure, it can obtain that the natural frequency mainly focus at 462 Hz , 627 Hz, 668Hz, 682 Hz, 702 Hz, 825 Hz, 858 Hz, 954 Hz, 1093 Hz, 1200 Hz, 1439 Hz, in it, 1439Hz is the most dangerous zone because the input shaft was turning at 1500r/min, which easily cause resonance. From the first generation prototype test, test Improvement Methods In order to avoid the danger frequency, the most valid method is to change the stiff matrix or mass matrix, in the second generation prototype design, reinforce the stiffness of gear case, and enlarge the diameter of output shaft to improve its torsional rigidity, change the eccentricity from 2mm to 3mm, change the transmission ratio of pin-cycloid from 34 to 20, figure 9-b is the natural frequency distribution after structure improved. 
   From the figure it can be seen that the natural frequency mainly focus on 395 Hz , 750 Hz, 1146 Hz, 1557Hz, 1895 Hz, which mostly avoid the danger frequency zone. Conclusion (1) On the assumption that the ring-plate and gear case as rigid body, taken into account the influence of arm bearing and support bearing’s stiffness, and the distortion of gear at meshing, paper built a dynamical model for double crank ring-plate-type pin-cycloidal gear planetary drive, calculated the meshing stiffness for the involute gear and the pin-cycloid gear by program, based on Newton second law, a 33-DOF dynamical model include input and output shaft, ring-plate, involute gear and gear box was formulated by lumped-parameter method， obtained the natural frequency and vibration character for the system with bending and torsion coupling working condition. (2) Calculate results show that between 600-800Hz and some other frequency bands the system may easily cause resonance when input shaft turning at 1500r/min, which was approximately match with the first generation prototype vibration test. For the problem that the prototype has obvious oscillation and noise, improvement method about reinforce the gear case stiffness, increase the first transmission  ratio and enlarge the output shaft diameter was applied, theory analysis show that this measures may better decrease the vibration and noise for this kind of new drive.   Acknowledgement Paper Supported by National Natural Science Foundation of China (No.50575030), the Doctoral Program of Higher Education of China (No. 20060150001), Program for Liaoning Excellent Talents in University (No. 2006R08), and Program for New Century Excellent Talents in University (No.NCET-07-0127). I would like to express my gratitude to the fund committee. Also I want to acknowledge the invaluable help of Professor HE Weidong, who has been my constant consultant in my writing this essay. References [1] Weidong He, Xin LI, Lixing LI: Force Analysis on the High-load Capacity Double Crank Ring-Plate-Type Cycloid Drivce[J],ASME Journal of Mechanical Design,2000,36(5): 84-88 [2]  Weidong He, Lixing LI, Linda C. Schmidt: A New Cycloid Drive With High-Load Capacity and High Efficiency. ASME Journal of Mechanical Design, 2004, 126(3): 683-686. [3] Gang WANG, Dawei ZHANG, and Tian HUANG, “A study on the method of dynamic modeling for RV reducer”, machine design,  TianJin, 1999(3)： 19-22. [4] Gang WANG, Liming ZHAO, and Mai WANG, “Research and Analysis on dynamics Formulation of RV Reducer”, China Mechanical Engineering, 2002, 13 (19)： p1652-1655 [5]  Da Wei ZHANG, Gang WANG, “Dynamic Formulation of RV reducer and Analysis of structural Parameters”, Chinese Journal OF Mechanical Engineering, 2001,37(1): 1,  p69-74 [6] JiYan LIU, Tao SUN, and Hou Jun QI, “Research on Natural Frequency and Dynamic Model of RV Reducer”, China Mechanical Engineering, 1999, (4), 381-386 [7]  XiHai YAN, Ce ZHANG, and Yun Ning LI, “Natural Frequency of Torsional Vibration of Rotary Vector Reducer and Its Influencing Factors”, Mechanical Science and Technology, 2004.vol. 23(8), p991-994 [8] YingHui ZHANG,  JunJun XIAO,  WeiDong HE, Dynamical Formulation and Analysis of RV Reducer，, ICEC2009, p201-204  [9] YingHui ZHANG,  WeiDong HE , JunJun XIAO, Dynamical model of RV reducer and key influence of stiffness to the nature character, ICIC2010, p 192-195 [10] YingHui ZHANG,  JunJun XIAO , WeiDong HE ,Meshing stiffness calculation of pin-cycloid on robot RV reducer, Journal of Dalian Jiaotong University, 2010（2）,p 20-23  双曲柄环板式针摆线齿轮行星传动英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_56501.html