On the Study of Motion Characteristics of Figure-Eight Trajectory Generated by Elliptical Gears

• Main Authors: Yi-Jia Shen, 沈意加
• Format: Others
• Language: zh-TW
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/ufkq8z

碩士 === 國立虎尾科技大學 === 動力機械工程研究所 === 94 === In this research, the motion characteristics of Figure-eight trajectory generated by elliptical gears are analyzed. By using the vector method, differential geometry, and geometry relationship, the mathematical model of follower link and Figure-eight trajectory which generated by a point on the coupler-link on elliptical gears is established. Moreover, the motion characteristics of Figure-eight trajectory generated by elliptical gears with different eccentricity are analyzed. The results of motion characteristics of Figure-eight trajectory generated by elliptical gears, the eccentricity is greater, Figure-eight trajectory has constant larger velocity part but the range of velocity and acceleration at start and finish are greater. In this research, the elliptical gears train is composed by two pairs elliptical gears is applied, the mathematical model of follower link and Figure-eight trajectory which generated by a point on the couple-link on elliptical gears train is also established. Moreover, the motion characteristics of Figure-eight trajectory generated by elliptical gears train have phase angles are analyzed. In different phase angles, the eccentricity is greater, the velocity and acceleration of Figure-eight trajectory generated by elliptical gears train at start and finish are greater. When the phase angles ???/2 and the eccentricity of elliptical gears e=0.4, the constant velocity part of Figure-eight trajectory generated by elliptical gears train is greater. In this research, normalized mathematical model of Figure-eight trajectory generated by elliptical gears is established. Applying the concept of variable input speed, the rule of design of variable input speed, and the defined optimal objective function, the optimal function of input speed are obtained. By the result of optimal design, variable input speed function can improve the peak value of velocity and acceleration of point on the coupler-link on elliptical gears. The constant velocity part of Figure-eight trajectory is longer than constant input speed. The results of this study can apply to design the path generated mechanism of polishing machine to polish the optical fiber end-face.