具接頭間隙平面連桿路徑產生機構之最佳化設計與分析

Optimal Design and Analysis of Planar Path Generators with Joint Clearance

康肇元(Chao-Yuan Kang)

指導教授 ： 吳文方

共同指導教授 ： 李志中(Jyh-Jone Lee)

國立臺灣大學/工學院/機械工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.01890

摘要

在製造或組裝機構過程中，為使桿件順暢運動，各旋轉接頭必定存在間隙(clearance)，此些間隙會導致機構傳動的誤差；尤其在精密機械定位中，間隙的影響更需特別留意。本論文探討平面四連桿與混合五連桿路徑產生機構受單一接頭間隙影響的機構尺寸合成方法，並特別分析接頭間隙造成路徑誤差之效應。文中首先應用差分演算法(Differential Evolution, DE)設計不考慮間隙之初始路徑產生機構及其尺寸，接著考慮接頭間隙，並引用等效間隙桿件(equivalent clearance link)概念，將間隙視為一無質量的虛擬桿件，利用遺傳演算法(Genetic Algorithm, GA)求解具間隙機構的Lagrange運動方程式，得到間隙桿件的角位置變化，再使用差分演算法進行具間隙路徑產生機構之最佳化設計，使其耦桿路徑與初始最佳化機構之路徑構造誤差降至最低。本研究方法於設計階段即將間隙對路徑之影響納入考慮，以設計出最符合實際要求之機構尺寸；而應用本研究方法可有效改善因間隙造成平面四連桿與混合五連桿路徑產生機構耦點路徑之誤差；此外，本研究方法具設計流程簡單、應用方便、程式撰寫容易、收斂快速等優點。

關鍵字

混合五連桿機構 ； 接頭間隙 ； 最佳化尺寸合成 ； 差分演算法 ； 遺傳演算法

並列摘要

The existence of clearances in revolute joints during manufacturing and assembling processes is essential for smooth motion of a mechanism. However, clearances frequently lead to positioning and orientation errors, especially for precision mechanisms. This thesis presents a methodology for designing planar four-bar and hybrid five-bar path generating mechanisms with single joint clearance. The position error due to clearance in the revolute joint is also investigated. In the analysis, differential evolution is first applied to initialize dimensions of path generating mechanism without clearances. The joint clearance is then treated as a massless virtual link base on the concept of equivalent clearance link. To obtain direction of the joint clearance, genetic algorithm is employed to solve the Lagrange equation of the path generating mechanism with joint clearance. Finally, the path generating mechanism is optimized by employing differential evolution again. The proposed method takes clearance into consideration to obtain the optimal design of a four-bar or hybrid five-bar path generating mechanism. It is shown to be effective in reducing the positioning error of the path generating mechanism due to clearance. Advantages of the proposed method include fast convergence to optimal solution, simplicity of application, and easy computer programming.

並列關鍵字

hybrid five-bar mechanism ； joint clearance ； optimal dimensional synthesis ； differential evolution ； genetic algorithm

參考文獻

[1] V. Parenti-Castelli and S. Venanzi, “Clearance influence analysis on mechanisms,” Mechanism and Machine Theory, Vol. 40, No. 12, pp. 1316-1329, Dec. 2005.

[2] S. G. Dhande and J. Chakraborty, “Analysis and synthesis of mechanical error in linkages—a stochastic approach,” Journal of Engineering for Industry, Transactions of ASME, Vol. 95, No. 3, pp. 672-676, 1973.

[3] J.-H. Choi, S. J. Lee, and D.-H. Choi, “Stochastic linkage modeling for mechanical error analysis of planar mechanisms,” Journal of Structural Mechanics, Vol. 26, No. 3, pp. 257-276, 1998.

[4] S. Dubowsky and F. Freudenstein, “Dynamic analysis of mechanical systems with clearances—Part 1: Formation of dynamic model,” Journal of Engineering for Industry, Transactions of ASME, Vol. 93, No. 1, pp. 305-309, 1971.

[5] B. Miedema and W. M. Mansour, “Mechanical joints with clearance: a three-mode model,” Journal of Engineering for Industry, Transactions of the ASME, Vol. 98, No. 4, pp. 1319-1323, 1976.