基于单杆矢量的机构复合分离位置函数综合

摘要/Abstract

摘要：

提出用单杆相对运动差单元构建平面机构函数综合方程式。首先建立单杆的相对位置运动差及高阶运动差通用单杆矢量公式,再通过引入变量和增加单杆矢量附加方程,消除了方程式中非独立的未知角变量及未知高阶角变量。然后用单杆矢量及其附加方程直接建立有限分离、无限接近分离及复合分离位置函数综合的统一通用的多项式方程组，且方程总次数低。讨论了在平面铰链四杆机构函数综合中的复合五位置问题及复合四位置问题上的应用，用实例计算了“实现函数”与“预期函数”的误差并作出误差波动图，结果表明在无限分离精确点及无限接近分离点上可以精确实现预期函数，但按高阶运动特性要求设计的机构不一定能使“实现函数”在所有0阶位置上更逼近“预期函数”。该方法比双杆组、三杆组法简单，模块性非常好，便于计算机自动建模与求解。

关键词: 相对运动理论；单杆矢量；函数综合, 复合分离位置, 同伦法

Abstract:

The relative motion differences of the monads were presented to model the systems of equations for kinematic function synthesis of planar linkages.The uniform formulae of the relative motion differences with 0-order to higher-order derivatives were constructed firstly,and then the new variables and corresponding special auxiliary equations of the monad vectors were used to eliminate trigonometric function,the angular unknowns and even their higher order angular unknowns.The monad vectors and their corresponding auxiliary equations could be directly used to construct synthesis systems for finitely, infinitesimally and multiply separated precision positions, and the systems were polynomial equations with smaller values of the total degrees.Applying the formulae to five and four multiply separated positions of function synthesis for pin-jointed four-bar planar linkages was discussed.Some cases of the multiply separated positions were exemplified and their differences between the generated y-value and required y-value were calculated and charted.The results show that the positions at finitely and infinitesimally separated positions were passed through exactly according to the required function.However,the y-values generated by the mechanism with the higher-order functional requirements may be no more close to the required y-value than those generated by the mechanism with the lower-order functional requirements at all 0-order positions in the required range.The procedure is simpler and the formulae of monad have the better modularity than the dyad and triad,and can be easily adapted to automatic modeling and solving the equations in a computer.

Key words: relative , motion , theory;monad vector;function generation;multiply separated position;homotopy method

中图分类号:

TH112.1

王成志, 张全明, 王淑可, 周球, 代婷. 基于单杆矢量的机构复合分离位置函数综合[J]. 中国机械工程, 2016, 27(02): 187-194,229.

Wang Chengzhi, Zhang Quanming, Wang Shuke, Zhou Qiu, Dai Ting. Multiply Separated Position Synthesis of Function Generation Mechanism Based on Monad Vectors[J]. China Mechanical Engineering, 2016, 27(02): 187-194,229.

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