基于序单开链法的空间4自由度并联机构位置正解

提出空间并联机构位置正解的一种新方法——序单开链(SOC)法。该方法依据机构的拓扑结构特征,将机构分解为若干个有序单开链单元,又进一步划分出各基本运动链。计算出机构的耦合度,并根据耦合度算法原理,按序单开链单元分解顺序建立与机构拓扑结构相统一的机构位置分析数学模型。无需技巧性降维即可得到维数最少恰等于机构耦合度的位置正解方程。当机构的耦合度为1时,可用一维搜索得到全部实数解。该方法分析过程简明、通用,且物理意义明晰。与消元法相比,没有繁杂的数学推导,且计算效率较高;与一般搜索法相比,具有可求出全部实数解的优点。以4自由度并联机构为实例,通过一维搜索得到其位置正解的全部实数解。

DIRECT DISPLACEMENT SOLUTION OF 4-DOF SPATIAL PARALLEL MECHANISM BASED ON ORDERED SINGLE-OPENED-CHAIN

Based on the ordered single-opened-chain, a new method of direct displacement solution for spatial parallel mechanism is presented. According to the topological structure characteristics of the mechanism, the mechanism can be decomposed into some ordered single-opened-chains, which can further compose same basic kinematic chains. The mechanism coupling-degree is given, and following the principle of the mechanism coupling degree calculation method and the decomposition order of the single-opened-chains, the mechanism displacement analysis mathematics model that is uniform with its topological structure characteristics is established. The direct displacement equations are derived, and the equations' number of dimension is just equal to the mechanism coupling-degree and no skill to decrease the dimension is needed. As the mechanism coupling-degree is 1, all real number direct displacement solutions can be obtained by one-dimension search. The analysis processing is concise and universal, and its physicals meaning is clear. Compared with other general search methods, this method is of higher calculation efficiency and can gain all real number solutions. As an example, all real number direct displacement solutions of a 4-DOF parallel mechanism are obtained by one-dimension search.