一类平转耦合并联机构运动学性能的评价方法

Kinematic performance evaluation of a class of parallel mechanisms having mixed DoFs of translation and rotation

三自由度平转耦合并联机构已在航空大型结构件加工中得到应用,但因这类机构的Jacobian矩阵量纲不统一,故难于用其代数特征评价机构的运动学性能.本文基于螺旋理论构造出3-PRS并联机构速度映射模型,采用虚功原理定义了两种可描述机构链内和链间瞬时功率传递特性的无量纲运动学性能评价指标,并通过算例说明其有效性.研究成果对指导这类并联机构的运动学优化设计具有重要的参考价值.

The parallel mechanisms having mixed degrees-of-freedom （DoFs） of one translation ana two roanons have been used in manufacturing the extra large structural aircraft components with complex geometries. This statement can be demonstrated practically by very successful applications of the Sprint Z3 head to aircraft industry. However, to evaluate the kinematic performance of these parallel mechanisms is a challenging issue because serious problems may occur due to dimensional inconsistencies of the Jacobian matrix. By taking a 3- PRS parallel mechanism as an example, this paper presents an approach to formulate a set of local dimensionless kinematic performance indices on the basis of the overall Jacobian developed by screw theory. The merits of these indices are that they can be represented by the instantaneous virtual power transmission ratios within one limb and amongst limbs, leading to the global ones represented by their mean values and standard deviations throughout the entire workspace. In-depth discussion is made via the example to illustrate the validity of these brand new indices. The outcome may provide with the designers a powerful tool for the kinematic performance evaluation and optimal design of the parallel mechanisms having combined DoFs in terms of translations and rotations.