含有球面4R环路锁定模式的球面7R机构模式变换分析

Mode Transformation Analysis of Spherical 7R Mechanism with Spherical 4R Loop Locking Mode

摘要:

具有运动和锁定模式的机构在变换为特定锁定模式位形后，可满足特定工况下的刚度需求。通过在球面4R机构连杆上，设置处于折叠位形的球面3R运动链，设计了一类具有锁定模式的双环球面7R机构。分析球面4R机构连杆曲线的几何特征，通过算例验证了球面4R机构连杆曲线方程的正确性。使用旋量理论分析球面4R环路处于奇异位形下连杆的瞬时转动轴线，确定了球面4R环路中连杆的瞬时转动轴线与球面3R运动链轴线共面，为机构模式变换必要条件。将球面4R环路作为广义转动副，对双环球面7R机构加速度进行分析，得到了球面4R机构环路连杆曲线尖点对应机构位形下，连杆瞬面切线与球面3R运动链轴线共面，为机构模式变换必要条件。结果表明，该类球面7R机构具有锁定模式，通过旋量理论分析球面4R机构环路连杆的瞬时运动旋量，可确定机构运动模式变换位形。对于分析设计满足运动和锁定生产作业变换需求的多模式机构，具有参考价值。

Abstract:

Mechanisms with motion and locking modes can meet the stiffness requirements under specific working conditions after being transformed into specific locking mode configurations. The geometric characteristics of the linkage curve of the spherical 4R mechanism was analyzed, and the correctness of the linkage curve equation of the spherical 4R mechanism was verified through numerical examples. A type of double loops spherical 7R mechanism with locking mode was designed by setting a spherical 3R motion chain in a folding position on the connecting rod of the spherical 4R mechanism. Using screw theory to analyze the instantaneous rotation axis of the connecting rod in a singular configuration of the spherical 4R loop, it was determined that the instantaneous rotation axis of the connecting rod in the spherical 4R loop was coplanar with the axis of the spherical 3R motion chain as a necessary condition for mechanism mode transformation. Using the spherical 4R loop as a generalized rotational pair, the acceleration of the double loops spherical 7R mechanism was analyzed, and the necessary condition for the mechanism mode transformation was obtained, which was that the tangent of the axodes of the connecting rod and the axis of the spherical 3R motion chain were coplanar under the corresponding mechanism configuration of the sharp point of the connecting rod curve in the spherical 4R mechanism loop. This kind of spherical 7R mechanism had lock-in mode. By analyzing the instantaneous rotation of the link in the loop of the spherical 4R mechanism with screw theory, the transformation of the motion mode of the mechanism can be determined. It had a certain application value in the analysis and design of multi-mode mechanism which can meet the requirements of motion and lockin production operation transformation.