一种冗余驱动并联机构的设计与奇异性分析

Structure Synthesis and Singularity Analysis of a Novel Redundantly Actuated Parallel Mechanism

在Delta机构的基础上提出一种含冗余驱动的三平移并联机构。基于螺旋理论计算了该并联机构的自由度,分析了位置反解,推导出雅可比矩阵,结合Gosselin奇异分析法,对Delta机构的奇异位形进行分析并找出两种新的奇异位形。将Delta机构和冗余驱动并联机构的奇异性进行比较,为了验证理论分析结果,引入可操作度这一运动性能指标,基于数值法对两种机构的奇异性进行比较。理论分析结果表明冗余驱动并联机构可以实现和Delta机构相同的功能,但其第二类奇异位形明显比Delta机构少;数值分析结果表明选取合适的工作空间和机构参数可减少并联机构的奇异位形,同时也验证了理论分析结果的正确性。

According to the structure of Delta parallel mechanism, a novel spatial parallel mechanism with actuation redundancy that can perform three-dimensional translations was presented. The degree of freedom of the parallel mechanism was calculated based on the screw theory and the inverse position solution was analyzed. Then the Jacobian matrix of the parallel mechanism with redundant actuation was deduced by inverse position kinematics and differential method. The singularity loci of the Delta parallel mechanism was analyzed and two novel singularity loci were presented by Gosselin singularity analysis and the singularity loci of Delta mechanism and redundantly actuated parallel mechanism was compared. In order to verify the result of theoretical analysis, the concept of manipulability was introduced to evaluate the kinematical performance of the two kind of parallel mechanism based on numerical analysis method. The results of theoretical analysis indicate that the redundant actuation parallel mechanism can realize the same function as the Delta mechanism, but the second type of singularity loci are significantly less than those of Delta mechanism. The results of numerical simulation show that the suitable workspace and mechanism parameters can reduce the singularity loci of parallel mechanism and the correctness of the theoretical analysis results are verified.