含双平行四边形结构支链的SCARA并联机构研究

Novel SCARA Parallel Mechanism with Double Parallelogram Branches

提出了一种含双平行四边形结构支链的新型SCARA并联机构,其包括4条相同支链,具有结构紧凑、承载力和刚度高的优点。首先,基于李群理论对机构的拓扑结构及其自由度进行阐述。其次,构建闭环矢量方程,推导出位置正/逆解,并通过2个数值算例验证位置解的正确性。通过对闭环矢量方程关于时间求导,得到机构的雅可比矩阵,由此建立输入角速度与末端输出速度之间、输入角加速度与末端输出加速度之间的映射关系,并对其进行数值仿真分析。然后,基于位置逆解,运用极限边界搜索法求解机构的工作空间,并绘制相应图谱加以分析。为明确机构动平台的转动性能,进一步研究不同工作平面下的动平台最大、最小转动角的空间分布图谱。在此基础上,借助特征因子构造量纲齐次雅可比矩阵,并利用条件数和可操作度两种方法分析机构的运动传递性能。基于直接和间接雅可比矩阵进一步对机构的3类奇异位置进行分析,明确奇异发生的条件。最后,借助Matlab与ADAMS软件开展仿真实验,验证了理论分析和设计结果的正确性与可行性。

A type of SCARA parallel mechanism with double parallelogram branches was proposed,which included four identical branches and had the advantages of compact structure,high bearing capacity and stiffness.Firstly,the topological structure and degree of freedom of the mechanism were described based on Lie group theory.Secondly,the closed-loop vector equation was constructed to derive the forward/inverse position solution,and two numerical examples were used to verify the correctness of the position solution.By deriving the closed-loop vector equation with respect to time,the Jacobian matrix of the mechanism was obtained,and the mapping relations between the input angular velocity and the end output velocity,and between the input angular acceleration and the end output acceleration were established,and the numerical simulation analysis was carried out.Then,based on the inverse position solution,the limit boundary search method was used to solve the workspace of the mechanism,and the corresponding atlas was drawn for analysis.In order to clarify the rotation performance of the moving platform of the mechanism,the spatial distribution maps of the maximum and minimum rotation angles of the moving platform under different working planes were drawn.On this basis,the dimensional homogeneous Jacobian matrix was constructed with the help of characteristic factors,and the motion transmission performance of the mechanism was analyzed by two methods of condition number and operability.Based on the direct and indirect Jacobian matrices,three kinds of singular positions of the mechanism were analyzed systematically,and the conditions of singularity occurrence were clarified.Finally,the correctness and feasibility of the theoretical analysis and design results were verified by simulation experiments with Matlab and ADAMS software.The research result can provides theoretical basis for the subsequent optimization and prototype manufacturing of the SCARA parallel mechanism in future.