Performance Improvement of 3-PUS/S Parallel Mechanism via Redundant Actuation Chain
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摘要: 研究了一种3-PUS/S并联机构，在3-PUS/S并联机构中添加一条冗余驱动支链形成4-PUS/S并联机构。主要运用对比分析方法，探究相同条件下引入冗余驱动支链对原机构性能的影响。具体研究内容有：采用空间矢量三角形法建立了两并联机构的位姿方程，得到了运动学反解模型；绘制两种并联机构在相同条件下的工作空间并进行对比分析；运用螺旋理论，得到了两种并联机构的约束雅克比矩阵、驱动雅克比矩阵，并进一步构建了完全雅克比矩阵；研究两种并联机构的静刚度，绘制了两种并联机构刚度矩阵最大特征值分布图谱并进行对比分析；采用朗格朗日方程建立了两种并联机构的动力学模型，在给定机构设计参数和动平台轨迹规划函数后，绘制了两种并联机构驱动力输出曲线并进行对比。最后得到了引入冗余驱动支链对原机构动平台的工作空间范围有略微减小、改善了刚度特性分布情况、提高了刚度、工作精度、改善了驱动性能的结论。Abstract: A type of 3-PUS/S parallel mechanism was proposed, and a redundant actuation chain was added to the 3-PUS/S parallel mechanism to form a 4-PUS/S parallel mechanism. The method of comparative analysis to explore the influence of the redundant actuation chain on the performance of the original mechanism under the same conditionsis used. The specific research contents include that the position and attitude equations of the two parallel mechanisms to establish with the space vector triangle method, and the kinematics inverse solution model. The workspace of the two parallel mechanisms under the same conditions were drawn and compared. The constraint Jacobian matrix and the actuation Jacobian matrix of the two parallel mechanisms were obtained with the screw theory, and the complete Jacobian matrix was further constructed. The static stiffness of two parallel mechanisms was studied, and the distribution map of the maximum eigenvalue of the stiffness matrix of the two parallel mechanisms was drawn and compared. The dynamic models of two parallel mechanisms were established with Langrange equation, and the actuation force output curves of the two parallel mechanisms were plotted and compared after the design parameters of the mechanism and the trajectory planning function of the moving platform were given. Finally, it was concluded thatthe introduction of redundant actuation chaincould slightly reduce the workspace range of the moving platform of the original mechanism, improvethe distribution of stiffness characteristics, improve the stiffness, working accuracy and improve the actuation performance.
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Key words:
- 3-PUS/S /
- 4-PUS/S /
- redundant actuation chain /
- comparative analysis
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表 1 机构参数
R/mm r/mm 滑块行程
hi/mm虎克铰最大
转角$ {\theta _v} $/(°)球副最大
转角$ {\theta _s} $/(°)180 95 170~290 60 60 
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表 2 两种机构最大特征值数据对比
γ
角度3-PUS/S机构
最大特征值4-PUS/S机构
最大特征值提高
比例0 1×109 N·m/rad 1.2×109 N·m/rad 20% $ {\text{π}} /4 $ 1.6×109 N·m/rad 2×109 N·m/rad 25%
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