A four degrees-of-freedom (DOF) Parallel Manipulator (PM) with a 4PPa-2PaR configuration has been proposed to generate 3-DOF Translational and 1-DOF Rotational (3T1R) motions in our early work. It has the advantages of symmetric geometry, simple kinematics and infinite extension of translational workspace along its linear guide direction. However, its V-type assembly mode results in a long distance between its moving platform and the base, which makes its stiffness and accuracy lower. Besides, its the other two translational workspaces are limited due to its kinematic singularities. To overcome such limitations, the PM is modified by utilizing its M-type assembly mode and placing an offset angle to the last parallelogram mechanism. To simplify the displacement analysis, a geometrical projection method is employed, while a closed-loop vector approach is used for its instantaneous kinematic analysis. Both singularity and workspace issues are investigated. An optimization algorithm based on Genetic Algorithm is proposed to maximize the reachable workspace. The optimization result indicates that the workspace is significantly increased. A prototype of the M-type PM is fabricated to validate the effectiveness of the modified design.

已提出具有4 P Pa-2PaR 配置的四自由度(DOF)并联机械手(PM)以生成3-DOF 平移和 1-DOF 旋转(3T1R) 我们早期工作中的动议。具有几何对称、运动学简单、平移工作空间沿直线导轨方向无限延伸等优点。然而，其V型装配方式导致其移动平台与底座之间的距离较长，从而使其刚度和精度较低。此外，它的其他两个平移工作空间由于其运动学奇点而受到限制。为了克服这些限制，通过利用其 M 型组装模式并在最后一个平行四边形机构上放置一个偏移角来修改 PM。为简化位移分析，采用几何投影法，同时采用闭环矢量法进行瞬时运动分析。奇点和工作空间问题都进行了研究。提出了一种基于遗传算法的优化算法，以最大化可达工作空间。优化结果表明工作空间显着增加。制造了 M 型 PM 的原型，以验证修改设计的有效性。