This paper proposes a new methodology for deriving a point-based dimensionally homogeneous Jacobian, intended for performance evaluation and optimization of parallel manipulators with mixed degrees of freedom. Optimal manipulator often rely on performance indices obtained from the Jacobian matrix. However, when manipulators exhibit mixed translational and rotational freedoms, the conventional Jacobian's inconsistency of units lead to unbalanced optimal result. Addressing this issue, a point-based dimensionally homogeneous Jacobian has appeared as a prominent solution. However, existing point-based approaches for formulating dimensionally homogeneous Jacobian are applicable to a limited variety of parallel manipulators. Moreover, they are complicated and less intuitive. This paper introduces an extended selection matrix that combines component velocities from different points to describe the entire motion of moving plate. This proposed approach enables us to formulate an intuitive point-based, dimensionally homogeneous Jacobian, which can be applied to a wide variety of constrained parallel manipulators. To prove the validity of proposed method, a numerical example is provided utilizing a four-degree-of-freedom parallel manipulator.

翻译：本文提出了一种新的方法，用于推导基于点的维度齐次雅可比矩阵，旨在对具有混合自由度的并联机构进行性能评估与优化。最优机构通常依赖于从雅可比矩阵获得的性能指标。然而，当机构同时具有平动和转动自由度时，传统雅可比矩阵的单位不一致会导致不均衡的优化结果。为解决此问题，基于点的维度齐次雅可比矩阵已成为一种重要解决方案。然而，现有的基于点的方法在构建维度齐次雅可比矩阵时仅适用于有限类型的并联机构，且复杂且缺乏直观性。本文引入了一种扩展选择矩阵，该矩阵整合来自不同点的分量速度以描述动平台的完整运动。所提出的方法能够构建一种直观的、基于点的维度齐次雅可比矩阵，可广泛应用于多种约束并联机构。为了验证所提方法的有效性，以四自由度并联机构为例进行了数值仿真。