This paper presents the workspace optimization of one-translational two-rotational (1T2R) parallel manipulators using a dimensionally homogeneous constraint-embedded Jacobian. The mixed degrees of freedom of 1T2R parallel manipulators, which cause dimensional inconsistency, make it difficult to optimize their architectural parameters. To solve this problem, a point-based approach with a shifting property, selection matrix, and constraint-embedded inverse Jacobian is proposed. A simplified formulation is provided, eliminating the complex partial differentiation required in previous approaches. The dimensional homogeneity of the proposed method was analytically proven, and its validity was confirmed by comparing it with the conventional point-based method using a 3-PRS manipulator. Furthermore, the approach was applied to an asymmetric 2-RRS/RRRU manipulator with no parasitic motion. This mechanism has a T-shape combination of limbs with different kinematic parameters, making it challenging to derive a dimensionally homogeneous Jacobian using the conventional method. Finally, optimization was performed, and the results show that the proposed method is more efficient than the conventional approach. The efficiency and simplicity of the proposed method were verified using two distinct parallel manipulators.

翻译：本文提出了一种利用维度齐次约束嵌入雅可比矩阵对一平移两转动（1T2R）并联机构进行工作空间优化的方法。1T2R并联机构的混合自由度导致维度不一致性，增加了其结构参数优化的难度。为解决该问题，提出了一种基于点的方法，该方法结合了平移特性、选择矩阵及约束嵌入逆雅可比矩阵。研究给出了简化公式，避免了传统方法所需的复杂偏微分运算。通过理论分析证明了所提方法的维度齐次性，并利用3-PRS并联机构与传统基于点的方法进行对比验证了其有效性。此外，将该方法应用于无寄生运动的不对称2-RRS/RRRU并联机构。该机构采用T型支链组合且各支链运动学参数不同，传统方法难以推导其维度齐次雅可比矩阵。最终优化结果表明，所提方法相比传统方法具有更高效率。通过两个不同类型的并联机构验证了该方法的有效性与简洁性。