Abstract

The article proposes a general approach for solving the unified formulas of the constrained Jacobian matrix and constrained Hessian matrix of three translational and one rotational (3T1R) parallel manipulators (PMs). First, based on the constraint properties of PMs, the constrained couples of the limbs are divided into two categories: invariable and variable constrained couples. The unified 2 × 6 constrained Jacobian matrix and 2 × 6 × 6 constrained Hessian matrix of the 3T1R PM are established. Then, a typical 2-(UPU)²R PM is selected, and the 6 × 6 Jacobian matrix and 6 × 6 × 6 Hessian matrix of the mechanism are deduced. The singularity of the mechanism is analyzed based on the 6 × 6 Jacobian matrix. Finally, the kinematics are derived, and results demonstrating the proposed method were provided.

摘要

本文提出了一种通用方法，用于求解三个平移和一个旋转（3T1R）并联机械手（PM）的约束雅可比矩阵和约束黑森州矩阵的统一公式。首先，基于PM的约束属性，将肢体的约束对分为两类：不变约束对和可变约束对。建立了3T1R PM的统一2×6约束Jacobian矩阵和2×6×6约束Hessian矩阵。然后，选择典型的2-（UPU）² R PM，并选择6×6雅可比矩阵和6×6 ×推导了该机制的6个Hessian矩阵。基于6×6雅可比矩阵分析了机构的奇异性。最后，得出了运动学，并提供了证明所提出方法的结果。