With a low moving inertia, high payload-to-weight ratio, and large workspace, cable-driven parallel robots (CDPRs) are relevant in many applications, especially redundant CDPRs. As there exist an infinite number of tension distributions, this paper presents a novel computational geometry-based method to calculate a tension feasible region (TFR)—a preimage of tension distribution—for multi-redundant CDPRs. The proposed TFR algorithm overcomes some of the limitations of conventional iterative and vertices search methods. The TFR is first interpreted as a convex intersection of multiple boundary-parallel spaces, where its dimension is equal to redundancy r. To obtain the centroid of TFR, the vertices coordinates and order for r = 2 and 3 only need to be determined on surface. Static simulations with 6 degrees-of-freedom using 8-cable and 9-cable CDPRs are employed to demonstrate the algorithmic accuracy. Additionally, to illustrate that the optimal tension distribution has continuity, motion trajectories for the same CDPRs are calculated. Furthermore, the proposed algorithm minimizes computational time when compared to the performance of existing algorithms. Thus, the proposed method could rapidly establish the optimal tension distribution.

由于具有较低的移动惯性，较高的有效负载重量比和较大的工作空间，因此电缆驱动的并行机器人（CDPR）在许多应用中都非常重要，尤其是冗余CDPR。由于存在无限数量的张力分布，因此本文提出了一种基于计算几何的新颖方法来计算多冗余CDPR的张力可行区域（TFR）（张力分布的原像）。所提出的TFR算法克服了传统的迭代和顶点搜索方法的一些局限性。首先将TFR解释为多个边界平行空间的凸交点，其尺寸等于冗余度r。要获得TFR的质心，顶点的坐标和r的阶数 = 2和3只需要在表面上确定。使用8电缆和9电缆CDPR对6度f面进行静态仿真，以证明算法的准确性。另外，为了说明最佳张力分布具有连续性，计算了相同CDPR的运动轨迹。此外，与现有算法的性能相比，所提出的算法将计算时间最小化。因此，所提出的方法可以迅速建立最佳的张力分布。