Algebraic expression and characteristics of static wrench-closure workspace boundary for planar cable-driven parallel robots
Algebraic expression and characteristics of static wrench-closure workspace boundary for planar cable-driven parallel robots
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DOI：
10.1177/1687814016638217
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发表时间：
2016-03
影响因子：
2.1
通讯作者：
Tiemin Li;Xiaoqiang Tang;Lewei Tang
中科院分区：
文献类型：
--
作者：
Tiemin Li;Xiaoqiang Tang;Lewei Tang
提出了一种基于对映定理的平面三自由度索驱动并联机器人静态扳手闭合工作空间边界代数表达式的推导方法。与区间法和离散化方法不同，该方法可以得到更精确的工作空间边界代数表达式，且不存在待确定区域和计算量，使设计过程和优化变得简单可行。为了说明和研究工作空间边界的二次曲线特性，以四索驱动三自由度并联机器人为例进行了研究。仿真结果表明，边界二次曲线的类型取决于具体推导矩阵的行列式，并对应于哪条索与交线共线。此外，研究结果还表明，工作空间的边界由两条相同类型的二次曲线（即椭圆、抛物线和双曲线）组成，当边界方程类型为抛物线时，这两条二次曲线所包围的区域最小。
This article proposes a deduction method of algebraic expression of static wrench-closure workspace boundary for planar 3-degree-of-freedom cable-driven parallel robots based on the antipodal theorem. Different from interval method and discretization approach, a more precise algebraic expression of workspace boundary can be obtained without undetermined region or costly computation burden to make the design process and optimization easy and feasible. In order to illustrate and study the conic characteristics of workspace boundary, a case study is conducted on a four-cable-driven 3-degree-of-freedom parallel robot. Simulation results show that the type of conic of boundary depends on the determinant of the specific deduced matrix and corresponds to which cable is collinear with the intersection line. In addition, the results also demonstrate that the boundary of workspace consists of the same type of two conics (i.e. ellipse, parabola, and hyperbola), and the region surrounded by these two quadratic curves is the smallest when the type of the border equation is parabola.