基于螺旋理论的Delta并联机器人自由度分析

螺旋理论以其几何概念清楚,物理意义明确,表达形式简单等优势,常被用于分析机构的自由度。按照传统的G-K(Grubler-Kutzbach)公式,能较容易地计算出串联机构的自由度,而对于一些特殊机构,尤其是含有闭环子链的复杂并联机构,往往无法便捷、正确地求解其自由度。为解决以上问题,以一种拓扑结构为[3-R(4S)1-RUPU]+R型的Delta并联机器人为研究对象,对其4S闭环子链进行了等效运动副螺旋系的求解,并判别了机构的局部自由度以及公共约束;利用修正的G-K公式,分别对原机构和等效后的机构进行了自由度的验证。结果表明:两种情形下的自由度数均为4,且自由度的性质为3平移1旋转,与实际设计相符。

Degree of Freedom Analysis of Delta Parallel Robot Based on Screw Theory

Screw theory has some advantages, such as legible geometry concept, explicit physical meaning and simple expression form and so on.With these advantages, it is often be used to analyze the DOF (Degree of Freedom) of mechanisms.According to the conventional G-K formula, it is easy to compute the DOF of serial mechanisms, but for some special mechanisms, in particular the complicated parallel mechanisms with closed-loop sub chains, it is difficult to get a reasonable DOF.A Delta robot was studied which was owning 3-R(4S)&1-RUPU]+R topology.To solve the problem which was mentioned above, the equivalent kinematic pair screw system was solved to the 4S closed-loop sub chain, and second, the idle DOF and common constraint were discriminated.Using the modified G-K formula, the DOF of the original mechanism and the equivalent one were examined.The results show that the number of the DOF is four in both case, and the character of DOF includes three translation and one rotation, which matches the practical case.