Previous work on controllability of underactuated serial horizontal planar manipulators mostly focused only on a specific number of links, whereas this paper considers a general $N$-link case. The main contribution of this paper is accessibility and small-time local controllability (STLC) results for $N$-link serial, horizontal, planar manipulators with one unactuated joint. An $N$-link ($N\ge 3$) manipulator with the first joint actuated is STLC for a subset of equilibrium points based on Sussmann’s general theorem for STLC. In contrast, if the first joint is not actuated, it is not accessible or STLC.

中文翻译：

---

具有一个未激活关节的N链接水平平面机械手的可控性和可及性结果

以前关于欠驱动串行水平平面机械手的可控性的研究主要集中在特定数量的链接上，而本文认为 $ñ$-link大小写。本文的主要贡献是可访问性和短期本地可控性（STLC）结果$ñ$-link带有一个未激活关节的串行，水平，平面操纵器。一个$ñ$-链接（$ñ\ge 3$）第一个关节被操纵的机械手是STLC，用于基于STLC的Sussmann通用定理的平衡点子集。相反，如果未激活第一关节，则无法访问它或STLC。