In this paper, the open-chain arm containing flexible links connected through telescopic joints is investigated so as to replace robotic chains with revolute joints. In this manipulator, telescopic joints are considered by a simultaneous motion combination of the prismatic and revolute joints. In comparison with revolute–prismatic joints in which prismatic joint hubs are utilized, telescopic joints lack the hub, and the linear motion is generated via a gear. Accordingly, the flexible link is not placed inside the hub. In fact, the link is merely divided into two sections each at a time step. The front section which is considered in the motion equations is placed at the back of the hinge’s point. This part solely creates vibration, which probably affects the motion of other sections. This type of manipulator’s joints due to the structure benefits consists of the optimum weight, simple mechanism, extended workspace acceptable for robotic tools, industrial machinery, and domestic systems. To derive motion equations of N-link flexible manipulator with telescopic joints system, the Euler–Lagrange formulation is employed. The obtained equations are in the time-varying form, and the manipulator link length changes during motion. The derived equations are simulated for a two-link system with different elasticity values, and the results are then analyzed to verify the outcomes. The bifurcation analysis has also been used to prevent unstable vibrations and chaotic responses. It should be noticed that this type of manipulator can be used in a fast and precise mechatronics' system for utilization in space exploration, space station, and spacecraft as well.

在本文中，研究了包含通过伸缩关节连接的柔性链节的开链臂，以便用旋转关节代替机器人链。在这种机械手中，伸缩关节是通过棱柱形关节和旋转关节的同时运动组合来考虑的。与使用棱柱形关节轮毂的旋转-棱柱形关节相比，伸缩式关节缺少轮毂，并且线性运动是通过齿轮产生的。因此，柔性连杆未放置在集线器内部。实际上，一次仅将链接分为两个部分。运动方程式中考虑的前部位于铰链点的后部。该部分仅产生振动，这可能会影响其他部分的运动。由于具有结构上的优势，这种类型的机械手关节包括最佳重量，简单的机械结构，可被机器人工具，工业机械和家用系统使用的扩展工作空间。为了推导带有伸缩缝系统的N连杆柔性机械臂的运动方程，采用了Euler–Lagrange公式。所获得的方程为时变形式，并且机械手连杆的长度在运动过程中发生变化。针对具有不同弹性值的双链接系统对导出的方程进行仿真，然后分析结果以验证结果。分叉分析也已用于防止不稳定的振动和混沌响应。应当注意，这种类型的机械手可用于快速精确的机电一体化系统中，以用于太空探索，空间站，