Abstract This article presents a method for modeling the dynamics and minimum vibration controller design of a 3-DOF parallel mechanism, the so-called Tripteron. The proposed comprehensive dynamic model consists of the dynamic model of the prismatic actuators, variable friction in them, and dynamics of flexibility in the limbs which caused vibration of the robot’s end-effector by considering a spring-damper element for each link based on the Tripteron structure. Then the identification procedure is carried out by collecting practical data from the robot. In order to design the oscillation damping controller, the Minimum Length Integral Sliding Mode Controller(MLISMC) is proposed in which the Phase Trajectory Length(PTL) approach is applied to ISMC for proper placement of closed-loop poles of the identified system. The foregoing method is based on numerical calculations to minimize the end-effector vibrations along the point-to-point control. Simulation and experimental results reveal that the PTL of the system have been reduced about 95% in simulation and 30% in the experimental test.

中文翻译：

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考虑虚拟柔性连杆的三自由度直角并联机器人建模、辨识及最小长度积分滑模控制

摘要 本文提出了一种对三自由度并联机构（即所谓的 Tripteron）的动力学和最小振动控制器设计进行建模的方法。所提出的综合动力学模型包括棱柱致动器的动力学模型、它们中的可变摩擦力以及通过考虑基于 Tripteron 的每个连杆的弹簧阻尼元件而引起机器人末端执行器振动的肢体柔性动力学结构体。然后通过从机器人收集实际数据来执行识别程序。为了设计振荡阻尼控制器，提出了最小长度积分滑模控制器（MLISMC），其中将相轨迹长度（PTL）方法应用于 ISMC，以正确放置已识别系统的闭环极点。前述方法基于数​​值计算以最小化沿点对点控制的末端执行器振动。仿真和实验结果表明，该系统的PTL在仿真中降低了95%左右，在实验测试中降低了30%左右。