Teleoperation is crucial for hazardous environment operations and serves as a key tool for collecting expert demonstrations in robot learning. However, existing methods face robotic hardware dependency and control frequency mismatches between teleoperation devices and robotic platforms. Our approach automatically extracts kinematic parameters from unified robot description format (URDF) files, and enables pluggable deployment across diverse robots through uniform interfaces. The proposed interpolation algorithm bridges the frequency gap between low-rate human inputs and high-frequency robotic control commands through online continuous trajectory generation, \n{while requiring no access to the closed, bottom-level control loop}. To enhance trajectory smoothness, we introduce a minimum-stretch spline that optimizes the motion quality. The system further provides precision and rapid modes to accommodate different task requirements. Experiments across various robotic platforms including dual-arm ones demonstrate generality and smooth operation performance of our methods. The code is developed in C++ with python interface, and available at https://github.com/IRMV-Manipulation-Group/UTTG.