Vibration analysis of cable-driven parallel robots to define critical speeds

Cable-driven manipulators are a generation of parallel cinematic chain robots which provide important features including wide workspace and cost effective high speed operations. However, due to wideness of the workspace and the flexibility of the cables, they are susceptible of unwanted vibrations which reduce their precision. Therefore, determination of velocity limits in the operation workspace is of high importance. In this study, stability analysis and critical velocities of a four cable plane robot is considered. Governing equations of the system are extracted by use of finite element method and employing variable length element. The characteristic coefficients of the extracted equations are nonlinear and velocity dependent ones. To provide a stability analysis, the equations are linearized assuming that the end-effector experiences quasi-static movements and the system is subjected to low amplitude vibrations. Afterwards, the corresponding eigenvalue problem is analyzed and critical speeds of the robot in whole workspace domain are calculate. Furthermore, vibration frequencies corresponding to the unstable eigenvalues are determined. It is observed that system critical speed reduces as the end-effector moves to the boundaries of the workspace. In contrast to this, the frequency of the corresponding unstable modes increase moving to the borders of the workspace.