In order to suppress vibration in flexible manipulators, a model of magneto-rheological vibration absorber based on internal resonance phenomenon between the flexible manipulator and vibration absorber is built. And the structure of magnetic circuit is designed, which is used to provide the applied magnetic field for the magneto-rheological elastomer. The total magnetic flux density in air gap of magnetic circuit is theoretically analyzed and verified via the real measured data. It is proved by frequency shift experiment on the beam structure platform that, the magneto-rheological elastomer has the adaptive ability of shifting its natural frequency as the applied electric current changes. Therefore, the magneto-rheological vibration absorber has a wider vibration absorption frequency.

An idea is proposed to use the controllable local degree of freedom to reduce vibration of the flexible manipulator performing the periodic task. The controllable local degree of freedom is incorporated into the flexible manipulator and used as an effective way to alleviate vibration through dynamic coupling. The feature of the periodic motion is utilized and a simple method is suggested to control vibration by constructing the appropriate modal control force via the controllable local degree of freedom, thereby counteracting the effects of the periodic exciting force. The numerical and experimental results preliminarily prove its effectiveness and feasibility in practical applications.

The key factors affecting the transmission error of gear mechanism are analyzed and the calculation formula of transmission error based on parts’ form and position errors is derived in this paper. Since the errors have different kinds of probability distributions, this paper calculate the expectation and variance of transmission error by statistical method, gives final transmission error value, and verify it by an example.

Worse than common vibration, resonance is a form of severe vibration. It is very important and useful to know what factors and conditions can result in resonance of flexible manipulators, when both link flexibility and joint flexibility are taken into account. In this paper, resonance analysis of the flexible manipulator with both link flexibility and joint flexibility is studied. Based on the flexible dynamic equations, main factors resulting in resonance of the flexible manipulator are analyzed. Furthermore, several conditions exciting resonance are derived and verified with numerical simulations. These conclusions are helpful to predict resonance and useful to the structure design and motion planning for a flexible manipulator to evade resonance

In order to suppress vibration of the flexible-joint manipulator, a new topological structure of the manipulator with the controllable local degrees of freedom is suggested. By kinematic and dynamic analysis, it is found that arbitrary motions introduced by the controllable local degrees of freedom are independent of the nominal end-effector motion, but can greatly affect dynamic performance of the manipulator. As a result, a vibration control strategy is put forward based on the controllable local degree of freedom. By planning the branch link motion, the vibration of the flexible-joint manipulator can be reduced. The results of numerical simulations verify the effectiveness of the vibration control strategy proposed in this paper.