Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.
In order to improve the working efficiency of serial robot, a new trajectory planning method is proposed. Taking 6-DOF robot as an example, the 6-DOF open-chain robot is transformed into a 12-DOF closed-chain robot by creating a virtual robot at the end-effecter. Then, the virtual joint variable of the virtual robot is used to represent the end position of the robot, and the direct relationship between the joint variable and the position attitude is obtained. The B-spline Curve is used to plan the trajectory in the Cartesian space, and the joint motion trajectories of the robot are controlled indirectly to meet the requirements of the joint space speed and acceleration. Finally, the time-optimal solution of the trajectory programming is solved by the Genetic Algorithm under the condition of satisfying the joint space and the Cartesian space.
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