Meshing synthesizing stiffness of teeth is the comprehensive effect of all teeth in the whole meshing region, which is related to elastic deformation of single tooth, comprehensive elastic deformation of a pair of teeth and overlap ratio of gear. This paper adopts Ishikawa method which is commonly used in the calculation of tooth deformation. MATLAB software is used for the programming of Ishikawa formula, and then the value and distribution of gear deformation stiffness are obtained, which realizes the purpose of reducing high-order harmonic excitation in the dynamic equation, thus providing a reference frequency to avoid resonation in low-frequency region.

Gregory’s decomposed theorem of isotropic plate is extended to investigate torsional circular shaft of cubic quasicrystal with homogeneous boundary conditions, and the theory of equivalence that Cheng’s refined theory and Gregory’s decomposed theorem is extended to the cylindrical coordinate. The general solution of torsional circular shaft on cubic quasicrystal with homogeneous boundary conditions is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal without ad hoc assumptions. At first expressions are obtained for all the displacements and stress components in term of some 1D functions. Using Lur’e method, the exact equations were given. And the exact equations for the torsional circular shaft on cubic quasicrystal without surface loadings consist of four governing differential equations: two harmonic equations and two transcendental equations. Using basic mathematic method and the general solutions, an example is examined.

This paper presents a novel, precision, maneuverable, 3-DOF translational parallel mechanism. The mechanism’s important feature is that all of the kinematic joints are the revolute joints. The paper derives the mechanism’s kinematic forward solution and inverse solution by using of coordinate transformation elimination method and vector method, and establishes proper kinematic modeling. Kinematic simulation is carried out by ADAMS virtual prototyping software. The operating data is obtained, it verifies the correctness of solving the forward and inverse solution, and solve the question of choices for many results during the theoretical solution. This technique can provide a useful tool in the design of kinematic trajectory of the parallel mechanism’s end-effector and the kinematic analysis of other parallel mechanism.

The model of vibration mechanism is built with Pro/E software. Simulate the vibration mechanism and obtain the cosine curve of the vibration table in the vertical direction by Pro/E. Afterwards, perform transient dynamics analysis of eccentric shaft in the vibration mechanism, and get the maximum average stress and the dangerous section. The simulation is correct and the dynamics analysis is accurate, which lays the foundation for the analysis, design and manufacture.

The solid models of the mechanical parts were built in ProE software to on the basis of the analysis of the structural characteristics and movement of the interior transmission mechanism of the hoist, and assemble the mechanical parts of the solid models through certain constraint conditions, and simulate the process of its transmission. By simulating tracing the specified key point to get the its variation curve of displacement, the stabilization of the transmission mechanism was verified; comparing the velocity curve of the input shaft and the drum, we can get a conclusion that the transmission ratios of the ProE movement simulation are consistent with the theoretical calculation value, which providing data fundmenatal for further design, analysis and manufacturing of the interior transmission mechanism of the hoist.