The variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear is a new type of gear. In order to research the contact characteristics of the VH-CATT cylindrical gear, tooth surface mathematical models of this kind of gear pair are derived based on the forming principle of the rotating double-edged cutting method with great cutter head in this regard. Then, according to the differential geometry theory and Hertz theory, the formula of the induced normal curvature and equation of the contact ellipse are derived based on the condition of continuous tangency of two meshing surfaces, which proves that the contact form of VH-CATT cylindrical gear is point contact. The present work establishes analytical solutions to research the effect of different parameters for the contact characteristic of the VH-CATT cylindrical gear by incorporating elastic deformation on the tooth surface, which have shown that the module, tooth number and cutter radius have a crucial effect on the induced normal curvature and contact ellipse of the VH-CATT cylindrical gear in the direction of tooth trace and tooth profile. Moreover, a theoretical analysis solution, a finite element analysis and the gear tooth contact pattern are carried out to verify the correctness of the computerized model and to investigate the contact type of the gear; it is verified that the contact form on the concave surface of the driving VH-CATT cylindrical gear rotates from dedendum at the heel to the addendum at toe and is an instantaneous oblique ellipse due to elastic deformation of the contact tooth profile, and the connecting line of the ellipse center is the contact trace path. It is indicated that the research results are beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The results also have a certain reference value for development of the VH-CATT cylindrical gear.

Wear is the main failure form of the gear transmission interface, runs through the whole life cycle of gear service, and the distributed error of the tooth surface due to the introduced assembly error will make the actual meshing state of the tooth surface different from the ideal meshing state, thus affecting the tooth surface wear trajectory and state. Therefore, considering the coupling relationship between assembly error and tooth surface contact analysis, the variation laws of the wear amount of the gear transmission interface of the variable hyperbolic circular-arc-tooth-trace cylindrical gear were studied under the consideration of assembly error in this article. Based on the tooth surface contact analysis method and Hertz contact theory, the transient linear load, the combined radius of curvature, the length axis and short axis of the contact ellipse, and the instantaneous sliding velocity were calculated. Through revising the calculation method of adhesive wear of variable hyperbolic circular-arc-tooth-trace cylindrical gears, the correlations between the tooth surface wear amount and gear parameters of variable hyperbolic circular-arc-tooth-trace cylindrical gears under different assembly errors were analyzed. The results show that the maximum wear occurs at the root of the tooth, and the wear at the indexing circle approaches zero, whether it is standard installation or non-standard installation. The vertical axial error and horizontal axial error have little effect on the wear, while the center distance error will aggravate the wear. The proposed method comprehensively considers the influence of assembly error and gear parameters on tooth surface wear, and this method can provide a theoretical reference for the design and analysis of anti-wear, wear reduction, and life extension of variable hyperbolic circular-arc-tooth-trace cylindrical gear tooth surface.

Machine tool error is one of the most important research contents in gear transmission error, and contact characteristics are important factors affecting gear transmission performance. The establishment of tooth contact analysis (TCA) model of gear pair plays a guiding role in analyzing contact characteristics of gear pair. Based on the forming principle of variable hyperbolic circular-arc-tooth-trace cylindrical gear (VH-CATT gear), the structure model and coordinate system of VH-CATT gear machine tool are established. Based on the gear meshing conditions, the tooth surface mathematical model of the VH-CATT gear with machine tool error are established, and the TCA model with machine tool error is established. The influence of different machine tool errors on the geometric contact characteristics of the gear pair is analyzed. The results show that the pressure angle error, rotation error in y direction, and rotation error in z direction, translation error in y direction, and rotation error in z direction have a significant impact on the contact characteristics of tooth profile of VH-CATT gear.

The kinematics of a robotic manipulator is critical to the real-time performance and robustness of the robot control system. This paper proposes a surrogate model of inverse kinematics for the serial six-degree of freedom (6-DOF) robotic manipulator, based on its kinematics symmetry. Herein, the inverse kinematics model is derived via the training of the Vector-Quantified Temporal Associative Memory (VQTAM) network, which originates from Self-Organized Mapping (SOM). During the processes of training, testing, and estimating of this neural network, a priority K-means tree search algorithm is utilized, thus improving the training efficacy. Furthermore, Local Linear Regression (LLR), Local Weighted Linear Regression (LWR), and Local Linear Embedding (LLE) algorithms are, respectively, combined with VQTAM to obtain three improvement algorithms, all of which aim to further optimize the prediction accuracy of the networks for subsequent comparison and selection. To speed up the solving of the least squared equation, which is common among the three algorithms, Singular Value Decomposition (SVD) is introduced. Finally, data from forward kinematics, in the form of the exponential product of a motion screw, are obtained, and are used for the construction and validation of the VQTAM neural network. Our results show that the prediction effect of the LLE algorithm is better than others, and that the LLE algorithm is a potential surrogate model to estimate the output of inverse kinematics.