We find the generating function for group tensors contained in the enveloping algebra of each simple compact group of rank three or less. The generating function depends on dummy variables which carry, as exponents, the degrees and representation labels of the tensors; it suggests an integrity basis, a finite number of elementary tensors, in terms of which all can be expressed as stretched tensor products. We show how the generating functions for tensors in the enveloping algebra of SO(5) and SU(3) reduce when the tensors are acting on the basis of representations for which one of the Cartan labels vanish. The missing label problem in the reduction SO(5) (R-HOOK) SO(3) restricted to SO(5) representations of the type (0,(nu)) is considered; the eigenvalues and eigenvectors of a missing label operator are found up to (including) representation (0,12).

No description available.

No description available.

Double-enveloping reducer is widely used in the industry due to its high transmission torque and high accuracy. The screw theory and the rigid-body transformation method are introduced and applied in this thesis to the determination of the worm surface. The equation of the worm surface is derived by the two methods based on different geometries of cutting tools (conical cutter and fly cutter). According to the Standards of American Gear Manufacturers Association (AGMA6030 C-87), the size and the shape of the cutters can be determined to conform the worm offset surface. Moreover, a measuring system is set up with a CMM (coordinate measuring machine) to measure and record the center point of the touch probe when it contacts with the surface of the double-enveloping worm. Finally, comparisons of measured results with different theoretical worm offset surfaces obtained from two types of cutting tools are made in this study. Geometric errors of the measured worm offset surface shows that the worm used in this thesis was machined by cutters with a conical form.

No description available.

Tires play an extremely important role in the operation of a vehicle as they transmit forces between the ground and the vehicle. Consistent efforts have been made over the years towards modeling and simulation of tires and more recently, there has been an increasing need to understand the transient response of tires to various high-frequency events such as anti-lock braking and short-wavelength disturbances from the road. Major thrust has been provided by the tire industry to develop simulation models that accurately predict the dynamic response of tires without the use of computationally intensive tools such as FEA. The objective of this research is to explain the development, implementation and validation of a simulation tool based on a dynamic tire model that would assist in the analysis of the effect of tire belt vibrations on the braking performance of a vehicle. A rigid ring tire model, tandem elliptical cam enveloping model and a rule-based ABS model have been developed for this purpose. These were combined together in a quarter vehicle model and implemented in Matlab-Simulink. These models were developed for adaptation with CarSim to provide a simulation tool that can be utilized in both tire and vehicle design processes. In addition to model implementation, a parameterization procedure was developed to estimate the parameters of the rigid ring tire and enveloping model based on experimental data for a given tire. Validation studies have also been performed to ensure the accuracy and validity of the tire model. Following this, the braking performance of ABS under different road surfaces were evaluated. Based on the simulation results, final conclusions were drawn with regards to the analysis and detailed recommendations for future work directed towards the improvement of the tool were provided. / Master of Science

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Bibliography: leaf 77. / by Devra Garfinkle. / Ph.D.

Double-Enveloping Reducers are used widely in various industries. In this study, a procedure is developed to analyze the geometric and kinematic properties of such a rotational reducer. In the mechanism, the globoidal worm profile is derived by using the sweeping method and the profile of the globoidal worm wheel is obtained by employing the screw theory. Based on Standards of the American Gear Manufacturers Association (AGMA 6030-C87), the involved parameters in designing and analyzing the reducer are revealed. Finally, the transmission errors based on tooth the contact analysis (TCA) are also reported.

In this thesis we propose a description of the operad defining post-Lie algebras in terms of rooted trees and we discuss some applications of such a construction. In particular, we re-derive both the free post-Lie algebra defined in [22] and the main result of the paper [8]. Furthermore, a possible extension of the concept of symmetric brace algebra to the category of the post-Lie algebras is proposed. / Nessa tese propomos a descrição da operad que define as álgebras pós-Lie em termos de árvores enraizadas e discutimos algumas aplicações dessa construção. Em particular, nós obtemos novamente a álgebra pós-Lie livre definida em [22] e o resultado principal do artigo [8]. Além disso, uma possível extensão do conceito de álgebra brace simétrica à categoria de álgebras pós-Lie é apresentada.

In this thesis we propose a description of the operad defining post-Lie algebras in terms of rooted trees and we discuss some applications of such a construction. In particular, we re-derive both the free post-Lie algebra defined in [22] and the main result of the paper [8]. Furthermore, a possible extension of the concept of symmetric brace algebra to the category of the post-Lie algebras is proposed. / Nessa tese propomos a descrição da operad que define as álgebras pós-Lie em termos de árvores enraizadas e discutimos algumas aplicações dessa construção. Em particular, nós obtemos novamente a álgebra pós-Lie livre definida em [22] e o resultado principal do artigo [8]. Além disso, uma possível extensão do conceito de álgebra brace simétrica à categoria de álgebras pós-Lie é apresentada.