No abstract

One of the most important steps in the structural synthesis of planetary gear trains is to eliminate degenerate structures. First, the graph theory is used to represent planetary gear trains (PGTs). Second, a procedure is developed to identify fundamental geared entities (FGEs). Further, the single-planet FGEs are shown to have one-DOF and, therefore, cannot constitute a degenerate structure. It is this that allows a significant reduction in the calculation in relation to other methods of diagnosing degenerate structures. Third, using the concepts of FGEs and the notation of the associated adjacency matrix, an algorithm is developed for the detection of degenerate structures in PGTs. The algorithm is based on the fact that any degenerate structure is a PGT formed by two fundamental geared entities with common edges and/or vertices equal to or more than 3. Forth, the concept of connectivity between single-planet FGEs is introduced and a simple, straightforward approach for deducting the connectivity matrix from the adjacency matrix is developed. The new vertex-edge mobility criterion does not require combinatorial analysis. Besides, the method is applicable to one and multiple degrees of freedom PGTs, it is also applicable to multi-planet PGTs and complex PGTs, including contrary examples found in the literature.

The various graphical representations of planetary gear trains (PGTs), including basic assumptions and graph rules, are first reviewed in this paper. They revealed that they had close relationships. Their similarity has stimulated the development of a unified graphical representation. When there are multiple joints in a graph, it can be reconfigured without affecting the information contained in the graph. To accomplish this, a rooted graph in which a multiple joint represents either the housing of the mechanism and/or a transfer vertex of a multi-planet fundamental geared entity is employed.

The various graphical representations of planetary gear trains (PGTs), including basic assumptions and graph rules, are first reviewed in this paper. They revealed that they had close relationships. Their similarity has stimulated the development of a unified graphical representation. When there is a multiple joints in a graph, it can be reconfigured without affecting the information contained in the graph. To accomplish this, a rooted graph in which a multiple joint represents either the housing of the mechanism and/or a transfer vertex of a multi-planet fundamental geared entity is employed.

In urban mobility, special attention must be paid to the energy requirements in vehicles, air quality and noise pollution. This can be achieved in two ways: the first is the use of low-emission hybrid vehicles, the second is the use of gear transmission system with improved efficiency. Both will reduce fuel consumption and provide more environmental protection. In the current work, a low-emission Ravigneaux hybrid transmission with thirteen operation modes is shown to be feasible. A fuel-efficient strategy is developed to control the fuel consumption of hybrid modes and reduce emissions. An efficiency analysis for all driving modes of the Ravigneaux hybrid transmission is conducted. The concept of potential power is used to determine the power ratios of any three links in the fixed reference frame (FRF) when the input link in the moving reference frame (MRF) is predictable. A single equation is developed that can be manipulated to determine all the powers flowing through the train. A numerical example is provided to give a complete view of the expected efficiency values. The proposed Ravigneaux hybrid transmission is found to be suitable for urban rather than external routes. The results can provide a theoretical bases for design works of hybrid transmissions with complex planetary gears.