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This study contributes to the development of a systematic methodology for the torque and power-flow analyses of multi-input multi-output (MIMO) epicyclic gear mechanisms (EGMs) with or without reaction link based on the concept of fundamental circuit. The studies on power-flow analysis of EGMs are mostly done in the context of efficiency formulations. In the opinion of the authors, the design process of the MIMO mechanism involves not only finding the configuration that provides the correct velocity ratios but also meeting other kinematic requirements and ensuring that the two inputs have a mutually constructive nature. To demonstrate the analysis, a new motor/generator integrated hybrid transmission design is used to show how the torque acting on each link of an epicyclic gear train (EGT) can be systematically solved in terms of input torque(s) and/or controlled output torque. This paper presents a unification of kinematic and torque balance approaches for the analysis of MIMO epicyclic-type transmission trains. The results presented are meant to deepen the knowledge as to how and why a MIMO epicyclic-type transmission should operate in a certain way under the given conditions. In the process, this paper explores the theoretical bases of operation of the Toyota Hybrid System and the root cause of some confusion in the field of EGTs.

A new methodology for the enumeration of feasible clutching sequences for a given epicyclic gear mechanism (EGM) is presented using the kinematic nomographs of epicyclic-type transmission mechanisms. From such nomographs, the kinematic characteristics of an epicyclic gear mechanism can be expressed in terms of the gear ratios of its gear pairs. From a single nomograph, the angular velocities for all of the coaxial links can be estimated and compared directly without specifying the exact size of each gear. In addition, the angular velocities can be arranged in a descending sequence without using complicated artificial intelligence or algorithmic techniques. Then, a procedure for the enumeration of feasible clutching sequences associated with a transmission mechanism composed of two or more fundamental gear entities (FGEs) is developed. The reliability of the methodology is established by applying it to two transmission gear trains for which solutions are either fully or partially available in the literature. In the process, an incomplete in the results reported in previous literature is brought to light. And the root cause of this incompleteness is explored. The present methodology is judged to be more efficient for enumeration of all feasible clutching sequences of an EGM.

Although there are many epicyclic-type automatic transmissions in production, the related configuration design methods are still tedious and borne to human error. A simple methodology for the systematic design of the Ravigneaux-type epicyclic gear transmissions needs to be developed. First, fundamentals and gear-shifting of four-speed and six-speed epicyclic-type automatic transmissions are illustrated to establish the design requirements. Second, based on the kinematic nomographs of the corresponding basic gear ratios, a simple clutching-sequence method is proposed and illustrated. Next, a planar-graph representation is presented to arrange the desired clutches for each possible clutching sequence into the epicyclic gear mechanism. Then, with the above methods, the systematic designs of the epicyclic gear mechanisms are given for demonstrating the feasibility of the proposed methodology. The result of this work shows that the seven-, eight-, and nine-link two-DOF Ravigneaux-type epicyclic gear mechanisms could reach four-, six-, and eight-forward speeds at most, respectively. New five-, six-, seven-, and eight-velocity automatic transmissions are enumerated from the two-ring eight-and nine-link Ravigneaux gear mechanisms. It is a major breakthrough to design completely satisfactory eight-speed automatic transmissions from the nine-link Ravigneaux gear mechanism.

The mechanical efficiency is a computed value for comparing the performance of the multi degrees-of-freedom geared transmissions of hybrid vehicles. Most of the current methods for estimating gear trains mechanical efficiency require the decomposition of gear transmissions in basic structural elements or planetary gear units (PGU). These are two degrees-of-freedom components whose mechanical efficiency has a deep influence on the overall device. The authors (E.L.E., E.P.) already evidenced that, under certain kinematic conditions, the classic Radzimovsky’s formulas, widely accepted for computing the mechanical efficiency of PGUs, are not adequate. In this paper, more general and reliable formulas for computing the mechanical efficiency are deduced. The proposed formulas herein, exploiting the concept of potential or virtual power, evidence the dependency between kinematics and efficiency. A numerical example compares our results with previous work on the subject.