Contents lists available at ScienceDirect Mechanism and Machine Theory journal homepage: www.elsevier.com/locate/mechmachtheory Design and analysis of a novel multi-speed automatic transmission with four degrees-of-freedom Peng Donga,b, Yanfang Liua,b,⁎, Peter Tenbergec, Xiangyang Xua,b aDepartment of Automotive Engineering, School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China bBeijing Key Laboratory for High-effi cient Power Transmission and System Control of New Energy Resource Vehicle, Beihang University, Beijing 100191, PR China cInstitute of Industrial and Automotive Drivetrains, Ruhr-University Bochum, Bochum 44801, Germany ARTICLE INFO Keywords: Automatic transmissionPlanetary gear setParallel-axis gear pair Genetic algorithm Power flow EfficiencyABSTRACT With the pressing demand of reducing fuel consumption and improving driving performance, automatic transmissions (ATs) tend to have a wider ratio spread and more speeds. However, it is difficult to achieve a compact design by using only planetary gear sets (PGSs) or only parallel- axis gear pairs (PGPs). In this paper, we propose a novel multi-speed AT characterized by a combination of PGSs and PGPs on two parallel axes. All feasible clutching sequences are synthesized through a systematic procedure. Results reveal that we can obtain a nine, eleven or thirteen-speed clutching sequence by tuning the stationary ratios of PGPs. A computationalmodel based on genetic algorithm (GA) is established to optimize the gear ratios. Within the constraints of stationary ratios and single transition shift, an optimal solution is found with a wide ratio spread. Furthermore, a matrix method is developed to analyze transmissionkinematics and kinetics, which is especially suitable for computer-aided analysis of complexfour degrees-of-freedom (DOFs) transmissions. Key parameters such as power flow, efficiency and clutching sequence of the proposed AT are evaluated and compared. This research may shedlight upon synthesis, design and analysis of complex ATs with a wider ratio spread and morespeeds. 1. Introduction In view of fuel economy and driving performance, there has been a rapid increase in market demand for ATs with a wider ratio spread and more speeds. On the one hand, the highest gear ratio becomes smaller to improve fuel economy at high vehicle speed. On the other hand, the first gear ratio becomes larger to improve drivability in the vehicle starting and creeping process. In addition, the increasing number of speeds allows smaller gear steps to achieve more comfortable and smooth gear shift. Hence a growing numberof automakers are introducing passenger cars with eight or nine-speed ATs, as a part of the continuing e ffort to improve drivability and fuel economy of their vehicles. However, energy loss of ATs with high number of gear ratios may increase depending on di fferent driving scenarios. On the highway, the vehicle usually runs at a certain speed for a long time after each gear shift. In this case, high number of gear ratiosenables the engine to work in the consumption-optimal speed range at di fferent vehicle cruising speed. The gains from the engine are http://dx.doi.org/10.1016/j.mechmachtheory.2016.10.013 Received 21 April 2016; Received in revised form 9 September 2016; Accepted 20 October 2016⁎Corresponding author at: Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang University, Beijing 100191, PR China. E-mail address: liuyanfangbeihang@163.com (Y. Liu).Mechanism and Machine Theory 108 (2017) 83–96 0094-114X/ © 2016 Elsevier Ltd. All rights reserved. crossmore than the loss from gear shifts in terms of vehicle e fficiency. Conversely, if the vehicle runs under urban conditions with continuous acceleration and deceleration, high frequency of gear shifts can lead to big energy loss which deteriorates the vehicle efficiency severely. By introducing direct multiple gear shifts in the shift logic, not o