## 1 Introduction  
One of the development goals for modern road vehicles is to enhance energy efficiency and reduce emissions. The powertrains usually combine multiple power inputs, such as internal combustion engines (ICEs) and electric motors/generators (M/Gs), to improve fuel economy. The role of the transmission system is to match the varying road resistance with the torque and the power characteristics of different power sources. Therefore, an ideal transmission should have a wide ratio coverage, a high torque capacity, and a smooth ratio variation to fulfill the requirements of efficiency and shifting quality.  
The V-belt continuously variable unit (CVU) has been widely applied in both on-road and off-road vehicles due to its light weight, mechanical simplicity, and seamless ratio variation. [1, 2, 3, 4] The variator of the V-belt CVU comprises a metal or rubber V-belt and two pulleys. The torque is transmitted by the traction between the V-belt and the two sheaves of the pulleys. Its ratio coverage and torque capacity have been proven sufficient for various road vehicles, which range from sport scooters and all-terrain vehicles (ATVs) with rubber V-belts to full-size sedans and sport utility vehicles (SUVs) with metal V-belts. Therefore, it is beneficial to develop a hybrid system based on the V-belt CVU.  
In this paper, 28 hybrid systems with V-belt or hydrostatic CVU [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31] have been studied. Their application cases vary from scooters, passenger cars, to buses and un manned aerial vehicles. Among the majority of them [5; 6; 7; 9; 10; 14; 19; 20; 23; 24; 25; 26; 27; 31], the second power input is connected to the driveline directly or via clutches. The CVUs of four systems [15; 29; 30] are connected after the electric variable transmissions (EVTs or e-CVTs) formed by two power inputs connected together via a planetary gearest(s). The CVUs of six systems [5; 8; 13; 16; 21; 22] are coupled with planetary gearsets, and the arrangement forms a power-split device which can reduce the torque load of the CVU [32; 33; 34]. Three systems [10; 11; 12; 17; 18] can exploit twice the ratio coverage of the CVU by transmitting the power through the CVU in opposite directions in different driving modes with the aid of clutches and gearsets. To efficiently analyze the topological structures and the characteristics of the hybrid systems with CVUs, there is a need for a simple and generic graphic method.  
In the three systems mentioned in [10; 11; 12; 17; 18], although the total ratio coverages are increased by the dual-way manipulated CVUs, the power is transmitted solely by the CVUs during the continuously variable ratio modes. Their torque capacities are still limited by the maximum allowable torque of their CVUs. In the researches done by [PERSON] [32; 33] and [PERSON] [34], the CVU can be combined with a planetary gearset, forming a power-split mechanism with a constant ratio path parallel to the CVU. The torque loading of the CVU can be shared by the constant ratio path, so the torque capacity of the system is higher than that of the CVU. However, as a trade-off, the overall ratio coverage of the system is less than that of the CVU [32]. Therefore, if the dual-way manipulated CVU and the power-split feature can be combined together, a hybrid system can have both a wider ratio coverage and higher torque capacity. Hence, a systematic process is required to synthesize the complex layout of the system.  
In this paper, a graphical method called the BPD is proposed to display and synthesize the topological layout of powertrain systems. The key characteristics of the system and their required conditions in the BPD are then identified. With the aid of BPD and the identified characteristics, the previous 28 hybrid systems are classified. With the BPD method, a new system suitable for heavier-duty application will be synthesized, with the features which the previous 28 systems cannot achieve.