## 4 Results
### Output Torque  
As previously mentioned, the mechanical work produced by an OP engine is split between the two crankshafts due to the presence of two pistons sharing the same cylinder, and each collecting part of the energy produced by the combustion of gases, represented by the indicating work \(pdV\). Moreover, when an offset is present, the two pistons do not move symmetrically, resulting in an unequal distribution of mechanical work between them. Defining expansion work as positive and compression work as negative, when the exhaust piston passes TDC and begins the expansion phase, the work collected by it becomes positive. Meanwhile, the intake piston has not reached TDC yet and remains in the compression stroke, meaning the work in this case is still negative [25]. Figure 11: _Cont._  
Figure 11: Resultant moment of co-rotating and counter-rotating shafts with \(M^{\prime}_{rec,t}\) balanced (scenario 2) and with different offset angles for 3-cylinder configuration; (**a**) co-rotating with \(0^{\circ}\) offset; (**b**) counter-rotating with \(0^{\circ}\) offset; (**c**) co-rotating with \(5^{\circ}\) offset; (**d**) counter-rotating with \(5^{\circ}\) offset; (**e**) co-rotating with \(10^{\circ}\) offset; (**f**) counter-rotating with \(10^{\circ}\) offset; (**g**) co-rotating with \(15^{\circ}\) offset; (**h**) counter-rotating with \(15^{\circ}\) offset. Figure 12: _Cont._  
The output torque is therefore computed as the sum of the contributions from the two crank mechanisms, which are evaluated separately. Figure 13 illustrates the output torque  
Figure 12: Resultant moment of co-rotating and counter-rotating shafts with \(M^{\prime}_{rec,r}\) balanced (scenario 2) and with different offset angles for 4-cylinder configuration; (**a**) co-rotating with \(0^{\circ}\) offset; (**b**) counter-rotating with \(0^{\circ}\) offset; (**c**) co-rotating with \(5^{\circ}\) offset; (**d**) counter-rotating with \(5^{\circ}\) offset; (**e**) co-rotating with \(10^{\circ}\) offset; (**f**) counter-rotating with \(10^{\circ}\) offset; (**g**) co-rotating with \(15^{\circ}\) offset; (**h**) counter-rotating with \(15^{\circ}\) offset. profile generated by each crankshaft over a complete engine cycle for a single cylinder. It is evident that, increasing the offset angle, the exhaust piston operates in a more favorable position than the intake piston, allowing it to generate greater torque. However, the intake piston generates less torque than the zero offset configuration and in extreme cases, for high offset values, the intake shaft may perform zero or negative work over an engine cycle. Figure 13: Output torque of a single cylinder; **(a)**\(0^{\circ}\) offset; **(b)**\(5^{\circ}\) offset; **(c)**\(10^{\circ}\) offset; **(d)**\(15^{\circ}\) offset. Figures 14 and 15 illustrate the output torque of the whole OP engine, the 3-cylinder, and the 4-cylinder, respectively. Neglecting the variation in trapping efficiency, the introduction of an offset results in a reduction in the total engine torque output (Table 4). This reduction is primarily due to the delayed intake shaft timing, the decrease in the effective compression ratio, and the earlier opening of the exhaust ports caused by the advanced timing of the exhaust piston. However, considering the improvement of the trapping efficiency related to the introduction of the offset and neglected in this contribution, the negative effects recorded here would be compensated and the output torque would be higher than in the case without offset [23]. Moreover, from a structural perspective, introducing the offset will result in a higher load on the exhaust piston and the exhaust-side portion of the liner due to the increased thrust force. Although it would be interesting to compare the presented results with engines designed for the same road applications, the purpose of this study is to quantify the differences that emerge between the torques output from the two crankshafts as a function of the offset rather than analyze the absolute value of the total torque output.