## 3 Engine Modifications and Mechanism Design
### Mechanism Design  
[PERSON] and [PERSON] [26] analyzed the dynamics of the slider-crank mechanism of a two-cylinder ICE analytically, using vector modeling. Figure 7 demonstrates schematic of the studied V-shaped ICE in this work. Their research aimed at finding optimum geometrical parameters, including the angle between the axis of the engine cylinders (\(a_{cyt}\)) and the angle between the crank and cylinders (\(a_{cr}\)), for which balancing moments and vibrational loads on the motor were the least. Figure 8 depicts the amplitude of balancing moments of inertia (\(\Delta I_{R}\)) and coefficient of mechanical losses (\(K_{ML}\)) for \(0^{\circ}\leq a_{cyl}\leq 360^{\circ}\). Each curve exhibits the dynamic behavior with respect to the angle between the cranks (\(a_{cr}\)), ranging from \(0^{\circ}\) to \(180^{\circ}\). As can be seen in Figure 8a, the maximum amplitudes of the moment of inertia occurred at \(a_{cr}=a_{cyl}+0^{\circ}\) or \(\pm\)\(180^{\circ}\). This horizontal layout could be used for applications where the engine is expected to endure high mechanical losses and stresses. On the other hand, they showed that by defining the optimum angle of the crankshaft as \(a_{cr}=a_{cyl}\pm 90^{\circ}\), cylinders generate less longitudinal (horizontal) vibrations. This finding is of particular interest in aviation applications where high-speed ICEs, such as aircraft, are required to attenuate the vibrations aro  
Figure 7: (**a**) Kinematic scheme of V-shaped ICE: 1—crankshaft, 2 and 4—couplers, 3 and 5—pistons [26]. Figure is reprinted with permission from publisher. Figure 8: (**a**) Amplitudes of the balancing moment of inertia and (**b**) the coefficient of mechanical losses, with respect to \(a_{cyl}\), for \(0^{\circ}\leq a_{cr}\leq 180^{\circ}\)[26]. Figures are reprinted with permission from publisher. [PERSON] and [PERSON] [27] synthesized a kinematically driven flywheel (KDF) to reduce the torsional crankshaft vibrations of an ICE through compensation of fluctuating engine torques, directly at the location where they arise. In their model, the flywheel was coupled to the crankshaft via a transmitting mechanism (Figure 9a). The proposed mechanism enabled a non-uniform conversion of the crankshaft rotation angle into the flywheel rotation angle to compensate the inertial flywheel torques (\(\theta_{FW}\dot{\psi}\)) by at least one harmonic of the fluctuating engine torque (Figure 9b). Since amplitude and phase angle of the excitation torque changed with the engine speed (\(\dot{\varphi}\)) and applied load, they prescribed a continuous adjustment of the compensated torque, \(M_{FW}(\varphi)\), with respect to the engine state. Also, due to the high amplitudes of the compensated torque generated by the non-uniform flywheel inertia, a direct force flow through the mechanism must be ensured. To meet the requirements mentioned above and expand the compatibility of their transmitting mechanism to ICEs with single/multiple-cylinders, those researchers also developed a geared double-crank mechanism (\(\overline{ABCD}\)) with cycloidal-crank input (\(\overline{BC}\)) to couple the flywheel (\(\overline{AD}\)) to the crankshaft (\(\overline{AB}\)) (see Figure 10). The amplitude of the non-uniformity of the kinematic transfer function, \(|\psi(\varphi)|\), was adjusted by the eccentricity (\(e\)) of the input crank. The topology of this mechanism enabled generating high relative accelerations, between the crankshaft and flywheel, and triggered high amplitude compensating torques, at a four-stroke three-cylinder inline diesel engine, under full load at 2000 rpm. Figure 10: Mechanism topology of the proposed KDF [27]. Figure is reprinted with permission from publisher. Figure 9: Kinematically driven flywheel (KDF) of a combustion engine: (**a**) schematic of the arrangement; (**b**) free-cut compensation system [27]. Figures are reprinted with permission from publisher.