## 3 Results and Discussion  
The results of solving the equations of motion (25) and (26) and calculating the mixing and whipping force power (27), as graphs of dependencies \(\varphi=\varphi(t)\), \(\dot{\varphi}=\dot{\varphi}(t)\), \(P=P(\varphi)\) and \(P=P(\dot{\varphi})\) at different parameters of the system, are shown in Figures 2-25. If the engine power (torque a) is insufficient for the rotary motion of the crank, then the crank will perform a damped oscillation process. The crank, under the action of torque a, initially rotates upwards by some angle and then falls downwards, before reaching the neutral equilibrium position under the action of torque; it rises again, etc., until the oscillations are completely damped out. The greater the engine torque \(a\), the greater the initial maximum crank angle (Figure 2). The crank deflection angle \(\varphi\) tends to a limit of constant value \(\varphi_{1}\) as time elapses after completing the oscillating process. The greater the engine torque \(a\), the greater the value of the crank angle \(\varphi_{l}\). This means that the crank makes damped oscillations not around the neutral equilibrium position, but around a certain value \(\varphi_{l}\) of angle \(\varphi\). This is caused by the fact that, at the rotational speed of the crank \(\dot{\varphi}\to 0\), its angle of rotation is \(\varphi\to\arcsin\big{[}a/\big{(}J_{mr}\omega_{0}^{2}\big{)}\big{]}\). With constant magnitude of \(J_{mr}\) and coefficient \(\omega_{0}^{2}\) the limiting angle of rotation of the crank \(\varphi_{l}\)-\(\arcsin k_{1}a\) (where \(k_{1}=1/\big{(}J_{mr}\omega_{0}^{2}\big{)}\)). Considering that the maximum crank angle is 1.57 rad, the larger the engine torque \(a\), the larger the limiting crank angle \(\varphi_{1}\) and the oscillation period. The rotational speed of the crank \(\dot{\varphi}\) also makes damped oscillations around the zero value with initial and subsequent amplitudes; the less the rotational speed, the less the corresponding torque value with decreased period (Figure 3). Dependency graphs \(P=P(\varphi)\) and \(P=P(\dot{\varphi})\) in Figures 4 and 5 show that during the upward rotation of the crank, the pressure force on the piston from above increases, and, accordingly, the power of the mixing-whipping force decreases and the value of \(P\) reaches its maximum in further increasing the crank angle (Figure 4). In this case, the rate of increase in the rotational speed of the excitation source shaft will be greatly attenuated and the motor shaft rotational speed will decrease by the end of the cycle (Figure 5). From the relations (27), \(P\)-\(\dot{\varphi}^{3}\sin^{3}\varphi\). The general character of dependence \(P=P(\varphi)\) (Figure 4) is determined by the relation \(P\)-\(\sin^{3}\varphi\), but the amplitude and periodicity of the function \(\sin^{3}\varphi\) are influenced by the value \(\dot{\varphi}\), to be more precise, by the value \(a\). Since \(\varphi=\varphi(\dot{\varphi})\) and \(\dot{\varphi}=\dot{\varphi}(a)\) (Figure 3), \(\varphi=\varphi(a)\) (Figure 2). The smaller the value of the \(a\) engine torque, the smaller is the amplitude and period of oscillation of the mixing-whipping force power \(P\) depending on the angle of rotation \(\varphi\) of the crank according to the graphical relationships \(\varphi=\varphi(t)\) and \(\dot{\varphi}=\dot{\varphi}(t)\) in Figures 2 and 3. Maximum magnitudes of the values  
Figure 4: Dependence \(P=P(\varphi)\) for different values of \(a\). Figure 5: Dependence \(P=P(\dot{\varphi})\) for different values of \(a\). Figure 6: Dependence \(\varphi=\varphi(t)\) for different values of \(m\). The vibrational characteristics of the motor shaft rotation depend on the parameters of the device members. At relatively small piston masses, the engine shaft performs a rotational motion. In Figure 7, at sufficiently large piston masses, the shaft of the force source makes a damped oscillation of the engine shaft speed \(\dot{\varphi}\).