## 3 Measurement of Connecting Rod Journal  
### Relationship between Sampling Angle and Motion Angle  
To realize the synchronous measurement of the crankshaft main journal and connecting rod journal, the measuring mechanism can follow the movement away from the connecting rod journal to complete the cross-section radial data collection without interfering with the measuring structure of the main journal. To simulate the motion state of the connecting rod when the engine is running, the crank arm of the crankshaft is regarded as a crank, the connecting rod journal and the measuring head part are regarded as a hinge and the measuring arm is regarded as a connecting rod. A crank-rocker measuring mechanism is designed, and the principle of the mechanism is shown in Figure 3. \(O\) is the center of the main journal, \(O_{1}\) is the center of the connecting rod journal, \(OO_{1}\) is the crank arm, \(O_{1}B\) is the measuring arm. Probe \(A\) is installed in the direction perpendicular to the measuring arm, and guide rail \(B\) is fixed on the lifting-lowering pipe. When guide rail \(B\) descends to the measuring point, the distance from the center of the main journal is \(L\). The measuring arm \(O_{1}B\) is a retractable structure, which can expand and contract with the rotary motion of the connecting rod journal.  
According to the schematic diagram of the measuring mechanism shown in Figure 3, the center \(O\) of the circle is the center of rotation, and the circular dotted line is the trajectory of the connecting rod journal center \(O_{1}\). The radius \(R\) of the dotted circle is the length of the crank arm, the radius \(r\) of the realization circle is the radius of the connecting rod journal. The angle between the crank arm \(OO_{1}\) and the vertical lifting table \(OB\) is \(\varepsilon\). In the process of crankshaft measurement, the counterclockwise direction is set as positive, and the angular velocity is \(\omega\). The angle between probe \(A\) in contact with the connecting rod journal and the crank arm \(OO_{1}\) is set as \(\theta\). According to the cosine theorem of \(\Delta OO_{1}B\), the functional relationship between the included angle \(\theta\) and the rotation angle \(\varepsilon\) is:  
\[\theta=\left\{\begin{array}{rl}\frac{\pi}{2}-\arccos\left(\frac{R-L\cos \varepsilon}{\sqrt{k^{2}+L^{2}-2 RL\cos\varepsilon}}\right)0^{\circ}\leq \varepsilon\leq 180^{\circ}\\ \frac{\pi}{2}+\arccos\left(\frac{R-L\cos\varepsilon}{\sqrt{k^{2}+L^{2}-2 RL \cos\varepsilon}}\right)180^{\circ}<\varepsilon\leq 360^{\circ}\end{array}\right. \tag{1}\]  
Figure 3: Principle diagram of connecting rod journal measurement mechanism.  
According to Equation (1), the relationship curve between \(\theta\) and \(\varepsilon\) can be obtained, as shown in Figure 4. When the journal rotates once a week, the angle \(\theta\) relative to the crank arm varies from \(-90^{\circ}\) to \(270^{\circ}\) as angle \(\varepsilon\) varies from \(0^{\circ}\) to \(360^{\circ}\). The probe scans the circumferential surface of the connecting rod journal and collects the radial dimension change while the main journal rotates around the rotary center. However, it is found that the relationship between the angle \(\theta\) and rotation angle \(\varepsilon\) is not linear. The relationship between the angular velocity \(\Omega\) and the angular \(\varepsilon\) is obtained by the derivation of the included angle \(\theta\), as shown in Figure 5. It is found that the motion of the probe on the circumferential surface of the connecting rod journal is not uniform, and the sampling interval is not equal.