## 2 Device Design
### Connecting Structure  
The test process of the load-lifting capacity of the tractor hydraulic linkage could be divided into the connection stage of hydraulic linkage and test device, and the load-lifting stage. To avoid the influence of the manual connection between the lower link and loading device on staff safety, Figure 4 showed the mechanism to realize the unmanned connection between the tractor and the loading device. Two connecting pins and a hydraulic cylinder were built in the loading link, and the connecting pin was driven to realize the connection between the device and the lower link under the action of the hydraulic cylinder. Whether the connection is successful can be confirmed by the color change of the sensor indicator.  
Figure 3: Catching mechanism of the lower link.  
Figure 2: Load-lifting device model for tractor hydraulic linkage.  
The spherical hinge of the lower link used to connect agricultural equipment is prone to tilt, and the axis of the spherical hinge is not parallel to the axis of the hole. Therefore, the manual way is often used to level during the previous test. The shape of the connecting pin in the device would affect whether the lower link could be connected to the device under this condition.  
During the movement of the connecting pin through the spherical hinge, it is necessary to overcome the frictional force of the rotation of the spherical hinge. Additionally, the load torque is required to be less than the driving torque of the spherical hinge. Hence, to ensure that the spherical hinge can rotate during the connection process, the shape of the connecting pin should meet the following conditions:  
\[\left\{\begin{array}{c}\left\{\begin{array}{c}F_{m}=f_{v}\cdot F_{q}\\ F_{q}=F\cdot\tan\lambda\\ F_{t}=F\cdot\sin\lambda\\ \end{array}\right.\\ \left\{\begin{array}{c}F_{t}\cdot\tau>F_{m}\cdot r\\ F\cdot\sin\lambda>F\cdot\tan\lambda\cdot f_{v}\\ \cos\lambda>f_{v}\end{array}\right.\\ \end{array}\right. \tag{2}\]  
where \(F\) is the thrust of the connecting pin during the move process; \(F_{t}\) is the positive pressure on the spherical hinge; \(F_{m}\) is the friction of the spherical hinge; \(f_{v}\) is the equivalent friction coefficient with a value of \(0.2\); \(F_{q}\) is the vertical component of the positive pressure of the spherical hinge; and \(\lambda\) and \(r\) are the taper angle and the radius of the connecting pin, respectively.  
Meanwhile, the connecting pin could also bear the test load. The radius of the connection pin should conform to Equation (3):  
\[\left\{\begin{array}{c}\tau=\frac{F}{A}=\frac{F}{\pi.\pi_{\min}^{2}}\leq[\tau] \\ \sigma=\frac{M.y}{\Gamma_{c}}=\frac{M_{\max}}{W_{z}}\leq[\sigma]\\ W_{z}=\frac{\pi.\pi_{\min}^{3}}{4}\end{array}\right. \tag{3}\]  
where \([\tau]\) and \([\sigma]\) are the characteristic strength parameters of 45# steel, and the safety factor was 1.5. \(r_{\min}\) is the minimum radius of the connection pin. \(I_{z}\) is the inertial moment of the cross-section of the connection pin to the neutral axis; \(W_{z}\) is the bending section coefficient of the connection pin; \(M_{\max}\) is the maximum bending moment borne by the connecting pin. The tensile strength of 45# steel with a hardness of 197 HB is 600 MPa [18].  
Figure 4: Connection mechanism of the lower link and the lifting device.  
Therefore, the taper angle \(\lambda\) ranged from 0\({}^{\circ}\) to 78\({}^{\circ}\), and the minimum radius of the connection pin was 7.8 mm. To facilitate penetration of the connection pin into the spherical hinge and meet the safety of the connection pin, the taper angle and diameter of the connection pin were 39\({}^{\circ}\) and 16 mm, respectively.