## 3 Kinetostatics of the Lift Lever Mechanism  
This section presents the equations in the d'Alembert-Lagrange form obtained for each link of the new lift lever mechanism. The system of equations was solved. The reaction forces in the joints and the force of balance on the driving link while lifting were determined, taking into account the forces of gravity, the inertia forces of the links and the load of 150 kg on the moving platform. Kinetostatic equations were used to analyze and evaluate the distribution of forces to analytically determine the reactions in the joints under the influence of a load on the upper platform. Note that link 4 performs translational motion, and links 1,2,3,5,6 and 7 perform rotational motion in planes parallel to the \(Oxy\) plane. The forces of inertia of the links are determined by the following formula:  
\[\Phi_{i}=-m_{i}a_{S},\ i=1,\ldots,7, \tag{11}\]  
Figure 7: Graphs of angular accelerations of links 5, 6 and 7.  
where \(m_{i}\) depicts the mass of \(i\) link and \(a_{S_{i}}\) depicts the acceleration of the center of mass of the \(i\) link. The moments of the forces of inertia of the rotational links are determined by the following formula:  
\[\mathrm{M}_{i}=-J_{i}\varepsilon_{i},\ \ i=1,\ldots,7, \tag{12}\]  
where \(J_{i}\) depicts the moment of inertia of link \(i\) relative to the center of mass and \(S_{i}\) and \(\varepsilon_{i}\) depict the angular acceleration of link \(i\). The gravity forces of the links are determined based on the following known formulas:  
\[G_{i}=m_{i}g,\ \ i=1,\ldots,7, \tag{13}\]  
where \(g\) depicts the acceleration of the Earth. At points \(K_{1}\) and \(L_{1}\), a force was applied from the pressure of the hydraulic cylinder \(P_{gc}\) and directed along the line \(K_{1}L_{1}\). A balancing moment \(\mathrm{M}_{u}\) is applied to link \(1\). On link \(4\), in the center of gravity of the link, \(P_{h}\) depicts the force from the action of the load on the mobile platform. Reactions in cylindrical pairs of link connections can be determined based on the general equations of dynamics in the form of the d'Alembert-Lagrange Equation (14). It allows us to determine the reactions of all releasing connections, including those with any redundancy number. \[\sum_{k=1}^{n}F_{k}\cdot\delta r_{k}+\sum_{k=1}^{n}\Phi_{k}\cdot\delta r_{k}=0 \tag{14}\]  
where, \(F_{k}\) depicts the active forces and reactions of connections, \(\Phi_{k}\) is the inertial forces and \(\delta r_{k}\) depicts the virtual displacement. Figure 8 shows the forces acting on the links of the lever mechanism, including inertia forces, moments of inertia forces, link gravity forces, an external force acting on the platform, balancing forces acting on link \(1\) and reaction forces in the joints. Figure 8: \(Cont\). Below are the equations of the projections of all forces acting on the links of the lever mechanism. Link 1. \[\left\{ \begin{array}{c}R_{01x}-R_{12x}-m_{1}a_{s1x}-P_{gc}\cos\bigl{(}\beta_{ gc}\bigr{)}=0\\ -R_{12y}+R_{01y}-m_{1}g-m_{1}a_{s1y}-P_{gc}\sin\bigl{(}\beta_{gc}\bigr{)}=0\\ -J_{s1}\varepsilon_{1}+M_{u}-R_{01y}\frac{1}{2}\cos(\varphi_{1})+R_{01x}\frac {1}{2}\sin(\varphi_{1})+R_{12x}\frac{1}{2}\sin(\varphi_{1})-R_{12y}\frac{1_{1} }{2}\cos(\varphi_{1})\\ -P_{gc}\cos\alpha_{1}\bigl{(}\frac{1}{2}-I_{k2\mathbb{C}}\bigr{)}-P_{gc}\sin( \alpha_{1})I_{k1K2}=0\end{array} \right. \tag{15}\]  
Link 2. \[\left\{ \begin{array}{c}-R_{23x}+R_{24x}+R_{12x}-m_{2}a_{s2x}=0\\ R_{23y}+R_{12y}-R_{24y}-m_{2}g-m_{2}a_{s2y}=0\\ -J_{s2}\varepsilon_{2}-R_{23y}\frac{1_{2}}{2}\cos(\varphi_{2}-\pi+\alpha_{2}) +R_{23x}\frac{1_{2}}{2}\sin(\varphi_{2}-\pi+\alpha_{2})\\ -R_{12x}l_{cs2}\sin(\varphi_{2}-\pi+\alpha_{2}+\alpha_{Cs2})-R_{12x}l_{cs2}\cos (\varphi_{2}-\pi+\alpha_{2}+\alpha_{Cs2})\\ -R_{24y}\frac{1_{2}}{2}\sin(\varphi_{2}-\pi+\alpha_{2})+R_{24x}\frac{1_{2}}{2} \sin(\varphi_{2}-\pi+\alpha_{2})=0\end{array} \right. \tag{16}\]  
Link 3. \[\left\{