## 2 Kinematic Analysis  
The kinematic scheme of a two-rod crank knee press with an internal engine arrangement is shown in Figure 1. The mechanism under consideration has the following design features: (a) between the lengths of the links there is an equality \(|\mathbf{E}\mathbf{D}|=|\mathbf{F}\mathbf{C}|,\ |\mathbf{C}\mathbf{D}|=|\mathbf{F}\mathbf{E}|,\ |\mathbf{F}\mathbf{P}|=|\mathbf{C} \mathbf{P}|\); (b) link 4 makes a forward motion [1], therefore \(\mathbf{\theta}=\mathbf{const}\), also there is \(\mathbf{\varphi_{6}}=\mathbf{\varphi_{5}}=\mathbf{\psi}\). Another feature of this mechanism structure is that the coordinates of the frame \(\mathbf{Q}\) lies on the straight line of the stroke of the working slider 7. Based on the kinematic scheme of the mechanism, we write down the equations in vector form:  
\[ \begin{array}{c}\overset{\rightarrow}{\mathbf{O}}\mathbf{A}+\overset{\rightarrow}{ \mathbf{A}}\mathbf{B}+\overset{\rightarrow}{\mathbf{C}}\mathbf{C}+\overset{\rightarrow}{\mathbf{C }}\mathbf{P}=\overset{\rightarrow}{\mathbf{h}}+\overset{\rightarrow}{\mathbf{e}}+ \overset{\rightarrow}{\mathbf{Q}}\mathbf{P},\\ \overset{\rightarrow}{\mathbf{h}}+\overset{\rightarrow}{\mathbf{e}}+\overset{ \rightarrow}{\mathbf{Q}}\mathbf{P}=\overset{\rightarrow}{\mathbf{S}}+\overset{ \rightarrow}{\mathbf{e}}+\frac{1}{2}\overset{\rightarrow}{\mathbf{b}}+\overset{ \rightarrow}{\mathbf{D}}\mathbf{C}+\overset{\rightarrow}{\mathbf{C}}\mathbf{P}.\end{array}  \tag{1}\]  
We introduce the following labeling \(\mathbf{l_{1}}=|\mathbf{A}\mathbf{O}|\), \(\mathbf{l_{2}}=|\mathbf{A}\mathbf{B}|\), \(\mathbf{l_{BC}}=|\mathbf{B}\mathbf{C}|\), \(\mathbf{l_{CP}}=|\mathbf{C}\mathbf{P}|\), \(\mathbf{l_{3}}=|\mathbf{P}\mathbf{Q}|\), \(\mathbf{l_{6}}=|\mathbf{D}\mathbf{C}|\), \(\mathbf{l_{5}}=|\mathbf{F}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\), \(\mathbf{l_{CP}}=|\mathbf{C}\mathbf{P}|\), \(\mathbf{\alpha_{6}}=\mathbf{\delta}\mathbf{DCB}=\mathbf{const}\), \(\mathbf{\varphi_{BC}}=\mathbf{\psi}+\mathbf{\alpha_{6}}\). Taking into account the adopted labeling, the projections of Equation (1) on the coordinate axes are written as follows:  
\[ \begin{array}{c}\mathbf{l_{1}}\mathbf{\cos}\mathbf{\varphi_{1}}+\mathbf{l_{2}}\mathbf{\cos}\bm {\varphi_{2}}+\mathbf{l_{BC}}\mathbf{\cos}(\mathbf{\psi}+\mathbf{\alpha_{6}})+\mathbf{l_{CP}}\mathbf{ \cos}\mathbf{\theta}=\mathbf{l_{3}}\mathbf{\cos}\mathbf{\varphi_{3}}+\mathbf{e}\\ \mathbf{l_{1}}\mathbf{\sin}\mathbf{\varphi_{1}}+\mathbf{l_{2}}\mathbf{\sin}\mathbf{\varphi_{2}}+\mathbf{l_ {BC}}\mathbf{\sin}(\mathbf{\psi}+\mathbf{\alpha_{6}})+\mathbf{l_{CP}}\mathbf{\sin}\mathbf{\theta}=\mathbf{ l_{3}}\mathbf{\sin}\mathbf{\varphi_{3}}+\mathbf{h}\\ \mathbf{l_{3}}\mathbf{\cos}\mathbf{\varphi_{3}}=\frac{1}{2}\mathbf{b}+\mathbf{l_{6}}\mathbf{\cos}\mathbf{ \psi}+\mathbf{l_{CP}}\mathbf{\cos}\mathbf{\theta}\\ \mathbf{h}+\mathbf{l_{3}}\mathbf{\sin}\mathbf{\varphi_{3}}=\mathbf{S}+\mathbf{l_{6}}\mathbf{\sin}\mathbf{\psi} +\mathbf{l_{CP}}\mathbf{\sin}\mathbf{\theta}\end{array}  \tag{2}\]  
System (2) will be written in the following form:  
\[ \begin{array}{c}\mathbf{l_{2}}\mathbf{\cos}\mathbf{\varphi_{2}}+\mathbf{l_{BC}}\mathbf{\cos}( \mathbf{\psi}+\mathbf{\alpha_{6}})-\mathbf{l_{3}}\mathbf{\cos}\mathbf{\varphi_{3}}=\mathbf{l_{g}}\mathbf{ \cos}\mathbf{\beta}\\ \mathbf{l_{2}}\mathbf{\sin}\mathbf{\varphi_{2}}+\mathbf{l_{BC}}\mathbf{\sin}(\mathbf{\psi}+\mathbf{\alpha_ {6}})-\mathbf{l_{3}}\mathbf{\sin}\mathbf{\varphi_{3}}=\mathbf{l_{g}}\mathbf{\sin}\mathbf{\beta}\\ \mathbf{l_{3}}\mathbf{\cos}\mathbf{\varphi_{3}}-\mathbf{l_{6}}\mathbf{\cos}\mathbf{\psi}=\mathbf{c}\\ \mathbf{l_{3}}\mathbf{\sin}\mathbf{\varphi_{3}}-\mathbf{l_{6}}\mathbf{\sin}\mathbf{\psi}-\mathbf{S}=\mathbf{d} \end{array}  \tag{3}\]  
where  
\[