## 2 Dynamic Model of the System  
The experimental system represents one of the most basic kinematic structures (a planar arm with two rotating joints moving in the x-y plane). The schematic diagram of the kinematic structure of the manipulator shown in Figure 1 serves to show the basic elements, their location within the whole system, but also the basic parameters. Two rigid arms, lengths \(l_{1}\) and \(l_{2}\), have a mass of \(m_{1}\) and \(m_{2}\). The distance from the axis of rotation of the joint to the center of gravity of the arm is denoted as \(c_{1}\) and \(c_{2}\). \(l_{1}\) and \(l_{2}\) represent the moments of inertia of the bodies (arms) concerning an axis that passes through the center of gravity of the body and is parallel to the horizontal axis \(x\). The deflection of the arm from the zero position (the angle of rotation of the joint is not equal to \(0^{\circ}\)) is indicated by the angles \(\varphi_{1}\), \(\varphi_{2}\), which represent the degrees of freedom of the manipulator. The deflection of the arm in the positive direction from the vertical \(y\)-axis is expressed by the angle of rotation of the joint \(\varphi_{1}\). The angle \(\varphi_{2}\) indicates the angle of rotation of the second joint, but concerning the axis of the first deflected link. [PERSON]'s equations were used to derivate a dynamic model of the described system, which has two degrees of freedom [29]. The general formulation for a robot with 2 degrees of freedom is given in Equation (1), where \(L\) is Lagrangian, \(\varphi_{i}\) is joint positions, derivation of the joint position is joint velocities, and \(\tau_{i}\) is force term. \[\frac{d}{dt}\bigg{[}\frac{\partial L}{\partial\dot{\varphi}_{i}}\bigg{]}- \frac{\partial L}{\partial\varphi_{i}}=\tau_{i}\qquad\qquad i=1,2 \tag{1}\]  
The Lagrangian is given by the difference of kinetic and potential energy, and therefore Equation (2) applies to its determination. Member \(E_{k}\left(\varphi,\,\dot{\varphi}\right)\) expresses the kinetic energy of the manipulator and is formed by the sum of individual kinetic energies of members 1 and  
Figure 1: Scheme of kinematic structure of experimental system. 2 (\(E_{k1}\) and \(E_{k2}\)). Member \(E_{p}\) (\(\varphi\)) characterizes the energy of the manipulator concerning its position and is given by the sum of individual potential energies of arms 1 and 2 (\(E_{p1}\) and \(E_{p2}\)). \[L\big{(}\varphi,\dot{\varphi}\big{)}=E_{k}\big{(}\varphi,\ \dot{\varphi}\big{)}-E_{p} (\varphi) \tag{2}\]  
_Determination Lagrange_'s _Equations_  
By calculating the Lagrangian and applying Equation (1), two nonlinear differential equations are obtained, which represent the equations of the manipulator dynamics. For link 1, the force component \(\tau_{1}\) is determined in the final form:  
\[\begin{array}{ll}\tau_{1}=&\big{[}m_{1}\!\cdot\!c_{1}\!^{2}+m_{2}\!\cdot  
Table 1 contains an overview of the main components used in the experimental system. In addition to the name of the component, its basic parameters are also given. A total of 4 fluid muscles of the same size and diameter were used. Each muscle had one electronic pressure regulator (a total of four were used). An incremental sensor was used to read the output variable. The mechanical parts of the stand (except the structure) consist of two arms, two joints, two chains and two sprockets with a diameter of 0.07 m.