Features of Loss of Stability of the Work of Two-Link Mechanisms That Have an Infinite Number of Degrees of Freedom

Abstract

Mechanisms consisting of two links, a leading (engine) and a slave (executive body), which are connected by long lines of force, are considered. With the use of the new method, general equations are derived in Laplace images describing the oscillations of the velocities of motion and stresses in mechanical and hydraulic systems. Obtained transfer functions. The functional coefficients in these equations take into account the properties of the mechanisms and the distribution of the parameters of the lines of force. As a result of the transition from equations in images to equations in the originals, expressions are obtained that describe in real-time oscillations of the velocities of motion. The criterion for the stability of the work is derived on the basis of Lyapunov's first method. As an example, a volumetric hydraulic drive with long hydraulic lines is considered. With the loss of stability in this mechanism, self-oscillations appeared. Areas of stable and unstable work are defined.

Keywords

• Two-link mechanism
• Force line
• Distributed parameters
• Executive body
• System stability
• Momentum
• Angular momentum
• Straight rod
• Oscillation frequency
• Volumetric hydraulic drive