On the force calculation of capture mechanisms and clamps using the «golden» rule of mechanics

When designing and reconstructing gripping devices or clamps, the issue of the geometric parameters of the research object that will ensure the required value of the power transmission coefficient is relevant. Usually, when performing calculations of such lever-rod mechanisms, which consist of several links, the balance of each link is considered and systems of algebraic equations are solved, which is a time-consuming process. In this paper, the power transmission coefficient, regardless of the scheme under consideration, is determined from one equation, the so-called «golden» rule of mechanics: «for the balance of a mechanical system, it is necessary and sufficient that the sum of the possible powers of active forces equals zero». In order to obtain the dependences between the speeds of the intermediate hinges for the links performing a planar movement, the "theorem on the projections of the velocity vectors of the points onto the line connecting these points" is applied. Common schemes of gripping devices of industrial robots and clamps, which are used in technological processes of metalworking and welding, are considered. Designers have the opportunity to apply the proposed method and, after performing numerous analyzes of the obtained formulas to determine the power transmission coefficient of a specific example, choose the most optimal combination of the dimensions of the mechanism and the angles between its rods. This will ensure the values of traction force or pressure in the pneumatic cylinder necessary for the operation of the mechanism, which will significantly save production resources. The algorithm proposed in the work can be applied to other flat mechanisms