A combined method for the kinematic and force analysis of complex mechanical systems
Authors: Timofeev G.A., Mor E.G., Barbashov N.N. | Published: 02.04.2015 |
Published in issue: #3(660)/2015 | |
Category: Calculation and Design of Machinery | |
Keywords: force analysis, complex mechanism, mechanical system, truss, link, Assur groups of high classes |
Methods for the kinematic and stress analysis of simple linkages with second-class Assur groups are currently most fully developed. However, there are many other, more complex mechanisms of practical interest. Therefore, the development of methods for the kinematic and force analysis of mechanisms with Assur groups of high classes is an important task. A universal method for the graphical analysis of mechanical systems (mechanisms) and statically determinate trusses including Assur groups of high classes is proposed. The mechanism under study is represented by a truss in which the output link connected to the fixed member is conventionally replaced with a hinged support. The reaction of the imaginary support to a unit moment applied to the input link of the mechanism under consideration is determined. The value of the reaction moment about the original link support defines relative angular velocities of the input and output links. The kinematic transfer functions of the real mechanism are determined from these velocities. If the reactions in the truss are difficult to determine, the truss is idealized by a mechanism in which one more link is removed and the reactions are determined by the kinematics of this simplified mechanism. If the resultant mechanism is also too complex to analyze, a new simpler truss should be considered. This process is continued until the simplified structure is represented only by dyads. Thus, the algorithm for the kinematic analysis is a linear chain of transformations from a mechanism to a truss and from a truss to a mechanism with a final return to the original mechanism along the same path. Similarly, the algorithm for the force analysis of a statically determinate truss implies the same recursion starting with a truss and ending with a mechanism. The proposed algorithm for the kinematic and force analysis allows developers to study mechanisms and mechanical systems with Assur groups of high classes used in carrying and lifting machines, structures, and equipment.
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