Lever Linkages in Mechanical Oscillatory Systems: Forms of Lever Interactions

Lever Linkages in Mechanical Oscillatory Systems: Forms of Lever Interactions

DOI: 10.4018/978-1-6684-7237-8.ch005
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Abstract

The chapter displays various forms and possibilities of lever interactions in the system of connections of typical elementary links. Elastic links in lever connections formed by devices for converting movements are considered. Systems with two and three lever connections of the second kind are considered. A new approach has been developed to assess the possibilities of sequential connection of typical elements in structural interpretations of vibration protection systems. A method for determining the reduced stiffness is presented, taking into account the introduction of devices with motion transformation. A generalized approach has been developed that takes into account the support of the lever on the link.
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Possibilities And Forms Of Lever Interactions In The System Of Connections Of Typical Elementary Units

If we take the usual mechanical oscillatory system, then the expressions for the kinetic and potential energy usually have a complete quadratic form for the potential energy and an incomplete quadratic form for the expression determining the kinetic energy of the system. Choosing the appropriate coordinate systems, it is possible to carry out an inversion and obtain the complete quadratic form for expressing the kinetic energy, and incomplete form for the potential energy. The solution of the problem of simultaneous reduction of expressions to incomplete form means a transition to the main coordinates, which is possible only for some special cases. Expressions for the kinetic and potential energies simultaneously in a complete quadratic form are possible, however, this requires the introduction of additional constraints, as shown, for example, in Eliseev et al. (2006). Essentially, the possibility of reducing the expressions for kinetic and potential energies to full quadratic forms predetermines the fundamental possibilities of the “legitimacy” of introducing additional feedbacks and expanding the typical element base of the vibration protection systems.

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