Use of Maclaurin Geometric Transformations in 3D Synthesis of Mechanisms

Abstract

This paper describes and explains MacLaurin’s transformations and their use in a 3D synthesis of mechanisms. An overview of the high order curves is provided, along with their degradation to the curves of the lower order. MacLaurin’s transcriptions are used to degrade the curves of the higher order to the desired curves of the lower order. This will allow us to generate different kinds of trajectories and, therefore, different kind of mechanisms. Furthermore, the implementation of the obtained curves into the CAD pragmas and 3D environment is presented. This allows a quick synthesis of a mechanism, its adaptation and simulation in order to get the desired final trajectories. Different kinds of trajectories implemented in a 3D environment are shown in this paper. Fully operational 3D models of mechanism trajectories and simulation are created and documented in the SolidWorks application. This research could be used further in the theory of mechanisms, 3D modelling, simulations and the synthesis of mechanisms. The exposed methods of the synthesis of mechanisms may be used in the design and construction of new mechanisms or the redesign of the existing mechanisms.