The structural analysis, which is one of the first and most fundamental topics in the Mechanism and Machines Science (MMS) study course, rarely deals with toothed mechanisms. The classification of kinematical pairs, mobility, inversions, and equivalent mechanisms are explained with numerous examples of linkages. However, once toothed mechanisms are considered, the previously presented structural concerns take on another importance. Several structural analysis concerns, such the various approaches to make motion transmission (gear ratio vs. velocity diagrams and instant centers) and the various methods of analysis, are equally beneficial in providing the mechanical students with a strong set of tools for both design and analysis. The technology of creating equivalent links for geared linkages, differential toothed mechanisms, and epicyclic planetary mechanisms is discussed in this paper. Students gain essential skills from the transformations between toothed mechanisms and links, which they can use to analyze the kinematics of epicyclic toothed mechanisms. There are a few limitations when using the Willis method for reversion of motion when more than one arm is involved. The graphical solution can be somewhat complex, and the simple double application of the Willis approach will not get the proper answer. Students who understand the mechanism transformation technique presented in the structural analysis module will be able to analyze the kinematics of planetary gear mechanisms using a combined method. The method presented in this paper is two-step: first, the motion of the mechanism is reversed, and then the linear velocities of kinematical pairs are analyzed (graphically or algebraically).

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Toothed Mechanisms as Objects of Structural Analysis in MMS Study Course

  • Eduard G. Krylov

摘要

The structural analysis, which is one of the first and most fundamental topics in the Mechanism and Machines Science (MMS) study course, rarely deals with toothed mechanisms. The classification of kinematical pairs, mobility, inversions, and equivalent mechanisms are explained with numerous examples of linkages. However, once toothed mechanisms are considered, the previously presented structural concerns take on another importance. Several structural analysis concerns, such the various approaches to make motion transmission (gear ratio vs. velocity diagrams and instant centers) and the various methods of analysis, are equally beneficial in providing the mechanical students with a strong set of tools for both design and analysis. The technology of creating equivalent links for geared linkages, differential toothed mechanisms, and epicyclic planetary mechanisms is discussed in this paper. Students gain essential skills from the transformations between toothed mechanisms and links, which they can use to analyze the kinematics of epicyclic toothed mechanisms. There are a few limitations when using the Willis method for reversion of motion when more than one arm is involved. The graphical solution can be somewhat complex, and the simple double application of the Willis approach will not get the proper answer. Students who understand the mechanism transformation technique presented in the structural analysis module will be able to analyze the kinematics of planetary gear mechanisms using a combined method. The method presented in this paper is two-step: first, the motion of the mechanism is reversed, and then the linear velocities of kinematical pairs are analyzed (graphically or algebraically).