Dynamic behaviour of linkage mechanisms

Abstract

General: The thesis concerns the prediction and control of vibrations in planar, kinematically determinate linkage mechanisms operating in a continuous manner, typically driven by a crankshaft. An array of simplified models of linkage components is used to assess the likely significance of the many factors concerned, assuming the components to be of realistic proportions. It is concluded that the effects of joint clearance and (in some cases) driving system flexibility, rather than link flexibility per-se, are likely to be the crucial factors. Attention is therefore focused on the former factors in the chapters that follow. Clearance Effects: The literature on the two-dimensional dynamic effects of clearance("ludodynamic" effects) in revolute joints is critically reviewed, with the conclusion that existing theoretical models need to be simplified to be of use for preliminary design synthesis, and that more discriminating experimental work is needed before any of the theories can be applied with confidence. A new theory is developed with a view to meeting the former need, the results being presented in the form of a design chart. An account is then given of the design, development and use of a novel experimental apparatus for studying a number of relevant aspects of the ludodynamic behaviour of a revolute joint. The new theory is supported in some respects for'larger clearances (250 um on 50mm diameter) but for smaller clearances (65 & 20 pm) the air 'squeeze film' is found to play an increasingly dominant role. Drive Flexibility Effects: The effects of driving system flexibility are approximately governed by an inhomogeneous Hill's equation. A numerical method is used to find the harmonic composition of the steady state solutions of this equation. A rule for predicting resonant and unstable speeds is hypothesized: it is shown to give excellent results, but the response at off-resonant speeds also has a large high-frequency element in some cases. Synthesis: A convenient method for modifying undesirable dynamic performance in a linkage mechanism is the attachment of auxiliary masses or springs. A method is developed for the efficient optimisation of counterweights by a weighted root mean square criterion, subject to bounds on the physical parameters. A known method for synthesis of auxiliary springs by the use of precision points in the objective function is extended, and methods for optimising the spacing of the precision points are introduced.