The beam flexure is an important constraint element in flexure mechanism design. Nonlinearities arising from the force equilibrium conditions in a beam significantly affect its properties as a constraint element. Consequently, beam-based flexure mechanisms suffer from performance tradeoffs in terms of motion range, accuracy and stiffness, while benefiting from elastic averaging. This paper presents simple yet accurate approximations that capture the effects of load-stiffening and elastokinematic nonlinearities in beams. A general analytical framework is developed that enables a designer to parametrically predict the performance characteristics such as mobility, over-constraint, stiffness variation, and error motions, of beam-based flexure mechanisms without resorting to tedious numerical or computational methods. To illustrate their effectiveness, these approximations and analysis approach are used in deriving the force–displacement relationships of several important beam-based flexure constraint modules, and the results are validated using finite element analysis. Effects of variations in shape and geometry are also analytically quantified.

This paper presents parallel kinematic XY flexure mechanism designs based on systematic constraint patterns that allow large ranges of motion without causing over-constraint or significant error motions. Key performance characteristics of XY mechanisms such as mobility, cross-axis coupling, parasitic errors, actuator isolation, drive stiffness, lost motion, and geometric sensitivity, are discussed. The standard double parallelogram flexure module is used as a constraint building-block and its nonlinear force-displacement characteristics are employed in analytically predicting the performance characteristics of two proposed XY flexure mechanism designs. Fundamental performance tradeoffs, including those resulting from the nonlinear load-stiffening and elastokinematic effects, in flexure mechanisms are highlighted. Comparisons between closed-form linear and nonlinear analyses are presented to emphasize the inadequacy of the former. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of computational finite element analysis and experimental measurements.

This paper presents parallel kinematic XY mechanism designs that are based on a systematic constraint pattern. The constraint pattern, realized by means of double parallelogram flexure modules, is such that it allows large ranges of motion without over-constraining the mechanism or generating significant error motions. Nonlinear force-displacement characteristics of the double parallelogram flexure are used in analytically predicting the performance measures of the proposed XY mechanisms. Comparisons between closed-form linear and nonlinear analyses are presented to highlight the inadequacy of the former. Fundamental design tradeoffs in flexure mechanism performance are discussed qualitatively and quantitatively. It is shown that geometric symmetry in the constraint arrangement relaxes some of the design tradeoffs, resulting in improved performance. The nonlinear analytical predictions are validated by means of Finite Element Analysis and experimental measurements.

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