Abstract
Generalized cross-spring pivots (CSPs) are widely used as revolute joints in precision machinery. However, pseudo-rigid-body (PRB) models cannot capture the parasitic motions of a generalized CSP exactly under combined loads; moreover, the characteristic parameters used in PRB methods must be recomputed using optimization techniques. In this study, we develop two simple and accurate PRB models for generalized CSPs. First, a PRB method for a beam is developed based on the beam constraint model and the instantaneous center model, where the beam is modeled as two rigid links joined at a pivot via a torsion spring. Subsequently, two PRB models of the generalized CSP, comprising a four-bar model for accuracy and a pin-joint model for stiffness, are constructed based on a kinematic analysis using the proposed PRB method. A deflection characteristic analysis is then conducted to determine the relationship between the proposed model and the existing models. Finally, the PRB models for the pivot under the action of combined loads are validated via finite element analysis. The error evaluation indicates that the proposed PRB models are more accurate than the results from existing methods. The PRB models proposed here can be used in parametric design of compliant mechanisms.
Highlights
Flexural pivots transform both motions and energies through elastic deformations.[1]
Adaptive PRB models have been developed to enhance the efficiency and accuracy of the models used for generalized cross-spring pivots (CSPs) under combined loads
(1) The deflection characteristic analysis indicates that the existing PRB models, when ignoring the force in the degree of constraint (DOC) direction described in Refs. 8, 41 and 42, can be regarded as special loading cases of the proposed PRB models; the stiffness model in Ref. 4 is equivalent to the proposed pin-joint model; and the proposed PRB models can show the linear relationship between the deflections of the pivots and the beams
Summary
Flexural pivots transform both motions and energies through elastic deformations.[1]. \ 10% of the beam length).[23,24] Analytical models for the stiffnesses and center shifts of generalized CSPs were derived from the BCM within a rotation angle range of up to 6 15°.4–6. The PRB methods described above cannot capture the center-shift and stiffness characteristics of generalized CSPs under the action of combined force and moment loads analytically. To investigate the deformation characteristics of generalized CSPs, a PRB method for a beam is established based on the beam constraint model and the instantaneous center model. Substitution of equation (26) into equation (11) shows that the lengths of links
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