Nonlinear evaluation of a large-stroke coiled L-shape compliant guiding mechanism with constant stiffness

Owing to the advantages of monolithic structure and little need for assembling, compliant guiding mechanisms appear to be an effective solution for decoupling multi-freedom precision motions but are still prone to geometric nonlinearities of parasitic error and stiffening effect for large strokes. This paper proposes a coiled L-shape compliant guiding mechanism featuring millimeter-scale strokes with a compact structure, constant stiffness and minimized parasitic error. The coiled compliant guiding mechanism is formed by convolving L-shape flexure beams in a zigzag configuration with decoupled XY motions achieved. Its geometrically nonlinear parasitic error, variation in stiffness and primary vibration are captured by using a dynamic beam constraint model (DBCM). It is theoretically, numerically and experimentally found, by comparing with double parallel guiding mechanisms, that the kinetostatic and dynamic behaviors of the coiled L-shape compliant mechanism are nearly independent on the applied force within the intermediate-deformation ranges. Such a weak geometric nonlinearity with the minimized influence of axially-loaded stiffening and kinematics-arching effects is much different from the double parallel guiding mechanisms. The obtained results indicate that large strokes with constant stiffness and invariable resonance frequency can be realized, which also allows small parasitic errors.