On the validity of compliance-based matrix method in output compliance modeling of flexure-hinge mechanism

Abstract Compliance-based matrix method (CMM) has been regarded as an efficient technique for output compliance modeling of the flexure hinge-based compliant mechanism, owing to its simplicity and high accuracy. However, this study demonstrates that CMM is not always valid due to the intrinsic ill-condition of the compliance matrix of right circular flexure hinge (RCFH). Inversion of compliance matrix can result in numerical instability in the calculation of its stiffness matrix. It is shown in this study that CMM can be effectively applied to serial compliant mechanism, while its adoption in modeling parallel compliant mechanism needs to be carefully examined due to the matrix inversion involved. The validity of CMM is highly dependent on the spatial configuration, degree of freedom, and singularity of the parallel mechanism. The validity criteria of CMM are discussed in detail with exemplary configurations of 3RRR, 2RR, and bridge-type compliant mechanisms.