Compliance and precision modeling of general notch flexure hinges using a discrete-beam transfer matrix

Enabling the transfer matrix method to model serial–parallel compliant mechanisms including curved flexure beams

“…The orientation angle of each constant beam segment for straight notch flexure hinges is identical, while the orientation angle of each constant beam segment is variable and equals to the tangent angle of the centroidal axis for curved beams. With such a discrete operation, the end‐tip displacements and forces of a notch flexure hinge or curved beam are directly related by successively postmultiplying the elemental transfer matrix of each discretized constant beam segment with the discrete number of N 56,69 : $$$\left\{\begin{array}{c}{{\boldsymbol{X}}}_{i,k}\\ -{{\boldsymbol{F}}}_{i,k}\end{array}\right\}=\left[\prod _{N}^{1}{{{\boldsymbol{R}}}_{p}}^{{\rm T}}{{\boldsymbol{T}}}_{p}^{e}(\omega ){{\boldsymbol{R}}}_{p}\right]\cdot \left\{\begin{array}{c}{{\boldsymbol{X}}}_{i,j}\\ {{\boldsymbol{F}}}_{i,j}\end{array}\right\},$$$where T p e ( ω ) denotes the transfer matrix of the p th discretized constant beam element ( p = 1, …, N ) and can be calculated using Equation (). R p denotes the coordinate transformation matrix of the p th discretized constant beam element.…”

A pseudo-rigid-body approach for determination of parasitic displacements of lumped compliant parallel-guiding mechanisms

“…In this way, the unwanted effects of friction, bucklash, and wear, which always appear during the exploitation of mechanisms with classic joints, were avoided. In the literature, various procedures have been developed for kinetostatic and dynamic analyses of compliant mechanisms such as the transfer matrix method [6][7][8][9][10], the dynamic stifness method [11,12], the beam theory based method [13][14][15], the pseudo-rigid-body model [16][17][18][19][20], the finite element method [21][22][23], the multi-compliant-body matrix method [24], the compliance matrix method [25][26][27], the Castigliano's second theorem based method [28], the unit-load method [29] etc. A survey of results, methods, and ongoing problems in compliant mechanisms research field was given in [30].…”