A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

A normalization-based approach to the mobility analysis of spatial compliant multi-beam modules

“…From the nonlinear analysis [27] of the single spatial TBM (Fig. 2), we learn that the axial displacement depends on three components: purely elastic effect only from the axial force, purely kinematic effect, from the three DOF, and elastokinematic effect (the elastokinematic effect is very smaller than purely kinematic effect) of the spatial TBM.…”

“…Equation (2), the linear load-displacement equations of a beam, will be used for the mobility analysis of spatial multi-beam modules under small deflection condition that usually assumes the normalized displacements to be less than 0.1 [27]. It should be noted that the smaller the motion range is, the more accurate the linear modeling is.…”

Design of 3-legged XYZ compliant parallel manipulators with minimised parasitic rotations

“…It is known [18] that increasing the spanning size or decreasing the beam's in-plane thickness of a parallelogram flexure mechanism can slightly alleviate the parasitic rotation that accompanies a primary translation produced by the force acting at the mechanism's tip. However, these approaches inevitably result in a bulky configuration, or one that is difficult to fabricate and has a dramatically decreased primary stiffness.…”

“…However, these approaches inevitably result in a bulky configuration, or one that is difficult to fabricate and has a dramatically decreased primary stiffness. Additionally, the primary translation coupling with the spanning parameter nonlinearly contributes to the parasitic rotation effect and reduces the parasitic rotation stiffness [18].…”

“…The indicated SC of an example parallelogram flexure module is the symmetric center of all compliant beams as clearly demonstrated in Fig. 1, which can be determined by the following nonlinear parasitic rotation equation [18]:…”