Simplified PRBMs of spatial compliant multi-beam modules for planar motion

PRBMs (pseudo-rigid-body models) have been becoming important engineering technologies/methods in the field of compliant mechanisms to simplify the design and analysis through the use of the knowledge body of rigid-body mechanisms coupling with springs. This article addresses the PRBMs of spatial multi-beam modules for planar motion, which are composed of three or more symmetrical wire/slender beams parallel to each other where the planar twisting DOF (degree of freedom) is assumed to be very small for specific applications/loading conditions. Simplified PRBMs are firstly proposed through replacing each beam in spatial multi-beam module with a rigid-body link plus two identical spherical joints at its two ends. The characteristics factor, bending stiffness and twisting stiffness for the spherical joint are determined. Load-displacement equations are then derived for a class of spatial multi-beam modules and general spatial multi-beam modules using the virtual work principle and kinematic relationships. Finally, nonlinear FEA (finite element analysis) is employed with comparisons with the PRBMs. The present PRBMs have shown the ability to predict the primary nonlinear constraint characteristics such as load-stiffening effect, cross-axis coupling in the two primary translational directions and buckling load.

CUBEs: decoupled, compact, and monolithic spatial translational compliant parallel manipulators

This paper deals with the conceptual design of decoupled, compact, and monolithic XYZ compliant parallel manipulators (CPMs): CUBEs. Position spaces of compliant P (P: prismatic) joints are first discussed, which are represented by circles about the translational directions. A design method of monolithic XYZ CPMs is then proposed in terms of both the kinematic substitution method and the position spaces. Three types of monolithic XYZ CPMs are finally designed using the proposed method with the help of three classes of kinematical decoupled 3-DOF (degree of freedom) translational parallel mechanisms (TPMs). These monolithic XYZ CPMs include a 3-PPP XYZ CPM composed of identical parallelogram modules (a previously reported design), a novel 3-PPPR (R: revolute) XYZ CPM composed of identical compliant four-beam modules, and a novel 3-PPPRR XYZ CPM. The latter two monolithic designs also have extended lives. It is shown that the proposed design method can be used to design other decoupled and compact XYZ CPMs by using the concept of position spaces, and the resulting XYZ CPM is the most compact one when the fixed ends of the three actuated compliant P joints thereof overlap.