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

Abstract

Abstract. 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. Loaddisplacement equations are then derived for a class of spatial multi-beam modules and general spatial multibeam 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.

Conceptual designs of multi-degree of freedom compliant parallel manipulators composed of wire-beam based compliant mechanisms

“…For example, a number of synthesis works for WBBCMs have been reported in [25][26][27][28][29][30][31], spatial 3-DOF translational compliant parallel manipulators only composed of identical WBBCMs have been proposed in [32,33], and nonlinear analysis/modelling has been carried out for WBBCMs in [34,35]. In comparison with the leaf-beam based distributed-compliance compliant mechanisms, the WBBCMs benefit from the following potential merits:…”

“…(b) The 3D modelling of the wire beam is easier and better developed compared with the 3D modelling of the conventional lumped-compliance hinge/pivot and distributed-compliance leaf/blade/sheet [34][35][36].…”

Nonlinear analytical modeling and characteristic analysis of symmetrical wire beam based composite compliant parallel modules for planar motion

“…These works will contribute to the design and analytical modeling of standalone desktop-size XY motion stages [17] and translational compliant parallel manipulators [14, 15, and 22] This paper is organized as follows. Section 2 revisits the previous work on basic multi-beam modules.…”

“…(b) The compliant multi-beam module may act as a standalone motion stage actuated by the non-contact electromagnetic actuators [17]. This motion stage has a very simple configuration and large out-of-plane stiffness, and has no heat effect from the electromagnetic actuator due to the non-contact actuation.…”

“…For example, a number of synthesis works have been reported in [7][8][9][10][11][12][13], spatial 3-DOF translational compliant parallel manipulators composed of only identical wire-beam based compliant mechanisms have been proposed in [14][15], and nonlinear analysis/modeling and mobility analysis have been presented in [16][17][18]. This paper is limited to a class of wire-beam based compliant modules with planar motion (two translations and one rotation) as the primary motion, which is composed of identical, uniform and parallel wire beams with symmetrical cross sections.…”