A 2-legged XY parallel flexure motion stage with minimised parasitic rotation

XY compliant parallel manipulators (aka XY parallel flexure motion stages) have been used as diverse applications such as atomic force microscope scanners due to their proved advantages such as eliminated backlash, reduced friction, reduced number of parts and monolithic configuration. This paper presents an innovative stiffness centre based approach to design a decoupled 2-legged XY compliant parallel manipulator in order to better minimise the inherent parasitic rotation and have a more compact configuration. This innovative design approach makes all of the stiffness centres, associated with the passive prismatic (P) modules, overlap at a point that all of the applied input forces can go through. A monolithic compact and decoupled XY compliant parallel manipulator with minimised parasitic rotation is then proposed using the proposed design approach based on a 2-PP kinematically decoupled translational parallel manipulator. Its load–displacement and motion range equations are derived, and geometrical parameters are determined for a specified motion range. Finite element analysis comparisons are also implemented to verify the analytical models with analysis of the performance characteristics including primary stiffness, cross-axis coupling, parasitic rotation, input and output motion difference and actuator nonisolation effect. Compared with the existing XY compliant parallel manipulators obtained using 4-legged mirror-symmetric constraint arrangement, the proposed XY compliant parallel manipulators based on stiffness centre approach mainly benefits from fewer legs resulting in reduced size, simpler modelling as well as smaller lost motion. Compared with existing 2-legged designs with the conventional arrangement, the present design has smaller parasitic rotation, which has been proved from the finite element analysis results

Design and analysis of symmetric and compact 2R1T (in-plane 3-DOC) flexure parallel mechanisms

Symmetry is very necessary in flexure mechanisms, which can eliminate parasitic motions, avoid buckling, and minimize thermal and manufacturing sensitivity. This paper proposes two symmetric and compact flexure designs, in-plane 3-DOC (degree of constraint) mechanisms, which are composed of 4 and 6 identical wire beams, respectively. Compared to traditional leaf-beam-based designs, the two present designs have lower stiffness in the primary motion directions, and have smaller stiffness reduction in the parasitic directions. Analytical modelling is conducted to derive the symbolic compliance equations, enabling quick analysis and comparisons of compliances of the two mechanisms. A prototype has been tested statically to compare with analytical models

Creative design and modelling of large-range translation compliant parallel manipulators

Compliant parallel mechanisms/manipulators (CPMs) are parallel manipulators that transmit motion/load by deformation of their compliant members. Due to their merits such as the eliminated backlash and friction, no need for lubrication, reduced wear and noise, and monolithic configuration, they have been used in many emerging applications as scanning tables, bio-cell injectors, nano-positioners, and etc. How to design large-range CPMs is still a challenging issue. To meet the needs for large-range translational CPMs for high-precision motion stages, this thesis focuses on the systematic conceptual design and modelling of large-range translational CPMs with distributed-compliance. Firstly, several compliant parallel modules with distributed-compliance, such as spatial multi-beam modules, are identified as building blocks of translational CPMs. A normalized, nonlinear and analytical model is then derived for the spatial multi-beam modules to address the non-linearity of load-equilibrium equations. Secondly, a new design methodology for translational CPMs is presented. The main characteristic of the proposed design approach is not only to replace kinematic joints as in the literature, but also to replace kinematic chains with appropriate multiple degrees-of-freedom (DOF) compliant parallel modules. Thirdly, novel large-range translational CPMs are constructed using the proposed design methodology and identified compliant parallel modules. The proposed novel CPMs include, for example, a 1-DOF compliant parallel gripper with auto-adaptive grasping function, a stiffness-enhanced XY CPM with a spatial compliant leg, and an improved modular XYZ CPM using identical spatial double four-beam modules. Especially, the proposed XY CPM and XYZ CPM can achieve a 10mm’s motion range along each axis in the case studies. Finally, kinematostatic modelling of the proposed translational CPMs is presented to enable rapid performance characteristic analysis. The proposed analytical models are also compared with finite element analysis

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough

A constraint and position identification (CPI) approach for the synthesis of decoupled spatial translational compliant parallel manipulators

This paper introduces a screw theory based method termed constraint and position identification (CPI) approach to synthesize decoupled spatial translational compliant parallel manipulators (XYZ CPMs) with consideration of actuation isolation. The proposed approach is based on a systematic arrangement of rigid stages and compliant modules in a three-legged XYZ CPM system using the constraint spaces and the position spaces of the compliant modules. The constraint spaces and the position spaces are firstly derived based on the screw theory instead of using the rigid-body mechanism design experience. Additionally, the constraint spaces are classified into different constraint combinations, with typical position spaces depicted via geometric entities. Furthermore, the systematic synthesis process based on the constraint combinations and the geometric entities is demonstrated via several examples. Finally, several novel decoupled XYZ CPMs with monolithic configurations are created and verified by finite elements analysis. The present CPI approach enables experts and beginners to synthesize a variety of decoupled XYZ CPMs with consideration of actuation isolation by selecting an appropriate constraint and an optimal position for each of the compliant modules according to a specific application

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

This paper deals with the design of 3-legged distributed-compliance XYZ compliant parallel manipulators (CPMs) with minimised parasitic rotations, based on the kinematically decoupled 3-PPPRR (P: prismatic joint, and R: revolute joint) and 3-PPPR translational parallel mechanisms (TPMs). The designs are firstly proposed using the kinematic substitution approach, with the help of the stiffness center (SC) overlapping based approach. This is done by an appropriate embedded arrangement so that all of the SCs associated with the passive compliant modules overlap at the point where all of the input forces applied at the input stages intersect. Kinematostatic modelling and characteristic analysis are then carried out for the proposed large-range 3-PPPRR XYZ CPM with overlapping SCs. The results from finite element analysis (FEA) are compared to the characteristics found for the developed analytical models, as are experimental testing results (primary motion) from the prototyped 3-PPPRR XYZ CPM with overlapping SCs. Finally, issues on large-range motion and dynamics of such designs are discussed, as are possible improvements of the actuated compliant P joint. It is shown that the potential merits of the designs presented here include a) minimised parasitic rotations by only using three identical compliant legs; b) compact configurations and small size due to the use of embedded designs; c) approximately kinematostatically decoupled designs capable of easy controls; and d) monolithic fabrication for each leg using existing planar manufacturing technologies such as electric discharge machining (EDM)

Damage equivalent method of fatigue reliability analysis of loading-sharing parallel system

As for load-sharing parallel system like multi-engine system and wire cable, dependence-failure must occur due to load redistributing, so the component life distributions changed. After the analysis of the disadvantage of failure probability equivalent principle and the transformation of equivalent working time of different life distribution based on damage equivalent principle, the parallel system reliability model applying full probability formula is established. The established reliability model provides a new method for reliability analysis of load-sharing parallel system whose component life follows any distribution

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

This paper proposes conceptual designs of multi-degree(s) of freedom (DOF) compliant parallel manipulators (CPMs) including 3-DOF translational CPMs and 6-DOF CPMs using a building block based pseudo-rigid-body-model (PRBM) approach. The proposed multi-DOF CPMs are composed of wire-beam based compliant mechanisms (WBBCMs) as distributed-compliance compliant building blocks (CBBs). Firstly, a comprehensive literature review for the design approaches of compliant mechanisms is conducted, and a building block based PRBM is then presented, which replaces the traditional kinematic sub-chain with an appropriate multi-DOF CBB. In order to obtain the decoupled 3-DOF translational CPMs (XYZ CPMs), two classes of kinematically decoupled 3-PPPR (P: prismatic joint, R: revolute joint) translational parallel mechanisms (TPMs) and 3-PPPRR TPMs are identified based on the type synthesis of rigid-body parallel mechanisms, and WBBCMs as the associated CBBs are further designed. Via replacing the traditional actuated P joint and the traditional passive PPR/PPRR sub-chain in each leg of the 3-DOF TPM with the counterpart CBBs (i.e. WBBCMs), a number of decoupled XYZ CPMs are obtained by appropriate arrangements. In order to obtain the decoupled 6-DOF CPMs, an orthogonally-arranged decoupled 6-PSS (S: spherical joint) parallel mechanism is first identified, and then two example 6-DOF CPMs are proposed by the building block based PRBM method. It is shown that, among these designs, two types of monolithic XYZ CPM designs with extended life have been presented

A completely kinematostatically decoupled XY compliant parallel manipulator through new topology structure

This paper deals with a completely kinematostaticaly decoupled XY compliant parallel manipulator (CPM) composed of exactly-constrained compliant modules. A new 4-PP XY translational parallel mechanism (TPM) with a new topology structure is firstly proposed where each two P (P: prismatic) joints on the base in two non-adjacent legs are rigidly connected. A novel 4-PP XY CPM is then obtained by replacing each traditional P join on the base in the 4-PP XY TPM with a compound basic parallelogram module (CBPM) and replacing each traditional P joint on the motion stage with a basic parallelogram module (BPM). Approximate analytical model is derived with comparison to the FEA (finite element analysis) model and experiment for a case study. The proposed novel XY CPM has a compact configuration with good dynamics, and is able to well constrain the parasitic rotation and the cross-axis coupling of the motion stage. The cross-axis motion of the input stage can be completely eliminated, and the lost motion between the input stage and the motion stage is significantly reduced

A structure design method for compliant parallel manipulators with actuation isolation

Since precise linear actuators of a compliant parallel manipulator suffer from their inability to tolerate the transverse motion/load in the multi-axis motion, actuation isolation should be considered in the compliant manipulator design to eliminate the transverse motion at the point of actuation. This paper presents an effective design method for constructing compliant parallel manipulators with actuation isolation, by adding the same number of actuation legs as the number of the DOF (degree of freedom) of the original mechanism. The method is demonstrated by two design case studies, one of which is quantitatively studied by analytical modelling. The modelling results confirm possible inherent issues of the proposed structure design method such as increased primary stiffness, introduced extra parasitic motions and cross-axis coupling motions