The reliability mathematical model of load-sharing parallel systems based on fatigue cumulative damage

Conventional reliability models for parallel systems are not applicable for the analysis of parallel systems with load transfer and sharing. In this short communication, firstly, the dependent failures of parallel systems are analyzed, and the reliability model of load-sharing parallel system is presented based on Miner cumulative damage theory and the full probability formula. Secondly, the parallel system reliability is calculated by Monte Carlo simulation when the component life follows the Weibull distribution. The research result shows that the proposed reliability mathematical model could analyze and evaluate the reliability of parallel systems in the presence of load transfer.

Towards the design of monolithic decoupled XYZ compliant parallel mechanisms for multi-function applications

This paper deals with the monolithic decoupled XYZ compliant parallel mechanisms (CPMs) for multi-function applications, which can be fabricated monolithically without assembly and has the capability of kinetostatic decoupling. At first, the conceptual design of monolithic decoupled XYZ CPMs is presented using identical spatial compliant multi-beam modules based on a decoupled 3-PPPR parallel kinematic mechanism. Three types of applications: motion/positioning stages, force/acceleration sensors and energy harvesting devices are described in principle. The kinetostatic and dynamic modelling is then conducted to capture the displacements of any stage under loads acting at any stage and the natural frequency with the comparisons with FEA results. Finally, performance characteristics analysis for motion stage applications is detailed investigated to show how the change of the geometrical parameter can affect the performance characteristics, which provides initial optimal estimations. Results show that the smaller thickness of beams and larger dimension of cubic stages can improve the performance characteristics excluding natural frequency under allowable conditions. In order to improve the natural frequency characteristic, a stiffness-enhanced monolithic decoupled configuration that is achieved through employing more beams in the spatial modules or reducing the mass of each cubic stage mass can be adopted. In addition, an isotropic variation with different motion range along each axis and same payload in each leg is proposed. The redundant design for monolithic fabrication is introduced in this paper, which can overcome the drawback of monolithic fabrication that the failed compliant beam is difficult to replace, and extend the CPM’s life.

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.

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.

Design and analysis of a compliant parallel pan-tilt platform

In combination of the advantages of both parallel mechanisms and compliant mechanisms, a compliant parallel mechanism with two rotational DOFs (degrees of freedom) is designed to meet the requirement of a lightweight and compact pan-tilt platform. Firstly, two commonly-used design methods i.e. direct substitution and FACT (Freedom and Constraint Topology) are applied to design the configuration of the pan-tilt system, and similarities and differences of the two design alternatives are compared. Then inverse kinematic analysis of the candidate mechanism is implemented by using the pseudo-rigid-body model (PRBM), and the Jacobian related to its differential kinematics is further derived to help designer realize dynamic analysis of the 8R compliant mechanism. In addition, the mechanism’s maximum stress existing within its workspace is tested by finite element analysis. Finally, a method to determine joint damping of the flexure hinge is presented, which aims at exploring the effect of joint damping on actuator selection and real-time control. To the authors’ knowledge, almost no existing literature concerns with this issue.

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.

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.