To meet the need for large-range high-precision motion stages, a design methodology of XYZ compliant parallel manipulators (CPMs) is introduced at first. A spatial double four-beam module and a compliant P (prismatic) joint, composed of two spatial double four-beam modules, are then proposed. Starting from a 3-PPPR (R: revolute) translational parallel manipulator, a large-range modular XYZ CPM with identical spatial modules is constructed using the proposed design approach. Normalized analytical models for the large-range modular XYZ CPM are further presented. As a case study, a modular XYZ CPM with a motion range of 10 m X 10 mm X 10 mm along the positive X-, Y-, and Z-axes is presented in detail, covering the geometrical parameter determination, performance characteristics analysis, buckling check, and actuation force check. The analytical models are compared with the finite element analysis (FEA) models. Finally, the dynamics consideration, manufacturability, and merits are discussed. It is shown that the proposed large-range modular XYZ CPM has the following main merits compared with existing designs: (1) large range of motion up to 20 mm X 20 mm X 20 mm and (2) reduced number of design parameters through the use of identical spatial modules, although the manufacturability is a challenging issue.

This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules—multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear-analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear-analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel mechanisms.

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 direct reliability model of load-sharing parallel systems is presented based on the Miner cumulative damage theory, the total probability formula and addition principle. Secondly, the parallel system reliability is calculated using Monte Carlo simulation when the component life follows the Weibull distribution. The research results show that the proposed reliability mathematical model and Monte Carlo calculation method can analyze and evaluate the reliability of parallel systems in the presence of load transfer well.