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

Abstract This paper mainly deals with the nonlinear analytical modeling and characteristic analysis of two types of composite multi-beam modules for planar motion to enable rapid analysis and design synthesis. Each type of composite multi-beam module consists of identical, uniform and parallel wire beams, distributing uniformly along circle(s), with symmetrical cross sections. Analytical models of basic multi-beam modules with all beams uniformly spaced around a circle are firstly revisited. Analytical and nonlinear load–displacement equations are derived for the composite multi-beam modules, each of which is composed of two basic multi-beam modules with the same type connected either serially or parallelly. Finite element analysis (FEA) is carried out to compare and verify the analytical models. Detailed characteristic analysis and comparisons are conducted to compare three types of compliant six-beam modules whose twisting rotations are well constrained. These analytical results are capable of capturing some key quantitative nonlinear characteristics, such as kinematic effects, load-stiffening effect and nonlinear twisting stiffness (torsional stiffness), and can promote the design and analytical modeling of compliant parallel manipulators composed of the compliant multi-beam modules. In addition, the nonlinear analytical models of other variations of parallel double multi-beam modules are derived.