This paper presents a symbolic formulation for analytical compliance analysis and synthesis of flexure mechanisms with serial, parallel, or hybrid topologies. Our approach is based on the screw theory that characterizes flexure deformations with motion twists and loadings with force wrenches. In this work, we first derive a symbolic formulation of the compliance and stiffness matrices for commonly used flexure elements, flexure joints, and simple chains. Elements of these matrices are all explicit functions of flexure parameters. To analyze a general flexure mechanism, we subdivide it into multiple structural modules, which we identify as serial, parallel, or hybrid chains. We then analyze each module with the known flexure structures in the library. At last, we use a bottom-up approach to obtain the compliance/stiffness matrix for the overall mechanism. This is done by taking appropriate coordinate transformation of twists and wrenches in space. Four practical examples are provided to demonstrate the approach. A numerical example is employed to compare analytical compliance models against a finite element model. The results show that the errors are sufficiently small (2%, compared with finite element (FE) model), if the range of motion is limited to linear deformations. This work provides a systematical approach for compliance analysis and synthesis of general flexure mechanisms. The symbolic formulation enables subsequent design tasks, such as compliance synthesis or sensitivity analysis.

There is an increasing need for XY compliant parallel micromanipulators (CPMs) providing good performance characteristics such as large motion range, well-constrained cross-axis coupling, and parasitic rotation. Decoupled topology design of the CPMs can easily realize these merits without increasing the difficulty of controlling. This paper proposes an improved 4-PP model on the basis of a classical 4-PP model and both of them are selected for manufacturing and testing to verify the effectiveness of the improvement. It has shown from experimental results that there is a large improvement on the performances of improved 4-PP compliant parallel manipulator (CPM): large range of motion up to 5 mm × 5 mm in the unidirection in the dimension of 311 mm × 311 mm × 24 mm, smaller compliance fluctuation (only 36.63% of that of the initial 4-PP model), smaller cross-axis coupling (only 28.10% of that of the initial 4-PP model generated by a single-axis 5 mm actuation), smaller in-plane parasitic yaw (only 57.14% of that of the initial 4-PP model generated by double-axis 5 mm actuation).

An isosceles-trapezoidal flexural pivot can be of great use for practical designs, especially in the cases that a pure rotation about a virtual pivot is required. The analysis of rotational precision for such a structure is important for the mechanical design in precise-required applications. For this purpose, a rigid isosceles-trapezoidal linkage model is first proposed to provide an accurate analytical result for its notch-type flexural counterpart. The influence of dimensional parameters on the center shift is discussed. In order to disclose the equivalence between leaf-type flexure structure and its pseudo-rigid-body model, a transitional model is introduced, from which an equivalent pseudo-rigid-body model for leaf-type isosceles-trapezoidal flexure structure is then derived. The results of both simulation and experiment verify that the equivalent rigid model is also accurate enough in the case of a larger deflection.

This paper deals with the structure synthesis and reconfiguration analysis of variable-DOF (variable-degree-of-freedom) single-loop mechanisms with prismatic joints based on a unified tool—the dual quaternion. According to motion polynomials over dual quaternions, an algebraic method is presented to synthesize variable-DOF single-loop 5R2P mechanisms (R and P denote revolute and prismatic joints, respectively), which are composed of the Bennett and RPRP mechanisms. Using this approach, variable-DOF single-loop RRPRPRR and RRPRRPR mechanisms are constructed by joints obtained from the factorization of motion polynomials. Then reconfiguration analysis of these variable-DOF single-loop mechanisms is performed in light of the kinematic mapping based on dual quaternions as well as the prime decomposition. The results show that the variable-DOF 5R2P mechanisms have a 1DOF spatial 5P2P motion mode and a 2DOF Bennett-RPRP motion mode. Furthermore, the variable-DOF 5R2P mechanisms have two transition configurations, from which the mechanisms can switch among their two motion modes.