H. Kunzmann

Bio: H. Kunzmann is an academic researcher. The author has contributed to research in topics: Parallel manipulator & Compliant mechanism. The author has an hindex of 1, co-authored 1 publications receiving 35 citations.

Constraint-force-based approach of modelling compliant mechanisms: Principle and application

Abstract: Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.

Position-Space-Based Design of a Symmetric Spatial Translational Compliant Mechanism for Micro-/Nano-Manipulation

Abstract: Symmetry enables excellent motion performance of compliant mechanisms, such as minimized parasitic motion, reduced cross-axis coupling, mitigated buckling, and decreased thermal sensitivity. However, most existing symmetric compliant mechanisms are heavily over-constrained due to the fact that they are usually obtained by directly adding over-constraints to the associated non-symmetric compliant mechanisms. Therefore, existing symmetric compliant mechanisms usually have relatively complex structures and relatively large actuation stiffness. This paper presents a position-space-based approach to the design of symmetric compliant mechanisms. Using this position-space-based approach, a non-symmetric compliant mechanism can be reconfigured into a symmetric compliant mechanism by rearranging the compliant modules and adding minimal over-constraints. A symmetric spatial translational compliant parallel mechanism (symmetric XYZ compliant parallel mechanism (CPM)) is designed using the position-space-based design approach in this paper. Furthermore, the actuation forces of the symmetric XYZ CPM are nonlinearly and analytically modelled, which are represented by the given primary translations and the geometrical parameters. The maximum difference, between the nonlinear analytical results and the nonlinear finite element analysis (FEA) results, is less than 2.58%. Additionally, a physical prototype of the symmetric XYZ CPM is fabricated, and the desirable motion characteristics such as minimized cross-axis coupling are also verified by FEA simulations and experimental testing.