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Nonlinear stiffness and kinetostatic modeling of a large-range 3-degree-of-freedom planar compliant parallel mechanism

Beam flexures are frequently used to design large-range Compliant Parallel Mechanisms (CPMs). But geometric nonlinearities induced by axial forces bring challenges to the design and modeling, especially for multi-degree-of-freedom CPMs. This paper presents a nonlinear modeling approach for the proposed 3-prismatic-prismatic-revolute planar CPM based on the beam constraint model. The load-displacement relations of three flexure joints involved in the CPM are derived. Then the force equilibrium conditions and geometric compatibility equations of the end-effector are combined to build the iterative nonlinear model. By giving different inputs, the nonlinear stiffness model and kinetostatic model are established. Based on the developed models, the characteristics of stiffness and actuation forces for the prescribed workspace are investigated. Finally, finite element analyses and experiments are carried out to validate the developed models, and the main reasons for the experimental errors are discussed. The proposed approach can be extended to the modeling of other CPMs, and the obtained model can be further used to guide the design or optimize geometric parameters.