Constraint-force-based (CFB) modeling of compliant mechanisms

Numerous works have been done on modeling compliant modules or joints, and the closed-form models of many widely- used compliant modules have been developed. However, the modeling of complex compliant mechanisms with considering external forces is still a challenging work. This paper introduces a constraint-force-based method to model compliant mechanisms. A compliant mechanism can be regarded as the combination of rigid stages and compliant modules. If a compliant mechanism is at static equilibrium under the influence of a series of external forces, all the rigid stages are also at static equilibrium. The rigid stages are restricted by the constraint forces of the compliant modules and the exerted external forces. This paper defines the constraint forces of the compliant modules to be variable constraint forces since the constraint forces vary with the deformation of the compliant modules, and defines the external forces as constant constraint forces due to the fact that the external forces are specific forces exerted which do not change with the deformation of the compliant mechanism. Therefore, the force equilibrium equations for all rigid stages in a compliant mechanism can be obtained based on the variable constraint forces and the constant constraint forces. Moreover, the model of the compliant mechanism can also be derived through solving all the force equilibrium equations. The constraint- force-based modeling method is finally detailed demonstrated via examples, and validated by the finite element analysis. Using this proposed modeling method, a complex compliant mechanism can be modelled with a particular emphasis on considering the position spaces of the associated compliant modules.