Nonlinear behaviour design using the kinematic singularity of a general type of double-slider four-bar linkage

Kinematic singularities existing in rigid-body linkages are applied to design the mechanism with nonlinear (stiffness) behaviours. The kinematic singularities of a general type of double-slider four-bar linkage, whose two paths of the sliders are not perpendicular, are identified by analysing the kinematic formulation. A new type of mechanism is synthesized by placing translational springs and torsional springs at corresponding joints. Two motion models are proposed to design the different types of nonlinear behaviours. After constructing the force-displacement formulation of the mechanism, four types of nonlinear behaviours including the bistable behaviour, the partial negative stiffness behaviour, the partial zero-stiffness behaviour and the positive stiffness behaviour are investigated. The influences of designed parameters including spring stiffness, geometry parameters, and initial input position on nonlinear characteristics are illustrated. The results indicate that the mechanism exhibits corresponding nonlinear behaviours with these different parameters. A method of generating an expected nonlinear behaviour over a range of input displacement is developed, with a particular emphasis on the constant-force behaviour. The approach of designing the nonlinear behaviour based on the rigid-body linkages with springs expands the application range of the kinematic singularities of rigid-body linkages, and can also be employed to construct nonlinear compliant mechanisms.